DirectXMath/Inc/DirectXCollision.inl

//-------------------------------------------------------------------------------------
// DirectXCollision.inl -- C++ Collision Math library
//
// THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF
// ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO
// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
// PARTICULAR PURPOSE.
//  
// Copyright (c) Microsoft Corporation. All rights reserved.
//
// http://go.microsoft.com/fwlink/?LinkID=615560
//-------------------------------------------------------------------------------------

#pragma once

XMGLOBALCONST XMVECTORF32 g_BoxOffset[8] =
{
    { -1.0f, -1.0f,  1.0f, 0.0f },
    {  1.0f, -1.0f,  1.0f, 0.0f },
    {  1.0f,  1.0f,  1.0f, 0.0f },
    { -1.0f,  1.0f,  1.0f, 0.0f },
    { -1.0f, -1.0f, -1.0f, 0.0f },
    {  1.0f, -1.0f, -1.0f, 0.0f },
    {  1.0f,  1.0f, -1.0f, 0.0f },
    { -1.0f,  1.0f, -1.0f, 0.0f },
};

XMGLOBALCONST XMVECTORF32 g_RayEpsilon = { 1e-20f, 1e-20f, 1e-20f, 1e-20f };
XMGLOBALCONST XMVECTORF32 g_RayNegEpsilon = { -1e-20f, -1e-20f, -1e-20f, -1e-20f };
XMGLOBALCONST XMVECTORF32 g_FltMin = { -FLT_MAX, -FLT_MAX, -FLT_MAX, -FLT_MAX };
XMGLOBALCONST XMVECTORF32 g_FltMax = { FLT_MAX, FLT_MAX, FLT_MAX, FLT_MAX };

namespace Internal
{

//-----------------------------------------------------------------------------
// Return true if any of the elements of a 3 vector are equal to 0xffffffff.
// Slightly more efficient than using XMVector3EqualInt.
//-----------------------------------------------------------------------------
inline bool XMVector3AnyTrue( _In_ FXMVECTOR V )
{
    // Duplicate the fourth element from the first element.
    XMVECTOR C = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_Z, XM_SWIZZLE_X>(V);

    return XMComparisonAnyTrue( XMVector4EqualIntR( C, XMVectorTrueInt() ) );
}


//-----------------------------------------------------------------------------
// Return true if all of the elements of a 3 vector are equal to 0xffffffff.
// Slightly more efficient than using XMVector3EqualInt.
//-----------------------------------------------------------------------------
inline bool XMVector3AllTrue( _In_ FXMVECTOR V )
{
    // Duplicate the fourth element from the first element.
    XMVECTOR C = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_Z, XM_SWIZZLE_X>( V );

    return XMComparisonAllTrue( XMVector4EqualIntR( C, XMVectorTrueInt() ) );
}

#if defined(_PREFAST) || !defined(NDEBUG)

XMGLOBALCONST XMVECTORF32 g_UnitVectorEpsilon = { 1.0e-4f, 1.0e-4f, 1.0e-4f, 1.0e-4f };
XMGLOBALCONST XMVECTORF32 g_UnitQuaternionEpsilon = { 1.0e-4f, 1.0e-4f, 1.0e-4f, 1.0e-4f };
XMGLOBALCONST XMVECTORF32 g_UnitPlaneEpsilon = { 1.0e-4f, 1.0e-4f, 1.0e-4f, 1.0e-4f };

//-----------------------------------------------------------------------------
// Return true if the vector is a unit vector (length == 1).
//-----------------------------------------------------------------------------
inline bool XMVector3IsUnit( _In_ FXMVECTOR V )
{
    XMVECTOR Difference = XMVectorSubtract( XMVector3Length( V ), XMVectorSplatOne() );
    return XMVector4Less( XMVectorAbs( Difference ), g_UnitVectorEpsilon );
}

//-----------------------------------------------------------------------------
// Return true if the quaterion is a unit quaternion.
//-----------------------------------------------------------------------------
inline bool XMQuaternionIsUnit( _In_ FXMVECTOR Q )
{
    XMVECTOR Difference = XMVectorSubtract( XMVector4Length( Q ), XMVectorSplatOne() );
    return XMVector4Less( XMVectorAbs( Difference ), g_UnitQuaternionEpsilon );
}

//-----------------------------------------------------------------------------
// Return true if the plane is a unit plane.
//-----------------------------------------------------------------------------
inline bool XMPlaneIsUnit( _In_ FXMVECTOR Plane )
{
    XMVECTOR Difference = XMVectorSubtract( XMVector3Length( Plane ), XMVectorSplatOne() );
    return XMVector4Less( XMVectorAbs( Difference ), g_UnitPlaneEpsilon );
}

#endif // __PREFAST__ || !NDEBUG

//-----------------------------------------------------------------------------
inline XMVECTOR XMPlaneTransform( _In_ FXMVECTOR Plane, _In_ FXMVECTOR Rotation, _In_ FXMVECTOR Translation )
{
    XMVECTOR vNormal = XMVector3Rotate( Plane, Rotation );
    XMVECTOR vD = XMVectorSubtract( XMVectorSplatW( Plane ), XMVector3Dot( vNormal, Translation ) );

    return XMVectorInsert<0, 0, 0, 0, 1>( vNormal, vD );
}

//-----------------------------------------------------------------------------
// Return the point on the line segement (S1, S2) nearest the point P.
//-----------------------------------------------------------------------------
inline XMVECTOR PointOnLineSegmentNearestPoint( _In_ FXMVECTOR S1, _In_ FXMVECTOR S2, _In_ FXMVECTOR P )
{
    XMVECTOR Dir = XMVectorSubtract( S2, S1 );
    XMVECTOR Projection = XMVectorSubtract( XMVector3Dot( P, Dir ), XMVector3Dot( S1, Dir ) );
    XMVECTOR LengthSq = XMVector3Dot( Dir, Dir );

    XMVECTOR t = XMVectorMultiply( Projection, XMVectorReciprocal( LengthSq ) );
    XMVECTOR Point = XMVectorMultiplyAdd( t, Dir, S1 );

    // t < 0
    XMVECTOR SelectS1 = XMVectorLess( Projection, XMVectorZero() );
    Point = XMVectorSelect( Point, S1, SelectS1 );

    // t > 1
    XMVECTOR SelectS2 = XMVectorGreater( Projection, LengthSq );
    Point = XMVectorSelect( Point, S2, SelectS2 );

    return Point;
}

//-----------------------------------------------------------------------------
// Test if the point (P) on the plane of the triangle is inside the triangle 
// (V0, V1, V2).
//-----------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV PointOnPlaneInsideTriangle( _In_ FXMVECTOR P, _In_ FXMVECTOR V0, _In_ FXMVECTOR V1, _In_ GXMVECTOR V2 )
{
    // Compute the triangle normal.
    XMVECTOR N = XMVector3Cross( XMVectorSubtract( V2, V0 ), XMVectorSubtract( V1, V0 ) );

    // Compute the cross products of the vector from the base of each edge to 
    // the point with each edge vector.
    XMVECTOR C0 = XMVector3Cross( XMVectorSubtract( P, V0 ), XMVectorSubtract( V1, V0 ) );
    XMVECTOR C1 = XMVector3Cross( XMVectorSubtract( P, V1 ), XMVectorSubtract( V2, V1 ) );
    XMVECTOR C2 = XMVector3Cross( XMVectorSubtract( P, V2 ), XMVectorSubtract( V0, V2 ) );

    // If the cross product points in the same direction as the normal the the
    // point is inside the edge (it is zero if is on the edge).
    XMVECTOR Zero = XMVectorZero();
    XMVECTOR Inside0 = XMVectorGreaterOrEqual( XMVector3Dot( C0, N ), Zero );
    XMVECTOR Inside1 = XMVectorGreaterOrEqual( XMVector3Dot( C1, N ), Zero );
    XMVECTOR Inside2 = XMVectorGreaterOrEqual( XMVector3Dot( C2, N ), Zero );

    // If the point inside all of the edges it is inside.
    return XMVectorAndInt( XMVectorAndInt( Inside0, Inside1 ), Inside2 );
}

//-----------------------------------------------------------------------------
inline bool SolveCubic( _In_ float e, _In_ float f, _In_ float g, _Out_ float* t, _Out_ float* u, _Out_ float* v )
{
    float p, q, h, rc, d, theta, costh3, sinth3;

    p = f - e * e / 3.0f;
    q = g - e * f / 3.0f + e * e * e * 2.0f / 27.0f;
    h = q * q / 4.0f + p * p * p / 27.0f;

    if( h > 0.0 )
    {
        *t = *u = *v = 0.f;
        return false; // only one real root
    }

    if( ( h == 0.0 ) && ( q == 0.0 ) ) // all the same root
    {
        *t = - e / 3;
        *u = - e / 3;
        *v = - e / 3;

        return true;
    }

    d = sqrtf( q * q / 4.0f - h );
    if( d < 0 )
        rc = -powf( -d, 1.0f / 3.0f );
    else
        rc = powf( d, 1.0f / 3.0f );

    theta = XMScalarACos( -q / ( 2.0f * d ) );
    costh3 = XMScalarCos( theta / 3.0f );
    sinth3 = sqrtf( 3.0f ) * XMScalarSin( theta / 3.0f );
    *t = 2.0f * rc * costh3 - e / 3.0f;
    *u = -rc * ( costh3 + sinth3 ) - e / 3.0f;
    *v = -rc * ( costh3 - sinth3 ) - e / 3.0f;

    return true;
}

//-----------------------------------------------------------------------------
inline XMVECTOR CalculateEigenVector( _In_ float m11, _In_ float m12, _In_ float m13,
                                      _In_ float m22, _In_ float m23, _In_ float m33, _In_ float e )
{
    float fTmp[3];
    fTmp[0] = ( float )( m12 * m23 - m13 * ( m22 - e ) );
    fTmp[1] = ( float )( m13 * m12 - m23 * ( m11 - e ) );
    fTmp[2] = ( float )( ( m11 - e ) * ( m22 - e ) - m12 * m12 );

    XMVECTOR vTmp = XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>(fTmp) );

    if( XMVector3Equal( vTmp, XMVectorZero() ) ) // planar or linear
    {
        float f1, f2, f3;

        // we only have one equation - find a valid one
        if( ( m11 - e != 0.0 ) || ( m12 != 0.0 ) || ( m13 != 0.0 ) )
        {
            f1 = m11 - e; f2 = m12; f3 = m13;
        }
        else if( ( m12 != 0.0 ) || ( m22 - e != 0.0 ) || ( m23 != 0.0 ) )
        {
            f1 = m12; f2 = m22 - e; f3 = m23;
        }
        else if( ( m13 != 0.0 ) || ( m23 != 0.0 ) || ( m33 - e != 0.0 ) )
        {
            f1 = m13; f2 = m23; f3 = m33 - e;
        }
        else
        {
            // error, we'll just make something up - we have NO context
            f1 = 1.0; f2 = 0.0; f3 = 0.0;
        }

        if( f1 == 0.0 )
            vTmp = XMVectorSetX( vTmp, 0.0f );
        else
            vTmp = XMVectorSetX( vTmp, 1.0f );

        if( f2 == 0.0 )
            vTmp = XMVectorSetY( vTmp, 0.0f );
        else
            vTmp = XMVectorSetY( vTmp, 1.0f );

        if( f3 == 0.0 )
        {
            vTmp = XMVectorSetZ( vTmp, 0.0f );
            // recalculate y to make equation work
            if( m12 != 0.0 )
                vTmp = XMVectorSetY( vTmp, ( float )( -f1 / f2 ) );
        }
        else
        {
            vTmp = XMVectorSetZ( vTmp, ( float )( ( f2 - f1 ) / f3 ) );
        }
    }

    if( XMVectorGetX( XMVector3LengthSq( vTmp ) ) > 1e-5f )
    {
        return XMVector3Normalize( vTmp );
    }
    else
    {
        // Multiply by a value large enough to make the vector non-zero.
        vTmp = XMVectorScale( vTmp, 1e5f );
        return XMVector3Normalize( vTmp );
    }
}

//-----------------------------------------------------------------------------
inline bool CalculateEigenVectors( _In_ float m11, _In_ float m12, _In_ float m13,
                                   _In_ float m22, _In_ float m23, _In_ float m33,
                                   _In_ float e1, _In_ float e2, _In_ float e3,
                                   _Out_ XMVECTOR* pV1, _Out_ XMVECTOR* pV2, _Out_ XMVECTOR* pV3 )
{
    *pV1 = DirectX::Internal::CalculateEigenVector( m11, m12, m13, m22, m23, m33, e1 );
    *pV2 = DirectX::Internal::CalculateEigenVector( m11, m12, m13, m22, m23, m33, e2 );
    *pV3 = DirectX::Internal::CalculateEigenVector( m11, m12, m13, m22, m23, m33, e3 );

    bool v1z = false;
    bool v2z = false;
    bool v3z = false;

    XMVECTOR Zero = XMVectorZero();

    if ( XMVector3Equal( *pV1, Zero ) )
        v1z = true;

    if ( XMVector3Equal( *pV2, Zero ) )
        v2z = true;

    if ( XMVector3Equal( *pV3, Zero ))
        v3z = true;

    bool e12 = ( fabsf( XMVectorGetX( XMVector3Dot( *pV1, *pV2 ) ) ) > 0.1f ); // check for non-orthogonal vectors
    bool e13 = ( fabsf( XMVectorGetX( XMVector3Dot( *pV1, *pV3 ) ) ) > 0.1f );
    bool e23 = ( fabsf( XMVectorGetX( XMVector3Dot( *pV2, *pV3 ) ) ) > 0.1f );

    if( ( v1z && v2z && v3z ) || ( e12 && e13 && e23 ) ||
        ( e12 && v3z ) || ( e13 && v2z ) || ( e23 && v1z ) ) // all eigenvectors are 0- any basis set
    {
        *pV1 = g_XMIdentityR0.v;
        *pV2 = g_XMIdentityR1.v;
        *pV3 = g_XMIdentityR2.v;
        return true;
    }

    if( v1z && v2z )
    {
        XMVECTOR vTmp = XMVector3Cross( g_XMIdentityR1, *pV3 );
        if( XMVectorGetX( XMVector3LengthSq( vTmp ) ) < 1e-5f )
        {
            vTmp = XMVector3Cross( g_XMIdentityR0, *pV3 );
        }
        *pV1 = XMVector3Normalize( vTmp );
        *pV2 = XMVector3Cross( *pV3, *pV1 );
        return true;
    }

    if( v3z && v1z )
    {
        XMVECTOR vTmp = XMVector3Cross( g_XMIdentityR1, *pV2 );
        if( XMVectorGetX( XMVector3LengthSq( vTmp ) ) < 1e-5f )
        {
            vTmp = XMVector3Cross( g_XMIdentityR0, *pV2 );
        }
        *pV3 = XMVector3Normalize( vTmp );
        *pV1 = XMVector3Cross( *pV2, *pV3 );
        return true;
    }

    if( v2z && v3z )
    {
        XMVECTOR vTmp = XMVector3Cross( g_XMIdentityR1, *pV1 );
        if( XMVectorGetX( XMVector3LengthSq( vTmp ) ) < 1e-5f )
        {
            vTmp = XMVector3Cross( g_XMIdentityR0, *pV1 );
        }
        *pV2 = XMVector3Normalize( vTmp );
        *pV3 = XMVector3Cross( *pV1, *pV2 );
        return true;
    }

    if( ( v1z ) || e12 )
    {
        *pV1 = XMVector3Cross( *pV2, *pV3 );
        return true;
    }

    if( ( v2z ) || e23 )
    {
        *pV2 = XMVector3Cross( *pV3, *pV1 );
        return true;
    }

    if( ( v3z ) || e13 )
    {
        *pV3 = XMVector3Cross( *pV1, *pV2 );
        return true;
    }

    return true;
}

//-----------------------------------------------------------------------------
inline bool CalculateEigenVectorsFromCovarianceMatrix( _In_ float Cxx, _In_ float Cyy, _In_ float Czz,
                                                       _In_ float Cxy, _In_ float Cxz, _In_ float Cyz,
                                                       _Out_ XMVECTOR* pV1, _Out_ XMVECTOR* pV2, _Out_ XMVECTOR* pV3 )
{
    // Calculate the eigenvalues by solving a cubic equation.
    float e = -( Cxx + Cyy + Czz );
    float f = Cxx * Cyy + Cyy * Czz + Czz * Cxx - Cxy * Cxy - Cxz * Cxz - Cyz * Cyz;
    float g = Cxy * Cxy * Czz + Cxz * Cxz * Cyy + Cyz * Cyz * Cxx - Cxy * Cyz * Cxz * 2.0f - Cxx * Cyy * Czz;

    float ev1, ev2, ev3;
    if( !DirectX::Internal::SolveCubic( e, f, g, &ev1, &ev2, &ev3 ) )
    {
        // set them to arbitrary orthonormal basis set
        *pV1 = g_XMIdentityR0.v;
        *pV2 = g_XMIdentityR1.v;
        *pV3 = g_XMIdentityR2.v;
        return false;
    }

    return DirectX::Internal::CalculateEigenVectors( Cxx, Cxy, Cxz, Cyy, Cyz, Czz, ev1, ev2, ev3, pV1, pV2, pV3 );
}

//-----------------------------------------------------------------------------
inline void XM_CALLCONV FastIntersectTrianglePlane( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2, GXMVECTOR Plane,
                                                    XMVECTOR& Outside, XMVECTOR& Inside )
{
    // Plane0
    XMVECTOR Dist0 = XMVector4Dot( V0, Plane );
    XMVECTOR Dist1 = XMVector4Dot( V1, Plane );
    XMVECTOR Dist2 = XMVector4Dot( V2, Plane );

    XMVECTOR MinDist = XMVectorMin( Dist0, Dist1 );
    MinDist = XMVectorMin( MinDist, Dist2 );

    XMVECTOR MaxDist = XMVectorMax( Dist0, Dist1 );
    MaxDist = XMVectorMax( MaxDist, Dist2 );

    XMVECTOR Zero = XMVectorZero();

    // Outside the plane?
    Outside = XMVectorGreater( MinDist, Zero );

    // Fully inside the plane?
    Inside = XMVectorLess( MaxDist, Zero );
}

//-----------------------------------------------------------------------------
inline void FastIntersectSpherePlane( _In_ FXMVECTOR Center, _In_ FXMVECTOR Radius, _In_ FXMVECTOR Plane,
                                      _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside )
{
    XMVECTOR Dist = XMVector4Dot( Center, Plane );

    // Outside the plane?
    Outside = XMVectorGreater( Dist, Radius );

    // Fully inside the plane?
    Inside = XMVectorLess( Dist, XMVectorNegate( Radius ) );
}

//-----------------------------------------------------------------------------
inline void FastIntersectAxisAlignedBoxPlane( _In_ FXMVECTOR Center, _In_ FXMVECTOR Extents, _In_ FXMVECTOR Plane,
                                              _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside )
{
    // Compute the distance to the center of the box.
    XMVECTOR Dist = XMVector4Dot( Center, Plane );

    // Project the axes of the box onto the normal of the plane.  Half the
    // length of the projection (sometime called the "radius") is equal to
    // h(u) * abs(n dot b(u))) + h(v) * abs(n dot b(v)) + h(w) * abs(n dot b(w))
    // where h(i) are extents of the box, n is the plane normal, and b(i) are the 
    // axes of the box. In this case b(i) = [(1,0,0), (0,1,0), (0,0,1)].
    XMVECTOR Radius = XMVector3Dot( Extents, XMVectorAbs( Plane ) );

    // Outside the plane?
    Outside = XMVectorGreater( Dist, Radius );

    // Fully inside the plane?
    Inside = XMVectorLess( Dist, XMVectorNegate( Radius ) );
}

//-----------------------------------------------------------------------------
inline void XM_CALLCONV FastIntersectOrientedBoxPlane( _In_ FXMVECTOR Center, _In_ FXMVECTOR Extents, _In_ FXMVECTOR Axis0, _In_ GXMVECTOR Axis1,
                                                       _In_ HXMVECTOR Axis2, _In_ HXMVECTOR Plane, _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside )
{
    // Compute the distance to the center of the box.
    XMVECTOR Dist = XMVector4Dot( Center, Plane );

    // Project the axes of the box onto the normal of the plane.  Half the
    // length of the projection (sometime called the "radius") is equal to
    // h(u) * abs(n dot b(u))) + h(v) * abs(n dot b(v)) + h(w) * abs(n dot b(w))
    // where h(i) are extents of the box, n is the plane normal, and b(i) are the 
    // axes of the box.
    XMVECTOR Radius = XMVector3Dot( Plane, Axis0 );
    Radius = XMVectorInsert<0, 0, 1, 0, 0>( Radius, XMVector3Dot( Plane, Axis1 ) );
    Radius = XMVectorInsert<0, 0, 0, 1, 0>( Radius, XMVector3Dot( Plane, Axis2 ) );
    Radius = XMVector3Dot( Extents, XMVectorAbs( Radius ) );

    // Outside the plane?
    Outside = XMVectorGreater( Dist, Radius );

    // Fully inside the plane?
    Inside = XMVectorLess( Dist, XMVectorNegate( Radius ) );
}

//-----------------------------------------------------------------------------
inline void XM_CALLCONV FastIntersectFrustumPlane( _In_ FXMVECTOR Point0, _In_ FXMVECTOR Point1, _In_ FXMVECTOR Point2, _In_ GXMVECTOR Point3,
                                                   _In_ HXMVECTOR Point4, _In_ HXMVECTOR Point5, _In_ CXMVECTOR Point6, _In_ CXMVECTOR Point7,
                                                   _In_ CXMVECTOR Plane, _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside )
{
    // Find the min/max projection of the frustum onto the plane normal.
    XMVECTOR Min, Max, Dist;

    Min = Max = XMVector3Dot( Plane, Point0 );

    Dist = XMVector3Dot( Plane, Point1 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    Dist = XMVector3Dot( Plane, Point2 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    Dist = XMVector3Dot( Plane, Point3 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    Dist = XMVector3Dot( Plane, Point4 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    Dist = XMVector3Dot( Plane, Point5 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    Dist = XMVector3Dot( Plane, Point6 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    Dist = XMVector3Dot( Plane, Point7 );
    Min = XMVectorMin( Min, Dist );
    Max = XMVectorMax( Max, Dist );

    XMVECTOR PlaneDist = XMVectorNegate( XMVectorSplatW( Plane ) );

    // Outside the plane?
    Outside = XMVectorGreater( Min, PlaneDist );

    // Fully inside the plane?
    Inside = XMVectorLess( Max, PlaneDist );
}

}; // namespace Internal


/****************************************************************************
 *
 * BoundingSphere
 *
 ****************************************************************************/

//-----------------------------------------------------------------------------
// Transform a sphere by an angle preserving transform.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV BoundingSphere::Transform( BoundingSphere& Out, FXMMATRIX M ) const
{
    // Load the center of the sphere.
    XMVECTOR vCenter = XMLoadFloat3( &Center );

    // Transform the center of the sphere.
    XMVECTOR C = XMVector3Transform( vCenter, M );
    
    XMVECTOR dX = XMVector3Dot( M.r[0], M.r[0] );
    XMVECTOR dY = XMVector3Dot( M.r[1], M.r[1] );
    XMVECTOR dZ = XMVector3Dot( M.r[2], M.r[2] );

    XMVECTOR d = XMVectorMax( dX, XMVectorMax( dY, dZ ) );

    // Store the center sphere.
    XMStoreFloat3( &Out.Center, C );

    // Scale the radius of the pshere.
    float Scale = sqrtf( XMVectorGetX(d) );
    Out.Radius = Radius * Scale;
}

_Use_decl_annotations_
inline void XM_CALLCONV BoundingSphere::Transform( BoundingSphere& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation ) const
{
    // Load the center of the sphere.
    XMVECTOR vCenter = XMLoadFloat3( &Center );

    // Transform the center of the sphere.
    vCenter = XMVectorAdd( XMVector3Rotate( XMVectorScale( vCenter, Scale ), Rotation ), Translation );

    // Store the center sphere.
    XMStoreFloat3( &Out.Center, vCenter );

    // Scale the radius of the pshere.
    Out.Radius = Radius * Scale;
}


//-----------------------------------------------------------------------------
// Point in sphere test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingSphere::Contains( FXMVECTOR Point ) const
{
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );

    XMVECTOR DistanceSquared = XMVector3LengthSq( XMVectorSubtract( Point, vCenter ) );
    XMVECTOR RadiusSquared = XMVectorMultiply( vRadius, vRadius );

    return XMVector3LessOrEqual( DistanceSquared, RadiusSquared ) ? CONTAINS : DISJOINT;
}


//-----------------------------------------------------------------------------
// Triangle in sphere test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingSphere::Contains( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    if ( !Intersects(V0,V1,V2) )
        return DISJOINT;

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );
    XMVECTOR RadiusSquared = XMVectorMultiply( vRadius, vRadius );

    XMVECTOR DistanceSquared = XMVector3LengthSq( XMVectorSubtract( V0, vCenter ) );
    XMVECTOR Inside = XMVectorLessOrEqual(DistanceSquared, RadiusSquared);

    DistanceSquared = XMVector3LengthSq( XMVectorSubtract( V1, vCenter ) );
    Inside = XMVectorAndInt( Inside, XMVectorLessOrEqual(DistanceSquared, RadiusSquared) );

    DistanceSquared = XMVector3LengthSq( XMVectorSubtract( V2, vCenter ) );
    Inside = XMVectorAndInt( Inside, XMVectorLessOrEqual(DistanceSquared, RadiusSquared) );

    return ( XMVector3EqualInt( Inside, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Sphere in sphere test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingSphere::Contains( const BoundingSphere& sh ) const
{
    XMVECTOR Center1 = XMLoadFloat3( &Center );
    float r1 = Radius;

    XMVECTOR Center2 = XMLoadFloat3( &sh.Center );
    float r2 = sh.Radius;

    XMVECTOR V = XMVectorSubtract( Center2, Center1 );

    XMVECTOR Dist = XMVector3Length( V );

    float d = XMVectorGetX( Dist );

    return (r1 + r2 >= d) ? ((r1 - r2 >= d) ? CONTAINS : INTERSECTS) : DISJOINT;
}


//-----------------------------------------------------------------------------
// Axis-aligned box in sphere test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingSphere::Contains( const BoundingBox& box ) const
{
    if ( !box.Intersects(*this) )
        return DISJOINT;

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );
    XMVECTOR RadiusSq = XMVectorMultiply( vRadius, vRadius );

    XMVECTOR boxCenter = XMLoadFloat3( &box.Center );
    XMVECTOR boxExtents = XMLoadFloat3( &box.Extents );

    XMVECTOR InsideAll = XMVectorTrueInt();

    XMVECTOR offset = XMVectorSubtract( boxCenter, vCenter );

    for( size_t i = 0; i < BoundingBox::CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorMultiplyAdd( boxExtents, g_BoxOffset[i], offset );
        XMVECTOR d = XMVector3LengthSq( C );
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( d, RadiusSq ) );
    }

    return ( XMVector3EqualInt( InsideAll, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Oriented box in sphere test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingSphere::Contains( const BoundingOrientedBox& box ) const
{
    if ( !box.Intersects(*this) )
        return DISJOINT;

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );
    XMVECTOR RadiusSq = XMVectorMultiply( vRadius, vRadius );

    XMVECTOR boxCenter = XMLoadFloat3( &box.Center );
    XMVECTOR boxExtents = XMLoadFloat3( &box.Extents );
    XMVECTOR boxOrientation = XMLoadFloat4( &box.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( boxOrientation ) );

    XMVECTOR InsideAll = XMVectorTrueInt();

    for( size_t i = 0; i < BoundingOrientedBox::CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( boxExtents, g_BoxOffset[i] ), boxOrientation ), boxCenter );
        XMVECTOR d = XMVector3LengthSq( XMVectorSubtract( vCenter, C ) );
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( d, RadiusSq ) );
    }

    return ( XMVector3EqualInt( InsideAll, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;

}


//-----------------------------------------------------------------------------
// Frustum in sphere test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingSphere::Contains( const BoundingFrustum& fr ) const
{
    if ( !fr.Intersects(*this) )
        return DISJOINT;

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );
    XMVECTOR RadiusSq = XMVectorMultiply( vRadius, vRadius );

    XMVECTOR vOrigin = XMLoadFloat3( &fr.Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &fr.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Build the corners of the frustum.
    XMVECTOR vRightTop = XMVectorSet( fr.RightSlope, fr.TopSlope, 1.0f, 0.0f );
    XMVECTOR vRightBottom = XMVectorSet( fr.RightSlope, fr.BottomSlope, 1.0f, 0.0f );
    XMVECTOR vLeftTop = XMVectorSet( fr.LeftSlope, fr.TopSlope, 1.0f, 0.0f );
    XMVECTOR vLeftBottom = XMVectorSet( fr.LeftSlope, fr.BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &fr.Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &fr.Far );

    XMVECTOR Corners[BoundingFrustum::CORNER_COUNT];
    Corners[0] = XMVectorMultiply( vRightTop, vNear );
    Corners[1] = XMVectorMultiply( vRightBottom, vNear );
    Corners[2] = XMVectorMultiply( vLeftTop, vNear );
    Corners[3] = XMVectorMultiply( vLeftBottom, vNear );
    Corners[4] = XMVectorMultiply( vRightTop, vFar );
    Corners[5] = XMVectorMultiply( vRightBottom, vFar );
    Corners[6] = XMVectorMultiply( vLeftTop, vFar );
    Corners[7] = XMVectorMultiply( vLeftBottom, vFar );

    XMVECTOR InsideAll = XMVectorTrueInt();
    for( size_t i = 0; i < BoundingFrustum::CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorAdd( XMVector3Rotate( Corners[i], vOrientation ), vOrigin );
        XMVECTOR d = XMVector3LengthSq( XMVectorSubtract( vCenter, C ) );
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( d, RadiusSq ) );
    }

    return ( XMVector3EqualInt( InsideAll, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Sphere vs. sphere test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingSphere::Intersects( const BoundingSphere& sh ) const
{
    // Load A.
    XMVECTOR vCenterA = XMLoadFloat3( &Center );
    XMVECTOR vRadiusA = XMVectorReplicatePtr( &Radius );

    // Load B.
    XMVECTOR vCenterB = XMLoadFloat3( &sh.Center );
    XMVECTOR vRadiusB = XMVectorReplicatePtr( &sh.Radius );

    // Distance squared between centers.    
    XMVECTOR Delta = XMVectorSubtract( vCenterB, vCenterA );
    XMVECTOR DistanceSquared = XMVector3LengthSq( Delta );

    // Sum of the radii squared.
    XMVECTOR RadiusSquared = XMVectorAdd( vRadiusA, vRadiusB );
    RadiusSquared = XMVectorMultiply( RadiusSquared, RadiusSquared );

    return XMVector3LessOrEqual( DistanceSquared, RadiusSquared );
}


//-----------------------------------------------------------------------------
// Box vs. sphere test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingSphere::Intersects( const BoundingBox& box ) const
{
    return box.Intersects( *this );
}

_Use_decl_annotations_
inline bool BoundingSphere::Intersects( const BoundingOrientedBox& box ) const
{
    return box.Intersects( *this );
}


//-----------------------------------------------------------------------------
// Frustum vs. sphere test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingSphere::Intersects( const BoundingFrustum& fr ) const
{
    return fr.Intersects( *this );
}


//-----------------------------------------------------------------------------
// Triangle vs sphere test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingSphere::Intersects( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    // Load the sphere.    
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );

    // Compute the plane of the triangle (has to be normalized).
    XMVECTOR N = XMVector3Normalize( XMVector3Cross( XMVectorSubtract( V1, V0 ), XMVectorSubtract( V2, V0 ) ) );

    // Assert that the triangle is not degenerate.
    assert( !XMVector3Equal( N, XMVectorZero() ) );

    // Find the nearest feature on the triangle to the sphere.
    XMVECTOR Dist = XMVector3Dot( XMVectorSubtract( vCenter, V0 ), N );

    // If the center of the sphere is farther from the plane of the triangle than
    // the radius of the sphere, then there cannot be an intersection.
    XMVECTOR NoIntersection = XMVectorLess( Dist, XMVectorNegate( vRadius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Dist, vRadius ) );

    // Project the center of the sphere onto the plane of the triangle.
    XMVECTOR Point = XMVectorNegativeMultiplySubtract( N, Dist, vCenter );

    // Is it inside all the edges? If so we intersect because the distance 
    // to the plane is less than the radius.
    XMVECTOR Intersection = DirectX::Internal::PointOnPlaneInsideTriangle( Point, V0, V1, V2 );

    // Find the nearest point on each edge.
    XMVECTOR RadiusSq = XMVectorMultiply( vRadius, vRadius );

    // Edge 0,1
    Point = DirectX::Internal::PointOnLineSegmentNearestPoint( V0, V1, vCenter );

    // If the distance to the center of the sphere to the point is less than 
    // the radius of the sphere then it must intersect.
    Intersection = XMVectorOrInt( Intersection, XMVectorLessOrEqual( XMVector3LengthSq( XMVectorSubtract( vCenter, Point ) ), RadiusSq ) );

    // Edge 1,2
    Point = DirectX::Internal::PointOnLineSegmentNearestPoint( V1, V2, vCenter );

    // If the distance to the center of the sphere to the point is less than 
    // the radius of the sphere then it must intersect.
    Intersection = XMVectorOrInt( Intersection, XMVectorLessOrEqual( XMVector3LengthSq( XMVectorSubtract( vCenter, Point ) ), RadiusSq ) );

    // Edge 2,0
    Point = DirectX::Internal::PointOnLineSegmentNearestPoint( V2, V0, vCenter );

    // If the distance to the center of the sphere to the point is less than 
    // the radius of the sphere then it must intersect.
    Intersection = XMVectorOrInt( Intersection, XMVectorLessOrEqual( XMVector3LengthSq( XMVectorSubtract( vCenter, Point ) ), RadiusSq ) );

    return XMVector4EqualInt( XMVectorAndCInt( Intersection, NoIntersection ), XMVectorTrueInt() );
}


//-----------------------------------------------------------------------------
// Sphere-plane intersection
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline PlaneIntersectionType XM_CALLCONV BoundingSphere::Intersects( FXMVECTOR Plane ) const
{
    assert( DirectX::Internal::XMPlaneIsUnit( Plane ) );

    // Load the sphere.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );

    // Set w of the center to one so we can dot4 with a plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    XMVECTOR Outside, Inside;
    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane, Outside, Inside );

    // If the sphere is outside any plane it is outside.
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return FRONT;

    // If the sphere is inside all planes it is inside.
    if ( XMVector4EqualInt( Inside, XMVectorTrueInt() ) )
        return BACK;

    // The sphere is not inside all planes or outside a plane it intersects.
    return INTERSECTING;
}


//-----------------------------------------------------------------------------
// Compute the intersection of a ray (Origin, Direction) with a sphere.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingSphere::Intersects( FXMVECTOR Origin, FXMVECTOR Direction, float& Dist ) const
{
    assert( DirectX::Internal::XMVector3IsUnit( Direction ) );

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );

    // l is the vector from the ray origin to the center of the sphere.
    XMVECTOR l = XMVectorSubtract( vCenter, Origin );

    // s is the projection of the l onto the ray direction.
    XMVECTOR s = XMVector3Dot( l, Direction );

    XMVECTOR l2 = XMVector3Dot( l, l );

    XMVECTOR r2 = XMVectorMultiply( vRadius, vRadius );

    // m2 is squared distance from the center of the sphere to the projection.
    XMVECTOR m2 = XMVectorNegativeMultiplySubtract( s, s, l2 );

    XMVECTOR NoIntersection;

    // If the ray origin is outside the sphere and the center of the sphere is 
    // behind the ray origin there is no intersection.
    NoIntersection = XMVectorAndInt( XMVectorLess( s, XMVectorZero() ), XMVectorGreater( l2, r2 ) );

    // If the squared distance from the center of the sphere to the projection
    // is greater than the radius squared the ray will miss the sphere.
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( m2, r2 ) );

    // The ray hits the sphere, compute the nearest intersection point.
    XMVECTOR q = XMVectorSqrt( XMVectorSubtract( r2, m2 ) );
    XMVECTOR t1 = XMVectorSubtract( s, q );
    XMVECTOR t2 = XMVectorAdd( s, q );

    XMVECTOR OriginInside = XMVectorLessOrEqual( l2, r2 );
    XMVECTOR t = XMVectorSelect( t1, t2, OriginInside );

    if( XMVector4NotEqualInt( NoIntersection, XMVectorTrueInt() ) )
    {
        // Store the x-component to *pDist.
        XMStoreFloat( &Dist, t );
        return true;
    }

    Dist = 0.f;
    return false;
}


//-----------------------------------------------------------------------------
// Test a sphere vs 6 planes (typically forming a frustum).
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingSphere::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2,
                                                                GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5 ) const
{
    // Load the sphere.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &Radius );

    // Set w of the center to one so we can dot4 with a plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    XMVECTOR Outside, Inside;

    // Test against each plane.
    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane0, Outside, Inside );

    XMVECTOR AnyOutside = Outside;
    XMVECTOR AllInside = Inside;

    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane1, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane2, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane3, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane4, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectSpherePlane( vCenter, vRadius, Plane5, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    // If the sphere is outside any plane it is outside.
    if ( XMVector4EqualInt( AnyOutside, XMVectorTrueInt() ) )
        return DISJOINT;

    // If the sphere is inside all planes it is inside.
    if ( XMVector4EqualInt( AllInside, XMVectorTrueInt() ) )
        return CONTAINS;

    // The sphere is not inside all planes or outside a plane, it may intersect.
    return INTERSECTS;
}


//-----------------------------------------------------------------------------
// Creates a bounding sphere that contains two other bounding spheres
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingSphere::CreateMerged( BoundingSphere& Out, const BoundingSphere& S1, const BoundingSphere& S2 )
{
    XMVECTOR Center1 = XMLoadFloat3( &S1.Center );
    float r1 = S1.Radius;

    XMVECTOR Center2 = XMLoadFloat3( &S2.Center );
    float r2 = S2.Radius;

    XMVECTOR V = XMVectorSubtract( Center2, Center1 );

    XMVECTOR Dist = XMVector3Length( V );

    float d = XMVectorGetX(Dist);

    if ( r1 + r2 >= d )
    {
        if ( r1 - r2 >= d )
        {
            Out = S1;
            return;
        }
        else if ( r2 - r1 >= d )
        {
            Out = S2;
            return;
        }
    }

    XMVECTOR N = XMVectorDivide( V, Dist );

    float t1 = XMMin( -r1, d-r2 );
    float t2 = XMMax( r1, d+r2 );
    float t_5 = (t2 - t1) * 0.5f;
    
    XMVECTOR NCenter = XMVectorAdd( Center1, XMVectorMultiply( N, XMVectorReplicate( t_5 + t1 ) ) );

    XMStoreFloat3( &Out.Center, NCenter );
    Out.Radius = t_5;
}


//-----------------------------------------------------------------------------
// Create sphere enscribing bounding box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingSphere::CreateFromBoundingBox( BoundingSphere& Out, const BoundingBox& box )
{
    Out.Center = box.Center;
    XMVECTOR vExtents = XMLoadFloat3( &box.Extents );
    Out.Radius = XMVectorGetX( XMVector3Length( vExtents ) );
}

_Use_decl_annotations_
inline void BoundingSphere::CreateFromBoundingBox( BoundingSphere& Out, const BoundingOrientedBox& box )
{
    // Bounding box orientation is irrelevant because a sphere is rotationally invariant
    Out.Center = box.Center;
    XMVECTOR vExtents = XMLoadFloat3( &box.Extents );
    Out.Radius = XMVectorGetX( XMVector3Length( vExtents ) );
}


//-----------------------------------------------------------------------------
// Find the approximate smallest enclosing bounding sphere for a set of 
// points. Exact computation of the smallest enclosing bounding sphere is 
// possible but is slower and requires a more complex algorithm.
// The algorithm is based on  Jack Ritter, "An Efficient Bounding Sphere", 
// Graphics Gems.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingSphere::CreateFromPoints( BoundingSphere& Out, size_t Count, const XMFLOAT3* pPoints, size_t Stride )
{
    assert( Count > 0 );
    assert( pPoints );

    // Find the points with minimum and maximum x, y, and z
    XMVECTOR MinX, MaxX, MinY, MaxY, MinZ, MaxZ;

    MinX = MaxX = MinY = MaxY = MinZ = MaxZ = XMLoadFloat3( pPoints );

    for( size_t i = 1; i < Count; ++i )
    {
        XMVECTOR Point = XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>( reinterpret_cast<const uint8_t*>(pPoints) + i * Stride ) );

        float px = XMVectorGetX( Point );
        float py = XMVectorGetY( Point );
        float pz = XMVectorGetZ( Point );

        if( px < XMVectorGetX( MinX ) )
            MinX = Point;

        if( px > XMVectorGetX( MaxX ) )
            MaxX = Point;

        if( py < XMVectorGetY( MinY ) )
            MinY = Point;

        if( py > XMVectorGetY( MaxY ) )
            MaxY = Point;

        if( pz < XMVectorGetZ( MinZ ) )
            MinZ = Point;

        if( pz > XMVectorGetZ( MaxZ ) )
            MaxZ = Point;
    }

    // Use the min/max pair that are farthest apart to form the initial sphere.
    XMVECTOR DeltaX = XMVectorSubtract( MaxX, MinX );
    XMVECTOR DistX = XMVector3Length( DeltaX );

    XMVECTOR DeltaY = XMVectorSubtract( MaxY, MinY );
    XMVECTOR DistY = XMVector3Length( DeltaY );

    XMVECTOR DeltaZ = XMVectorSubtract( MaxZ, MinZ );
    XMVECTOR DistZ = XMVector3Length( DeltaZ );

    XMVECTOR vCenter;
    XMVECTOR vRadius;

    if( XMVector3Greater( DistX, DistY ) )
    {
        if( XMVector3Greater( DistX, DistZ ) )
        {
            // Use min/max x.
            vCenter = XMVectorLerp(MaxX,MinX,0.5f);
            vRadius = XMVectorScale( DistX, 0.5f );
        }
        else
        {
            // Use min/max z.
            vCenter = XMVectorLerp(MaxZ,MinZ,0.5f);
            vRadius = XMVectorScale( DistZ, 0.5f );
        }
    }
    else // Y >= X
    {
        if( XMVector3Greater( DistY, DistZ ) )
        {
            // Use min/max y.
            vCenter = XMVectorLerp(MaxY,MinY,0.5f);
            vRadius = XMVectorScale( DistY, 0.5f );
        }
        else
        {
            // Use min/max z.
            vCenter = XMVectorLerp(MaxZ,MinZ,0.5f);
            vRadius = XMVectorScale( DistZ, 0.5f );
        }
    }

    // Add any points not inside the sphere.
    for( size_t i = 0; i < Count; ++i )
    {
        XMVECTOR Point = XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>( reinterpret_cast<const uint8_t*>(pPoints) + i * Stride ) );

        XMVECTOR Delta = XMVectorSubtract( Point, vCenter );

        XMVECTOR Dist = XMVector3Length( Delta );

        if( XMVector3Greater( Dist, vRadius ) )
        {
            // Adjust sphere to include the new point.
            vRadius = XMVectorScale( XMVectorAdd( vRadius, Dist ), 0.5f );
            vCenter = XMVectorAdd( vCenter, XMVectorMultiply( XMVectorSubtract( XMVectorReplicate(1.0f), XMVectorDivide(vRadius, Dist) ), Delta ) );
        }
    }

    XMStoreFloat3( &Out.Center, vCenter );
    XMStoreFloat( &Out.Radius, vRadius );
}


//-----------------------------------------------------------------------------
// Create sphere containing frustum
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingSphere::CreateFromFrustum( BoundingSphere& Out, const BoundingFrustum& fr )
{
    XMFLOAT3 Corners[BoundingFrustum::CORNER_COUNT];
    fr.GetCorners( Corners );
    CreateFromPoints( Out, BoundingFrustum::CORNER_COUNT, Corners, sizeof(XMFLOAT3) );
}


/****************************************************************************
 *
 * BoundingBox
 *
 ****************************************************************************/

//-----------------------------------------------------------------------------
// Transform an axis aligned box by an angle preserving transform.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV BoundingBox::Transform( BoundingBox& Out, FXMMATRIX M ) const
{
    // Load center and extents.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    // Compute and transform the corners and find new min/max bounds.
    XMVECTOR Corner = XMVectorMultiplyAdd( vExtents, g_BoxOffset[0], vCenter );
    Corner = XMVector3Transform( Corner, M );

    XMVECTOR Min, Max;
    Min = Max = Corner;

    for( size_t i = 1; i < CORNER_COUNT; ++i )
    {
        Corner = XMVectorMultiplyAdd( vExtents, g_BoxOffset[i], vCenter );
        Corner = XMVector3Transform( Corner, M );

        Min = XMVectorMin( Min, Corner );
        Max = XMVectorMax( Max, Corner );
    }

    // Store center and extents.
    XMStoreFloat3( &Out.Center, XMVectorScale( XMVectorAdd( Min, Max ), 0.5f ) );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( Max, Min ), 0.5f ) );
}

_Use_decl_annotations_
inline void XM_CALLCONV BoundingBox::Transform( BoundingBox& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation ) const
{
    assert( DirectX::Internal::XMQuaternionIsUnit( Rotation ) );

    // Load center and extents.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    XMVECTOR VectorScale = XMVectorReplicate( Scale );

    // Compute and transform the corners and find new min/max bounds.
    XMVECTOR Corner = XMVectorMultiplyAdd( vExtents, g_BoxOffset[0], vCenter );
    Corner = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( Corner, VectorScale ), Rotation ), Translation );

    XMVECTOR Min, Max;
    Min = Max = Corner;

    for( size_t i = 1; i < CORNER_COUNT; ++i )
    {
        Corner = XMVectorMultiplyAdd( vExtents, g_BoxOffset[i], vCenter );
        Corner = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( Corner, VectorScale ), Rotation ), Translation );

        Min = XMVectorMin( Min, Corner );
        Max = XMVectorMax( Max, Corner );
    }

    // Store center and extents.
    XMStoreFloat3( &Out.Center, XMVectorScale( XMVectorAdd( Min, Max ), 0.5f ) );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( Max, Min ), 0.5f ) );
}


//-----------------------------------------------------------------------------
// Get the corner points of the box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingBox::GetCorners( XMFLOAT3* Corners ) const
{
    assert( Corners != nullptr );

    // Load the box
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    for( size_t i = 0; i < CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorMultiplyAdd( vExtents, g_BoxOffset[i], vCenter );
        XMStoreFloat3( &Corners[i], C );
    }
}


//-----------------------------------------------------------------------------
// Point in axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingBox::Contains( FXMVECTOR Point ) const
{
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    return XMVector3InBounds( XMVectorSubtract( Point, vCenter ), vExtents ) ? CONTAINS : DISJOINT;
}


//-----------------------------------------------------------------------------
// Triangle in axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingBox::Contains( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    if ( !Intersects(V0,V1,V2) )
        return DISJOINT;

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    XMVECTOR d = XMVectorAbs( XMVectorSubtract( V0, vCenter ) );
    XMVECTOR Inside = XMVectorLessOrEqual( d, vExtents );

    d = XMVectorAbs( XMVectorSubtract( V1, vCenter ) );
    Inside = XMVectorAndInt( Inside, XMVectorLessOrEqual( d, vExtents ) );

    d = XMVectorAbs( XMVectorSubtract( V2, vCenter ) );
    Inside = XMVectorAndInt( Inside, XMVectorLessOrEqual( d, vExtents ) );

    return ( XMVector3EqualInt( Inside, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Sphere in axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingBox::Contains( const BoundingSphere& sh ) const
{
    XMVECTOR SphereCenter = XMLoadFloat3( &sh.Center );
    XMVECTOR SphereRadius = XMVectorReplicatePtr( &sh.Radius );

    XMVECTOR BoxCenter = XMLoadFloat3( &Center );
    XMVECTOR BoxExtents = XMLoadFloat3( &Extents );

    XMVECTOR BoxMin = XMVectorSubtract( BoxCenter, BoxExtents );
    XMVECTOR BoxMax = XMVectorAdd( BoxCenter, BoxExtents );

    // Find the distance to the nearest point on the box.
    // for each i in (x, y, z)
    // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2
    // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2

    XMVECTOR d = XMVectorZero();

    // Compute d for each dimension.
    XMVECTOR LessThanMin = XMVectorLess( SphereCenter, BoxMin );
    XMVECTOR GreaterThanMax = XMVectorGreater( SphereCenter, BoxMax );

    XMVECTOR MinDelta = XMVectorSubtract( SphereCenter, BoxMin );
    XMVECTOR MaxDelta = XMVectorSubtract( SphereCenter, BoxMax );

    // Choose value for each dimension based on the comparison.
    d = XMVectorSelect( d, MinDelta, LessThanMin );
    d = XMVectorSelect( d, MaxDelta, GreaterThanMax );

    // Use a dot-product to square them and sum them together.
    XMVECTOR d2 = XMVector3Dot( d, d );

    if ( XMVector3Greater( d2, XMVectorMultiply( SphereRadius, SphereRadius ) ) )
        return DISJOINT;

    XMVECTOR InsideAll = XMVectorLessOrEqual( XMVectorAdd( BoxMin, SphereRadius ), SphereCenter );
    InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( SphereCenter, XMVectorSubtract( BoxMax, SphereRadius ) ) );
    InsideAll = XMVectorAndInt( InsideAll, XMVectorGreater( XMVectorSubtract( BoxMax, BoxMin ), SphereRadius ) );

    return ( XMVector3EqualInt( InsideAll, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Axis-aligned box in axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingBox::Contains( const BoundingBox& box ) const
{
    XMVECTOR CenterA = XMLoadFloat3( &Center );
    XMVECTOR ExtentsA = XMLoadFloat3( &Extents );

    XMVECTOR CenterB = XMLoadFloat3( &box.Center );
    XMVECTOR ExtentsB = XMLoadFloat3( &box.Extents );

    XMVECTOR MinA = XMVectorSubtract( CenterA, ExtentsA );
    XMVECTOR MaxA = XMVectorAdd( CenterA, ExtentsA );

    XMVECTOR MinB = XMVectorSubtract( CenterB, ExtentsB );
    XMVECTOR MaxB = XMVectorAdd( CenterB, ExtentsB );

    // for each i in (x, y, z) if a_min(i) > b_max(i) or b_min(i) > a_max(i) then return false
    XMVECTOR Disjoint = XMVectorOrInt( XMVectorGreater( MinA, MaxB ), XMVectorGreater( MinB, MaxA ) );

    if ( DirectX::Internal::XMVector3AnyTrue( Disjoint ) )
        return DISJOINT;

    // for each i in (x, y, z) if a_min(i) <= b_min(i) and b_max(i) <= a_max(i) then A contains B
    XMVECTOR Inside = XMVectorAndInt( XMVectorLessOrEqual( MinA, MinB ), XMVectorLessOrEqual( MaxB, MaxA ) );

    return DirectX::Internal::XMVector3AllTrue( Inside ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Oriented box in axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingBox::Contains( const BoundingOrientedBox& box ) const
{
    if ( !box.Intersects( *this ) )
        return DISJOINT;

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    // Subtract off the AABB center to remove a subtract below
    XMVECTOR oCenter = XMVectorSubtract( XMLoadFloat3( &box.Center ), vCenter );

    XMVECTOR oExtents = XMLoadFloat3( &box.Extents );
    XMVECTOR oOrientation = XMLoadFloat4( &box.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( oOrientation ) );

    XMVECTOR Inside = XMVectorTrueInt();

    for( size_t i=0; i < BoundingOrientedBox::CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( oExtents, g_BoxOffset[i] ), oOrientation ), oCenter );
        XMVECTOR d = XMVectorAbs(C);
        Inside = XMVectorAndInt( Inside, XMVectorLessOrEqual( d, vExtents ) );
    }

    return ( XMVector3EqualInt( Inside, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Frustum in axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingBox::Contains( const BoundingFrustum& fr ) const
{
    if ( !fr.Intersects( *this ) )
        return DISJOINT;

    XMFLOAT3 Corners[BoundingFrustum::CORNER_COUNT];
    fr.GetCorners( Corners );

    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    XMVECTOR Inside = XMVectorTrueInt();

    for( size_t i=0; i < BoundingFrustum::CORNER_COUNT; ++i )
    {
        XMVECTOR Point = XMLoadFloat3( &Corners[i] );
        XMVECTOR d = XMVectorAbs( XMVectorSubtract( Point, vCenter ) );
        Inside = XMVectorAndInt( Inside, XMVectorLessOrEqual( d, vExtents ) );
    }

    return ( XMVector3EqualInt( Inside, XMVectorTrueInt() ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Sphere vs axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingBox::Intersects( const BoundingSphere& sh ) const
{
    XMVECTOR SphereCenter = XMLoadFloat3( &sh.Center );
    XMVECTOR SphereRadius = XMVectorReplicatePtr( &sh.Radius );

    XMVECTOR BoxCenter = XMLoadFloat3( &Center );
    XMVECTOR BoxExtents = XMLoadFloat3( &Extents );

    XMVECTOR BoxMin = XMVectorSubtract( BoxCenter, BoxExtents );
    XMVECTOR BoxMax = XMVectorAdd( BoxCenter, BoxExtents );

    // Find the distance to the nearest point on the box.
    // for each i in (x, y, z)
    // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2
    // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2

    XMVECTOR d = XMVectorZero();

    // Compute d for each dimension.
    XMVECTOR LessThanMin = XMVectorLess( SphereCenter, BoxMin );
    XMVECTOR GreaterThanMax = XMVectorGreater( SphereCenter, BoxMax );

    XMVECTOR MinDelta = XMVectorSubtract( SphereCenter, BoxMin );
    XMVECTOR MaxDelta = XMVectorSubtract( SphereCenter, BoxMax );

    // Choose value for each dimension based on the comparison.
    d = XMVectorSelect( d, MinDelta, LessThanMin );
    d = XMVectorSelect( d, MaxDelta, GreaterThanMax );

    // Use a dot-product to square them and sum them together.
    XMVECTOR d2 = XMVector3Dot( d, d );

    return XMVector3LessOrEqual( d2, XMVectorMultiply( SphereRadius, SphereRadius ) );
}


//-----------------------------------------------------------------------------
// Axis-aligned box vs. axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingBox::Intersects( const BoundingBox& box ) const
{
    XMVECTOR CenterA = XMLoadFloat3( &Center );
    XMVECTOR ExtentsA = XMLoadFloat3( &Extents );

    XMVECTOR CenterB = XMLoadFloat3( &box.Center );
    XMVECTOR ExtentsB = XMLoadFloat3( &box.Extents );

    XMVECTOR MinA = XMVectorSubtract( CenterA, ExtentsA );
    XMVECTOR MaxA = XMVectorAdd( CenterA, ExtentsA );

    XMVECTOR MinB = XMVectorSubtract( CenterB, ExtentsB );
    XMVECTOR MaxB = XMVectorAdd( CenterB, ExtentsB );

    // for each i in (x, y, z) if a_min(i) > b_max(i) or b_min(i) > a_max(i) then return false
    XMVECTOR Disjoint = XMVectorOrInt( XMVectorGreater( MinA, MaxB ), XMVectorGreater( MinB, MaxA ) );

    return !DirectX::Internal::XMVector3AnyTrue( Disjoint );
}


//-----------------------------------------------------------------------------
// Oriented box vs. axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingBox::Intersects( const BoundingOrientedBox& box ) const
{
    return box.Intersects( *this );
}


//-----------------------------------------------------------------------------
// Frustum vs. axis-aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingBox::Intersects( const BoundingFrustum& fr ) const
{
    return fr.Intersects( *this );
}


//-----------------------------------------------------------------------------
// Triangle vs. axis aligned box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingBox::Intersects( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    XMVECTOR Zero = XMVectorZero();

    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    XMVECTOR BoxMin = XMVectorSubtract( vCenter, vExtents );
    XMVECTOR BoxMax = XMVectorAdd( vCenter, vExtents );

    // Test the axes of the box (in effect test the AAB against the minimal AAB 
    // around the triangle).
    XMVECTOR TriMin = XMVectorMin( XMVectorMin( V0, V1 ), V2 );
    XMVECTOR TriMax = XMVectorMax( XMVectorMax( V0, V1 ), V2 );

    // for each i in (x, y, z) if a_min(i) > b_max(i) or b_min(i) > a_max(i) then disjoint
    XMVECTOR Disjoint = XMVectorOrInt( XMVectorGreater( TriMin, BoxMax ), XMVectorGreater( BoxMin, TriMax ) );
    if( DirectX::Internal::XMVector3AnyTrue( Disjoint ) )
        return false;

    // Test the plane of the triangle.
    XMVECTOR Normal = XMVector3Cross( XMVectorSubtract( V1, V0 ), XMVectorSubtract( V2, V0 ) );
    XMVECTOR Dist = XMVector3Dot( Normal, V0 );

    // Assert that the triangle is not degenerate.
    assert( !XMVector3Equal( Normal, Zero ) );

    // for each i in (x, y, z) if n(i) >= 0 then v_min(i)=b_min(i), v_max(i)=b_max(i)
    // else v_min(i)=b_max(i), v_max(i)=b_min(i)
    XMVECTOR NormalSelect = XMVectorGreater( Normal, Zero );
    XMVECTOR V_Min = XMVectorSelect( BoxMax, BoxMin, NormalSelect );
    XMVECTOR V_Max = XMVectorSelect( BoxMin, BoxMax, NormalSelect );

    // if n dot v_min + d > 0 || n dot v_max + d < 0 then disjoint
    XMVECTOR MinDist = XMVector3Dot( V_Min, Normal );
    XMVECTOR MaxDist = XMVector3Dot( V_Max, Normal );

    XMVECTOR NoIntersection = XMVectorGreater( MinDist, Dist );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( MaxDist, Dist ) );

    // Move the box center to zero to simplify the following tests.
    XMVECTOR TV0 = XMVectorSubtract( V0, vCenter );
    XMVECTOR TV1 = XMVectorSubtract( V1, vCenter );
    XMVECTOR TV2 = XMVectorSubtract( V2, vCenter );

    // Test the edge/edge axes (3*3).
    XMVECTOR e0 = XMVectorSubtract( TV1, TV0 );
    XMVECTOR e1 = XMVectorSubtract( TV2, TV1 );
    XMVECTOR e2 = XMVectorSubtract( TV0, TV2 );

    // Make w zero.
    e0 = XMVectorInsert<0, 0, 0, 0, 1>( e0, Zero );
    e1 = XMVectorInsert<0, 0, 0, 0, 1>( e1, Zero );
    e2 = XMVectorInsert<0, 0, 0, 0, 1>( e2, Zero );

    XMVECTOR Axis;
    XMVECTOR p0, p1, p2;
    XMVECTOR Min, Max;
    XMVECTOR Radius;

    // Axis == (1,0,0) x e0 = (0, -e0.z, e0.y)
    Axis = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_0X>( e0, XMVectorNegate( e0 ) );
    p0 = XMVector3Dot( TV0, Axis );
    // p1 = XMVector3Dot( V1, Axis ); // p1 = p0;
    p2 = XMVector3Dot( TV2, Axis );
    Min = XMVectorMin( p0, p2 );
    Max = XMVectorMax( p0, p2 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (1,0,0) x e1 = (0, -e1.z, e1.y)
    Axis = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_0X>( e1, XMVectorNegate( e1 ) );
    p0 = XMVector3Dot( TV0, Axis );
    p1 = XMVector3Dot( TV1, Axis );
    // p2 = XMVector3Dot( V2, Axis ); // p2 = p1;
    Min = XMVectorMin( p0, p1 );
    Max = XMVectorMax( p0, p1 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (1,0,0) x e2 = (0, -e2.z, e2.y)
    Axis = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_0X>( e2, XMVectorNegate( e2 ) );
    p0 = XMVector3Dot( TV0, Axis );
    p1 = XMVector3Dot( TV1, Axis );
    // p2 = XMVector3Dot( V2, Axis ); // p2 = p0;
    Min = XMVectorMin( p0, p1 );
    Max = XMVectorMax( p0, p1 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (0,1,0) x e0 = (e0.z, 0, -e0.x)
    Axis = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_0Y>( e0, XMVectorNegate( e0 ) );
    p0 = XMVector3Dot( TV0, Axis );
    // p1 = XMVector3Dot( V1, Axis ); // p1 = p0;
    p2 = XMVector3Dot( TV2, Axis );
    Min = XMVectorMin( p0, p2 );
    Max = XMVectorMax( p0, p2 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (0,1,0) x e1 = (e1.z, 0, -e1.x)
    Axis = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_0Y>( e1, XMVectorNegate( e1 ) );
    p0 = XMVector3Dot( TV0, Axis );
    p1 = XMVector3Dot( TV1, Axis );
    // p2 = XMVector3Dot( V2, Axis ); // p2 = p1;
    Min = XMVectorMin( p0, p1 );
    Max = XMVectorMax( p0, p1 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (0,0,1) x e2 = (e2.z, 0, -e2.x)
    Axis = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_0Y>( e2, XMVectorNegate( e2 ) );
    p0 = XMVector3Dot( TV0, Axis );
    p1 = XMVector3Dot( TV1, Axis );
    // p2 = XMVector3Dot( V2, Axis ); // p2 = p0;
    Min = XMVectorMin( p0, p1 );
    Max = XMVectorMax( p0, p1 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) )  );

    // Axis == (0,0,1) x e0 = (-e0.y, e0.x, 0)
    Axis = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_0Z>( e0, XMVectorNegate( e0 ) );
    p0 = XMVector3Dot( TV0, Axis );
    // p1 = XMVector3Dot( V1, Axis ); // p1 = p0;
    p2 = XMVector3Dot( TV2, Axis );
    Min = XMVectorMin( p0, p2 );
    Max = XMVectorMax( p0, p2 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (0,0,1) x e1 = (-e1.y, e1.x, 0)
    Axis = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_0Z>( e1, XMVectorNegate( e1 ) );
    p0 = XMVector3Dot( TV0, Axis );
    p1 = XMVector3Dot( TV1, Axis );
    // p2 = XMVector3Dot( V2, Axis ); // p2 = p1;
    Min = XMVectorMin( p0, p1 );
    Max = XMVectorMax( p0, p1 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    // Axis == (0,0,1) x e2 = (-e2.y, e2.x, 0)
    Axis = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_0Z>( e2, XMVectorNegate( e2 ) );
    p0 = XMVector3Dot( TV0, Axis );
    p1 = XMVector3Dot( TV1, Axis );
    // p2 = XMVector3Dot( V2, Axis ); // p2 = p0;
    Min = XMVectorMin( p0, p1 );
    Max = XMVectorMax( p0, p1 );
    Radius = XMVector3Dot( vExtents, XMVectorAbs( Axis ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( Min, Radius ) );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( Max, XMVectorNegate( Radius ) ) );

    return XMVector4NotEqualInt( NoIntersection, XMVectorTrueInt() );
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline PlaneIntersectionType XM_CALLCONV BoundingBox::Intersects( FXMVECTOR Plane ) const
{
    assert( DirectX::Internal::XMPlaneIsUnit( Plane ) );

    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    // Set w of the center to one so we can dot4 with a plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    XMVECTOR Outside, Inside;
    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane, Outside, Inside );

    // If the box is outside any plane it is outside.
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return FRONT;

    // If the box is inside all planes it is inside.
    if ( XMVector4EqualInt( Inside, XMVectorTrueInt() ) )
        return BACK;

    // The box is not inside all planes or outside a plane it intersects.
    return INTERSECTING;
}


//-----------------------------------------------------------------------------
// Compute the intersection of a ray (Origin, Direction) with an axis aligned 
// box using the slabs method.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingBox::Intersects( FXMVECTOR Origin, FXMVECTOR Direction, float& Dist ) const
{
    assert( DirectX::Internal::XMVector3IsUnit( Direction ) );

    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    // Adjust ray origin to be relative to center of the box.
    XMVECTOR TOrigin = XMVectorSubtract( vCenter, Origin );

    // Compute the dot product againt each axis of the box.
    // Since the axii are (1,0,0), (0,1,0), (0,0,1) no computation is necessary.
    XMVECTOR AxisDotOrigin = TOrigin;
    XMVECTOR AxisDotDirection = Direction;

    // if (fabs(AxisDotDirection) <= Epsilon) the ray is nearly parallel to the slab.
    XMVECTOR IsParallel = XMVectorLessOrEqual( XMVectorAbs( AxisDotDirection ), g_RayEpsilon );

    // Test against all three axii simultaneously.
    XMVECTOR InverseAxisDotDirection = XMVectorReciprocal( AxisDotDirection );
    XMVECTOR t1 = XMVectorMultiply( XMVectorSubtract( AxisDotOrigin, vExtents ), InverseAxisDotDirection );
    XMVECTOR t2 = XMVectorMultiply( XMVectorAdd( AxisDotOrigin, vExtents ), InverseAxisDotDirection );

    // Compute the max of min(t1,t2) and the min of max(t1,t2) ensuring we don't
    // use the results from any directions parallel to the slab.
    XMVECTOR t_min = XMVectorSelect( XMVectorMin( t1, t2 ), g_FltMin, IsParallel );
    XMVECTOR t_max = XMVectorSelect( XMVectorMax( t1, t2 ), g_FltMax, IsParallel );

    // t_min.x = maximum( t_min.x, t_min.y, t_min.z );
    // t_max.x = minimum( t_max.x, t_max.y, t_max.z );
    t_min = XMVectorMax( t_min, XMVectorSplatY( t_min ) );  // x = max(x,y)
    t_min = XMVectorMax( t_min, XMVectorSplatZ( t_min ) );  // x = max(max(x,y),z)
    t_max = XMVectorMin( t_max, XMVectorSplatY( t_max ) );  // x = min(x,y)
    t_max = XMVectorMin( t_max, XMVectorSplatZ( t_max ) );  // x = min(min(x,y),z)

    // if ( t_min > t_max ) return false;
    XMVECTOR NoIntersection = XMVectorGreater( XMVectorSplatX( t_min ), XMVectorSplatX( t_max ) );

    // if ( t_max < 0.0f ) return false;
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( XMVectorSplatX( t_max ), XMVectorZero() ) );

    // if (IsParallel && (-Extents > AxisDotOrigin || Extents < AxisDotOrigin)) return false;
    XMVECTOR ParallelOverlap = XMVectorInBounds( AxisDotOrigin, vExtents );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorAndCInt( IsParallel, ParallelOverlap ) );

    if( !DirectX::Internal::XMVector3AnyTrue( NoIntersection ) )
    {
        // Store the x-component to *pDist
        XMStoreFloat( &Dist, t_min );
        return true;
    }

    Dist = 0.f;
    return false;
}


//-----------------------------------------------------------------------------
// Test an axis alinged box vs 6 planes (typically forming a frustum).
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingBox::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2,
                                                             GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5 ) const
{
    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );

    // Set w of the center to one so we can dot4 with a plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    XMVECTOR Outside, Inside;

    // Test against each plane.
    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane0, Outside, Inside );

    XMVECTOR AnyOutside = Outside;
    XMVECTOR AllInside = Inside;

    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane1, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane2, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane3, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane4, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectAxisAlignedBoxPlane( vCenter, vExtents, Plane5, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    // If the box is outside any plane it is outside.
    if ( XMVector4EqualInt( AnyOutside, XMVectorTrueInt() ) )
        return DISJOINT;

    // If the box is inside all planes it is inside.
    if ( XMVector4EqualInt( AllInside, XMVectorTrueInt() ) )
        return CONTAINS;

    // The box is not inside all planes or outside a plane, it may intersect.
    return INTERSECTS;
}


//-----------------------------------------------------------------------------
// Create axis-aligned box that contains two other bounding boxes
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingBox::CreateMerged( BoundingBox& Out, const BoundingBox& b1, const BoundingBox& b2 )
{
    XMVECTOR b1Center = XMLoadFloat3( &b1.Center );
    XMVECTOR b1Extents = XMLoadFloat3( &b1.Extents );

    XMVECTOR b2Center = XMLoadFloat3( &b2.Center );
    XMVECTOR b2Extents = XMLoadFloat3( &b2.Extents );

    XMVECTOR Min = XMVectorSubtract( b1Center, b1Extents );
    Min = XMVectorMin( Min, XMVectorSubtract( b2Center, b2Extents ) );

    XMVECTOR Max = XMVectorAdd( b1Center, b1Extents );
    Max = XMVectorMax( Max, XMVectorAdd( b2Center, b2Extents ) );

    assert( XMVector3LessOrEqual( Min, Max ) );

    XMStoreFloat3( &Out.Center, XMVectorScale( XMVectorAdd( Min, Max ), 0.5f ) );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( Max, Min ), 0.5f ) );
}


//-----------------------------------------------------------------------------
// Create axis-aligned box that contains a bounding sphere
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingBox::CreateFromSphere( BoundingBox& Out, const BoundingSphere& sh )
{
    XMVECTOR spCenter = XMLoadFloat3( &sh.Center );
    XMVECTOR shRadius = XMVectorReplicatePtr( &sh.Radius );

    XMVECTOR Min = XMVectorSubtract( spCenter, shRadius );
    XMVECTOR Max = XMVectorAdd( spCenter, shRadius );

    assert( XMVector3LessOrEqual( Min, Max ) );

    XMStoreFloat3( &Out.Center, XMVectorScale( XMVectorAdd( Min, Max ), 0.5f ) );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( Max, Min ), 0.5f ) );
}


//-----------------------------------------------------------------------------
// Create axis-aligned box from min/max points
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV BoundingBox::CreateFromPoints( BoundingBox& Out, FXMVECTOR pt1, FXMVECTOR pt2 )
{
    XMVECTOR Min = XMVectorMin( pt1, pt2 );
    XMVECTOR Max = XMVectorMax( pt1, pt2 );

    // Store center and extents.
    XMStoreFloat3( &Out.Center, XMVectorScale( XMVectorAdd( Min, Max ), 0.5f ) );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( Max, Min ), 0.5f ) );
}


//-----------------------------------------------------------------------------
// Find the minimum axis aligned bounding box containing a set of points.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingBox::CreateFromPoints( BoundingBox& Out, size_t Count, const XMFLOAT3* pPoints, size_t Stride )
{
    assert( Count > 0 );
    assert( pPoints );

    // Find the minimum and maximum x, y, and z
    XMVECTOR vMin, vMax;

    vMin = vMax = XMLoadFloat3( pPoints );

    for( size_t i = 1; i < Count; ++i )
    {
        XMVECTOR Point = XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>( reinterpret_cast<const uint8_t*>(pPoints) + i * Stride ) );

        vMin = XMVectorMin( vMin, Point );
        vMax = XMVectorMax( vMax, Point );
    }

    // Store center and extents.
    XMStoreFloat3( &Out.Center, XMVectorScale( XMVectorAdd( vMin, vMax ), 0.5f ) );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( vMax, vMin ), 0.5f ) );
}


/****************************************************************************
 *
 * BoundingOrientedBox
 *
 ****************************************************************************/

//-----------------------------------------------------------------------------
// Transform an oriented box by an angle preserving transform.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV BoundingOrientedBox::Transform( BoundingOrientedBox& Out, FXMMATRIX M ) const
{
    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Composite the box rotation and the transform rotation.
    XMMATRIX nM;
    nM.r[0] = XMVector3Normalize( M.r[0] );
    nM.r[1] = XMVector3Normalize( M.r[1] );
    nM.r[2] = XMVector3Normalize( M.r[2] );
    nM.r[3] = g_XMIdentityR3;
    XMVECTOR Rotation = XMQuaternionRotationMatrix( nM );
    vOrientation = XMQuaternionMultiply( vOrientation, Rotation );

    // Transform the center.
    vCenter = XMVector3Transform( vCenter, M );

    // Scale the box extents.
    XMVECTOR dX = XMVector3Length( M.r[0] );
    XMVECTOR dY = XMVector3Length( M.r[1] );
    XMVECTOR dZ = XMVector3Length( M.r[2] );

    XMVECTOR VectorScale = XMVectorSelect( dY, dX, g_XMSelect1000 );
    VectorScale = XMVectorSelect( dZ, VectorScale, g_XMSelect1100 );
    vExtents = XMVectorMultiply( vExtents, VectorScale );

    // Store the box.
    XMStoreFloat3( &Out.Center, vCenter );
    XMStoreFloat3( &Out.Extents, vExtents );
    XMStoreFloat4( &Out.Orientation, vOrientation );
}

_Use_decl_annotations_
inline void XM_CALLCONV BoundingOrientedBox::Transform( BoundingOrientedBox& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation ) const
{
    assert( DirectX::Internal::XMQuaternionIsUnit( Rotation ) );

    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Composite the box rotation and the transform rotation.
    vOrientation = XMQuaternionMultiply( vOrientation, Rotation );

    // Transform the center.
    XMVECTOR VectorScale = XMVectorReplicate( Scale );
    vCenter = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( vCenter, VectorScale ), Rotation ), Translation );

    // Scale the box extents.
    vExtents = XMVectorMultiply( vExtents, VectorScale );

    // Store the box.
    XMStoreFloat3( &Out.Center, vCenter );
    XMStoreFloat3( &Out.Extents, vExtents );
    XMStoreFloat4( &Out.Orientation, vOrientation );
}


//-----------------------------------------------------------------------------
// Get the corner points of the box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingOrientedBox::GetCorners( XMFLOAT3* Corners ) const
{
    assert( Corners != 0 );

    // Load the box
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    for( size_t i = 0; i < CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( vExtents, g_BoxOffset[i] ), vOrientation ), vCenter );
        XMStoreFloat3( &Corners[i], C );
    }
}


//-----------------------------------------------------------------------------
// Point in oriented box test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingOrientedBox::Contains( FXMVECTOR Point ) const
{
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Transform the point to be local to the box.
    XMVECTOR TPoint = XMVector3InverseRotate( XMVectorSubtract( Point, vCenter ), vOrientation );

    return XMVector3InBounds( TPoint, vExtents ) ? CONTAINS : DISJOINT;
}


//-----------------------------------------------------------------------------
// Triangle in oriented bounding box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingOrientedBox::Contains( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    // Load the box center & orientation.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Transform the triangle vertices into the space of the box.
    XMVECTOR TV0 = XMVector3InverseRotate( XMVectorSubtract( V0, vCenter ), vOrientation );
    XMVECTOR TV1 = XMVector3InverseRotate( XMVectorSubtract( V1, vCenter ), vOrientation );
    XMVECTOR TV2 = XMVector3InverseRotate( XMVectorSubtract( V2, vCenter ), vOrientation );

    BoundingBox box;
    box.Center = XMFLOAT3( 0.0f, 0.0f, 0.0f );
    box.Extents = Extents;

    // Use the triangle vs axis aligned box intersection routine.
    return box.Contains( TV0, TV1, TV2 );
}


//-----------------------------------------------------------------------------
// Sphere in oriented bounding box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingOrientedBox::Contains( const BoundingSphere& sh ) const
{
    XMVECTOR SphereCenter = XMLoadFloat3( &sh.Center );
    XMVECTOR SphereRadius = XMVectorReplicatePtr( &sh.Radius );

    XMVECTOR BoxCenter = XMLoadFloat3( &Center );
    XMVECTOR BoxExtents = XMLoadFloat3( &Extents );
    XMVECTOR BoxOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( BoxOrientation ) );

    // Transform the center of the sphere to be local to the box.
    // BoxMin = -BoxExtents
    // BoxMax = +BoxExtents
    SphereCenter = XMVector3InverseRotate( XMVectorSubtract( SphereCenter, BoxCenter ), BoxOrientation );

    // Find the distance to the nearest point on the box.
    // for each i in (x, y, z)
    // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2
    // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2

    XMVECTOR d = XMVectorZero();

    // Compute d for each dimension.
    XMVECTOR LessThanMin = XMVectorLess( SphereCenter, XMVectorNegate( BoxExtents ) );
    XMVECTOR GreaterThanMax = XMVectorGreater( SphereCenter, BoxExtents );

    XMVECTOR MinDelta = XMVectorAdd( SphereCenter, BoxExtents );
    XMVECTOR MaxDelta = XMVectorSubtract( SphereCenter, BoxExtents );

    // Choose value for each dimension based on the comparison.
    d = XMVectorSelect( d, MinDelta, LessThanMin );
    d = XMVectorSelect( d, MaxDelta, GreaterThanMax );

    // Use a dot-product to square them and sum them together.
    XMVECTOR d2 = XMVector3Dot( d, d );
    XMVECTOR SphereRadiusSq = XMVectorMultiply( SphereRadius, SphereRadius );

    if ( XMVector4Greater( d2, SphereRadiusSq ) )
        return DISJOINT;

    // See if we are completely inside the box
    XMVECTOR SMin = XMVectorSubtract( SphereCenter, SphereRadius );
    XMVECTOR SMax = XMVectorAdd( SphereCenter, SphereRadius );

    return ( XMVector3InBounds( SMin, BoxExtents ) && XMVector3InBounds( SMax, BoxExtents ) ) ? CONTAINS : INTERSECTS;
}


//-----------------------------------------------------------------------------
// Axis aligned box vs. oriented box. Constructs an oriented box and uses
// the oriented box vs. oriented box test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingOrientedBox::Contains( const BoundingBox& box ) const
{
    // Make the axis aligned box oriented and do an OBB vs OBB test.
    BoundingOrientedBox obox( box.Center, box.Extents, XMFLOAT4( 0.f, 0.f, 0.f, 1.f ) );
    return Contains( obox );
}


//-----------------------------------------------------------------------------
// Oriented bounding box in oriented bounding box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingOrientedBox::Contains( const BoundingOrientedBox& box ) const
{
    if ( !Intersects(box) )
        return DISJOINT;

    // Load the boxes
    XMVECTOR aCenter = XMLoadFloat3( &Center );
    XMVECTOR aExtents = XMLoadFloat3( &Extents );
    XMVECTOR aOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( aOrientation ) );

    XMVECTOR bCenter = XMLoadFloat3( &box.Center );
    XMVECTOR bExtents = XMLoadFloat3( &box.Extents );
    XMVECTOR bOrientation = XMLoadFloat4( &box.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( bOrientation ) );

    XMVECTOR offset = XMVectorSubtract( bCenter, aCenter );

    for( size_t i = 0; i < CORNER_COUNT; ++i )
    {
        // Cb = rotate( bExtents * corneroffset[i], bOrientation ) + bcenter
        // Ca = invrotate( Cb - aCenter, aOrientation )

        XMVECTOR C = XMVectorAdd( XMVector3Rotate( XMVectorMultiply( bExtents, g_BoxOffset[i] ), bOrientation ), offset );
        C = XMVector3InverseRotate( C , aOrientation );

        if ( !XMVector3InBounds( C, aExtents ) )
            return INTERSECTS;
    }

    return CONTAINS;
}


//-----------------------------------------------------------------------------
// Frustum in oriented bounding box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingOrientedBox::Contains( const BoundingFrustum& fr ) const
{
    if ( !fr.Intersects(*this) )
        return DISJOINT;

    XMFLOAT3 Corners[BoundingFrustum::CORNER_COUNT];
    fr.GetCorners( Corners );

    // Load the box
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    for( size_t i = 0; i < BoundingFrustum::CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVector3InverseRotate( XMVectorSubtract( XMLoadFloat3( &Corners[i] ), vCenter ), vOrientation );

        if ( !XMVector3InBounds( C, vExtents ) )
            return INTERSECTS;
    }

    return CONTAINS;
}


//-----------------------------------------------------------------------------
// Sphere vs. oriented box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingOrientedBox::Intersects( const BoundingSphere& sh ) const
{
    XMVECTOR SphereCenter = XMLoadFloat3( &sh.Center );
    XMVECTOR SphereRadius = XMVectorReplicatePtr( &sh.Radius );

    XMVECTOR BoxCenter = XMLoadFloat3( &Center );
    XMVECTOR BoxExtents = XMLoadFloat3( &Extents );
    XMVECTOR BoxOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( BoxOrientation ) );

    // Transform the center of the sphere to be local to the box.
    // BoxMin = -BoxExtents
    // BoxMax = +BoxExtents
    SphereCenter = XMVector3InverseRotate( XMVectorSubtract( SphereCenter, BoxCenter ), BoxOrientation );

    // Find the distance to the nearest point on the box.
    // for each i in (x, y, z)
    // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2
    // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2

    XMVECTOR d = XMVectorZero();

    // Compute d for each dimension.
    XMVECTOR LessThanMin = XMVectorLess( SphereCenter, XMVectorNegate( BoxExtents ) );
    XMVECTOR GreaterThanMax = XMVectorGreater( SphereCenter, BoxExtents );

    XMVECTOR MinDelta = XMVectorAdd( SphereCenter, BoxExtents );
    XMVECTOR MaxDelta = XMVectorSubtract( SphereCenter, BoxExtents );

    // Choose value for each dimension based on the comparison.
    d = XMVectorSelect( d, MinDelta, LessThanMin );
    d = XMVectorSelect( d, MaxDelta, GreaterThanMax );

    // Use a dot-product to square them and sum them together.
    XMVECTOR d2 = XMVector3Dot( d, d );

    return XMVector4LessOrEqual( d2, XMVectorMultiply( SphereRadius, SphereRadius ) ) ? true : false;
}


//-----------------------------------------------------------------------------
// Axis aligned box vs. oriented box. Constructs an oriented box and uses
// the oriented box vs. oriented box test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingOrientedBox::Intersects( const BoundingBox& box ) const
{
    // Make the axis aligned box oriented and do an OBB vs OBB test.
    BoundingOrientedBox obox( box.Center, box.Extents, XMFLOAT4( 0.f, 0.f, 0.f, 1.f ) );
    return Intersects( obox );
}


//-----------------------------------------------------------------------------
// Fast oriented box / oriented box intersection test using the separating axis 
// theorem.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingOrientedBox::Intersects( const BoundingOrientedBox& box ) const
{
    // Build the 3x3 rotation matrix that defines the orientation of B relative to A.
    XMVECTOR A_quat = XMLoadFloat4( &Orientation );
    XMVECTOR B_quat = XMLoadFloat4( &box.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( A_quat ) );
    assert( DirectX::Internal::XMQuaternionIsUnit( B_quat ) );

    XMVECTOR Q = XMQuaternionMultiply( A_quat, XMQuaternionConjugate( B_quat ) );
    XMMATRIX R = XMMatrixRotationQuaternion( Q );

    // Compute the translation of B relative to A.
    XMVECTOR A_cent = XMLoadFloat3( &Center );
    XMVECTOR B_cent = XMLoadFloat3( &box.Center );
    XMVECTOR t = XMVector3InverseRotate( XMVectorSubtract( B_cent, A_cent ), A_quat );

    //
    // h(A) = extents of A.
    // h(B) = extents of B.
    //
    // a(u) = axes of A = (1,0,0), (0,1,0), (0,0,1)
    // b(u) = axes of B relative to A = (r00,r10,r20), (r01,r11,r21), (r02,r12,r22)
    //  
    // For each possible separating axis l:
    //   d(A) = sum (for i = u,v,w) h(A)(i) * abs( a(i) dot l )
    //   d(B) = sum (for i = u,v,w) h(B)(i) * abs( b(i) dot l )
    //   if abs( t dot l ) > d(A) + d(B) then disjoint
    //

    // Load extents of A and B.
    XMVECTOR h_A = XMLoadFloat3( &Extents );
    XMVECTOR h_B = XMLoadFloat3( &box.Extents );

    // Rows. Note R[0,1,2]X.w = 0.
    XMVECTOR R0X = R.r[0];
    XMVECTOR R1X = R.r[1];
    XMVECTOR R2X = R.r[2];

    R = XMMatrixTranspose( R );

    // Columns. Note RX[0,1,2].w = 0.
    XMVECTOR RX0 = R.r[0];
    XMVECTOR RX1 = R.r[1];
    XMVECTOR RX2 = R.r[2];

    // Absolute value of rows.
    XMVECTOR AR0X = XMVectorAbs( R0X );
    XMVECTOR AR1X = XMVectorAbs( R1X );
    XMVECTOR AR2X = XMVectorAbs( R2X );

    // Absolute value of columns.
    XMVECTOR ARX0 = XMVectorAbs( RX0 );
    XMVECTOR ARX1 = XMVectorAbs( RX1 );
    XMVECTOR ARX2 = XMVectorAbs( RX2 );

    // Test each of the 15 possible seperating axii.
    XMVECTOR d, d_A, d_B;

    // l = a(u) = (1, 0, 0)
    // t dot l = t.x
    // d(A) = h(A).x
    // d(B) = h(B) dot abs(r00, r01, r02)
    d = XMVectorSplatX( t );
    d_A = XMVectorSplatX( h_A );
    d_B = XMVector3Dot( h_B, AR0X );
    XMVECTOR NoIntersection = XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) );

    // l = a(v) = (0, 1, 0)
    // t dot l = t.y
    // d(A) = h(A).y
    // d(B) = h(B) dot abs(r10, r11, r12)
    d = XMVectorSplatY( t );
    d_A = XMVectorSplatY( h_A );
    d_B = XMVector3Dot( h_B, AR1X );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(w) = (0, 0, 1)
    // t dot l = t.z
    // d(A) = h(A).z
    // d(B) = h(B) dot abs(r20, r21, r22)
    d = XMVectorSplatZ( t );
    d_A = XMVectorSplatZ( h_A );
    d_B = XMVector3Dot( h_B, AR2X );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = b(u) = (r00, r10, r20)
    // d(A) = h(A) dot abs(r00, r10, r20)
    // d(B) = h(B).x
    d = XMVector3Dot( t, RX0 );
    d_A = XMVector3Dot( h_A, ARX0 );
    d_B = XMVectorSplatX( h_B );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = b(v) = (r01, r11, r21)
    // d(A) = h(A) dot abs(r01, r11, r21)
    // d(B) = h(B).y
    d = XMVector3Dot( t, RX1 );
    d_A = XMVector3Dot( h_A, ARX1 );
    d_B = XMVectorSplatY( h_B );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = b(w) = (r02, r12, r22)
    // d(A) = h(A) dot abs(r02, r12, r22)
    // d(B) = h(B).z
    d = XMVector3Dot( t, RX2 );
    d_A = XMVector3Dot( h_A, ARX2 );
    d_B = XMVectorSplatZ( h_B );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(u) x b(u) = (0, -r20, r10)
    // d(A) = h(A) dot abs(0, r20, r10)
    // d(B) = h(B) dot abs(0, r02, r01)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_0X>( RX0, XMVectorNegate( RX0 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_Y, XM_SWIZZLE_X>( ARX0 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_Y, XM_SWIZZLE_X>( AR0X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(u) x b(v) = (0, -r21, r11)
    // d(A) = h(A) dot abs(0, r21, r11)
    // d(B) = h(B) dot abs(r02, 0, r00)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_0X>( RX1, XMVectorNegate( RX1 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_Y, XM_SWIZZLE_X>( ARX1 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Y>( AR0X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(u) x b(w) = (0, -r22, r12)
    // d(A) = h(A) dot abs(0, r22, r12)
    // d(B) = h(B) dot abs(r01, r00, 0)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_0X>( RX2, XMVectorNegate( RX2 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_Y, XM_SWIZZLE_X>( ARX2 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_Z>( AR0X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(v) x b(u) = (r20, 0, -r00)
    // d(A) = h(A) dot abs(r20, 0, r00)
    // d(B) = h(B) dot abs(0, r12, r11)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_0Y>( RX0, XMVectorNegate( RX0 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Y>( ARX0 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_Y, XM_SWIZZLE_X>( AR1X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(v) x b(v) = (r21, 0, -r01)
    // d(A) = h(A) dot abs(r21, 0, r01)
    // d(B) = h(B) dot abs(r12, 0, r10)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_0Y>( RX1, XMVectorNegate( RX1 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Y>( ARX1 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Y>( AR1X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(v) x b(w) = (r22, 0, -r02)
    // d(A) = h(A) dot abs(r22, 0, r02)
    // d(B) = h(B) dot abs(r11, r10, 0)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_0Y>( RX2, XMVectorNegate( RX2 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Y>( ARX2 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_Z>( AR1X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(w) x b(u) = (-r10, r00, 0)
    // d(A) = h(A) dot abs(r10, r00, 0)
    // d(B) = h(B) dot abs(0, r22, r21)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_0Z>( RX0, XMVectorNegate( RX0 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_Z>( ARX0 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_Y, XM_SWIZZLE_X>( AR2X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(w) x b(v) = (-r11, r01, 0)
    // d(A) = h(A) dot abs(r11, r01, 0)
    // d(B) = h(B) dot abs(r22, 0, r20)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_0Z>( RX1, XMVectorNegate( RX1 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_Z>( ARX1 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Y>( AR2X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // l = a(w) x b(w) = (-r12, r02, 0)
    // d(A) = h(A) dot abs(r12, r02, 0)
    // d(B) = h(B) dot abs(r21, r20, 0)
    d = XMVector3Dot( t, XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_0Z>( RX2, XMVectorNegate( RX2 ) ) );
    d_A = XMVector3Dot( h_A, XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_Z>( ARX2 ) );
    d_B = XMVector3Dot( h_B, XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_Z>( AR2X ) );
    NoIntersection = XMVectorOrInt( NoIntersection, 
                                    XMVectorGreater( XMVectorAbs(d), XMVectorAdd( d_A, d_B ) ) );

    // No seperating axis found, boxes must intersect.
    return XMVector4NotEqualInt( NoIntersection, XMVectorTrueInt() ) ? true : false;
}


//-----------------------------------------------------------------------------
// Frustum vs. oriented box test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingOrientedBox::Intersects( const BoundingFrustum& fr ) const
{
    return fr.Intersects( *this );
}


//-----------------------------------------------------------------------------
// Triangle vs. oriented box test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingOrientedBox::Intersects( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    // Load the box center & orientation.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Transform the triangle vertices into the space of the box.
    XMVECTOR TV0 = XMVector3InverseRotate( XMVectorSubtract( V0, vCenter ), vOrientation );
    XMVECTOR TV1 = XMVector3InverseRotate( XMVectorSubtract( V1, vCenter ), vOrientation );
    XMVECTOR TV2 = XMVector3InverseRotate( XMVectorSubtract( V2, vCenter ), vOrientation );

    BoundingBox box;
    box.Center = XMFLOAT3( 0.0f, 0.0f, 0.0f );
    box.Extents = Extents;

    // Use the triangle vs axis aligned box intersection routine.
    return box.Intersects( TV0, TV1, TV2 );
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline PlaneIntersectionType XM_CALLCONV BoundingOrientedBox::Intersects( FXMVECTOR Plane ) const
{
    assert( DirectX::Internal::XMPlaneIsUnit( Plane ) );

    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR BoxOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( BoxOrientation ) );

    // Set w of the center to one so we can dot4 with a plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    // Build the 3x3 rotation matrix that defines the box axes.
    XMMATRIX R = XMMatrixRotationQuaternion( BoxOrientation );

    XMVECTOR Outside, Inside;
    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane, Outside, Inside );

    // If the box is outside any plane it is outside.
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return FRONT;

    // If the box is inside all planes it is inside.
    if ( XMVector4EqualInt( Inside, XMVectorTrueInt() ) )
        return BACK;

    // The box is not inside all planes or outside a plane it intersects.
    return INTERSECTING;
}


//-----------------------------------------------------------------------------
// Compute the intersection of a ray (Origin, Direction) with an oriented box
// using the slabs method.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingOrientedBox::Intersects( FXMVECTOR Origin, FXMVECTOR Direction, float& Dist ) const
{
    assert( DirectX::Internal::XMVector3IsUnit( Direction ) );

    static const XMVECTORU32 SelectY =
    {
        XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0
    };
    static const XMVECTORU32 SelectZ =
    {
        XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0
    };

    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Get the boxes normalized side directions.
    XMMATRIX R = XMMatrixRotationQuaternion( vOrientation );

    // Adjust ray origin to be relative to center of the box.
    XMVECTOR TOrigin = XMVectorSubtract( vCenter, Origin );

    // Compute the dot product againt each axis of the box.
    XMVECTOR AxisDotOrigin = XMVector3Dot( R.r[0], TOrigin );
    AxisDotOrigin = XMVectorSelect( AxisDotOrigin, XMVector3Dot( R.r[1], TOrigin ), SelectY );
    AxisDotOrigin = XMVectorSelect( AxisDotOrigin, XMVector3Dot( R.r[2], TOrigin ), SelectZ );

    XMVECTOR AxisDotDirection = XMVector3Dot( R.r[0], Direction );
    AxisDotDirection = XMVectorSelect( AxisDotDirection, XMVector3Dot( R.r[1], Direction ), SelectY );
    AxisDotDirection = XMVectorSelect( AxisDotDirection, XMVector3Dot( R.r[2], Direction ), SelectZ );

    // if (fabs(AxisDotDirection) <= Epsilon) the ray is nearly parallel to the slab.
    XMVECTOR IsParallel = XMVectorLessOrEqual( XMVectorAbs( AxisDotDirection ), g_RayEpsilon );

    // Test against all three axes simultaneously.
    XMVECTOR InverseAxisDotDirection = XMVectorReciprocal( AxisDotDirection );
    XMVECTOR t1 = XMVectorMultiply( XMVectorSubtract( AxisDotOrigin, vExtents ), InverseAxisDotDirection );
    XMVECTOR t2 = XMVectorMultiply( XMVectorAdd( AxisDotOrigin, vExtents ), InverseAxisDotDirection );

    // Compute the max of min(t1,t2) and the min of max(t1,t2) ensuring we don't
    // use the results from any directions parallel to the slab.
    XMVECTOR t_min = XMVectorSelect( XMVectorMin( t1, t2 ), g_FltMin, IsParallel );
    XMVECTOR t_max = XMVectorSelect( XMVectorMax( t1, t2 ), g_FltMax, IsParallel );

    // t_min.x = maximum( t_min.x, t_min.y, t_min.z );
    // t_max.x = minimum( t_max.x, t_max.y, t_max.z );
    t_min = XMVectorMax( t_min, XMVectorSplatY( t_min ) );  // x = max(x,y)
    t_min = XMVectorMax( t_min, XMVectorSplatZ( t_min ) );  // x = max(max(x,y),z)
    t_max = XMVectorMin( t_max, XMVectorSplatY( t_max ) );  // x = min(x,y)
    t_max = XMVectorMin( t_max, XMVectorSplatZ( t_max ) );  // x = min(min(x,y),z)

    // if ( t_min > t_max ) return false;
    XMVECTOR NoIntersection = XMVectorGreater( XMVectorSplatX( t_min ), XMVectorSplatX( t_max ) );

    // if ( t_max < 0.0f ) return false;
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( XMVectorSplatX( t_max ), XMVectorZero() ) );

    // if (IsParallel && (-Extents > AxisDotOrigin || Extents < AxisDotOrigin)) return false;
    XMVECTOR ParallelOverlap = XMVectorInBounds( AxisDotOrigin, vExtents );
    NoIntersection = XMVectorOrInt( NoIntersection, XMVectorAndCInt( IsParallel, ParallelOverlap ) );

    if( !DirectX::Internal::XMVector3AnyTrue( NoIntersection ) )
    {
        // Store the x-component to *pDist
        XMStoreFloat( &Dist, t_min );
        return true;
    }

    Dist = 0.f;
    return false;
}


//-----------------------------------------------------------------------------
// Test an oriented box vs 6 planes (typically forming a frustum).
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingOrientedBox::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2,
                                                                     GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5 ) const
{
    // Load the box.
    XMVECTOR vCenter = XMLoadFloat3( &Center );
    XMVECTOR vExtents = XMLoadFloat3( &Extents );
    XMVECTOR BoxOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( BoxOrientation ) );

    // Set w of the center to one so we can dot4 with a plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    // Build the 3x3 rotation matrix that defines the box axes.
    XMMATRIX R = XMMatrixRotationQuaternion( BoxOrientation );

    XMVECTOR Outside, Inside;

    // Test against each plane.
    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane0, Outside, Inside );

    XMVECTOR AnyOutside = Outside;
    XMVECTOR AllInside = Inside;

    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane1, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane2, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane3, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane4, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectOrientedBoxPlane( vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane5, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    // If the box is outside any plane it is outside.
    if ( XMVector4EqualInt( AnyOutside, XMVectorTrueInt() ) )
        return DISJOINT;

    // If the box is inside all planes it is inside.
    if ( XMVector4EqualInt( AllInside, XMVectorTrueInt() ) )
        return CONTAINS;

    // The box is not inside all planes or outside a plane, it may intersect.
    return INTERSECTS;
}


//-----------------------------------------------------------------------------
// Create oriented bounding box from axis-aligned bounding box
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingOrientedBox::CreateFromBoundingBox( BoundingOrientedBox& Out, const BoundingBox& box )
{
    Out.Center = box.Center;
    Out.Extents = box.Extents;
    Out.Orientation = XMFLOAT4( 0.f, 0.f, 0.f, 1.f );
}


//-----------------------------------------------------------------------------
// Find the approximate minimum oriented bounding box containing a set of 
// points.  Exact computation of minimum oriented bounding box is possible but 
// is slower and requires a more complex algorithm.
// The algorithm works by computing the inertia tensor of the points and then
// using the eigenvectors of the intertia tensor as the axes of the box.
// Computing the intertia tensor of the convex hull of the points will usually 
// result in better bounding box but the computation is more complex. 
// Exact computation of the minimum oriented bounding box is possible but the
// best know algorithm is O(N^3) and is significanly more complex to implement.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingOrientedBox::CreateFromPoints( BoundingOrientedBox& Out, size_t Count, const XMFLOAT3* pPoints, size_t Stride )
{
    assert( Count > 0 );
    assert( pPoints != 0 );

    XMVECTOR CenterOfMass = XMVectorZero();

    // Compute the center of mass and inertia tensor of the points.
    for( size_t i = 0; i < Count; ++i )
    {
        XMVECTOR Point = XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>( reinterpret_cast<const uint8_t*>(pPoints) + i * Stride ) );

        CenterOfMass = XMVectorAdd( CenterOfMass, Point );
    }

    CenterOfMass = XMVectorMultiply( CenterOfMass, XMVectorReciprocal( XMVectorReplicate( float( Count ) ) ) );

    // Compute the inertia tensor of the points around the center of mass.
    // Using the center of mass is not strictly necessary, but will hopefully
    // improve the stability of finding the eigenvectors.
    XMVECTOR XX_YY_ZZ = XMVectorZero();
    XMVECTOR XY_XZ_YZ = XMVectorZero();

    for( size_t i = 0; i < Count; ++i )
    {
        XMVECTOR Point = XMVectorSubtract( XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>( reinterpret_cast<const uint8_t*>(pPoints) + i * Stride ) ), CenterOfMass );

        XX_YY_ZZ = XMVectorAdd( XX_YY_ZZ, XMVectorMultiply( Point, Point ) );

        XMVECTOR XXY = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_W>( Point );
        XMVECTOR YZZ = XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_Z, XM_SWIZZLE_Z, XM_SWIZZLE_W>( Point );

        XY_XZ_YZ = XMVectorAdd( XY_XZ_YZ, XMVectorMultiply( XXY, YZZ ) );
    }

    XMVECTOR v1, v2, v3;

    // Compute the eigenvectors of the inertia tensor.
    DirectX::Internal::CalculateEigenVectorsFromCovarianceMatrix( XMVectorGetX( XX_YY_ZZ ), XMVectorGetY( XX_YY_ZZ ),
                                                                  XMVectorGetZ( XX_YY_ZZ ),
                                                                  XMVectorGetX( XY_XZ_YZ ), XMVectorGetY( XY_XZ_YZ ),
                                                                  XMVectorGetZ( XY_XZ_YZ ),
                                                                  &v1, &v2, &v3 );

    // Put them in a matrix.
    XMMATRIX R;

    R.r[0] = XMVectorSetW( v1, 0.f );
    R.r[1] = XMVectorSetW( v2, 0.f );
    R.r[2] = XMVectorSetW( v3, 0.f );
    R.r[3] = g_XMIdentityR3.v;

    // Multiply by -1 to convert the matrix into a right handed coordinate 
    // system (Det ~= 1) in case the eigenvectors form a left handed 
    // coordinate system (Det ~= -1) because XMQuaternionRotationMatrix only 
    // works on right handed matrices.
    XMVECTOR Det = XMMatrixDeterminant( R );

    if( XMVector4Less( Det, XMVectorZero() ) )
    {
        R.r[0] = XMVectorMultiply( R.r[0], g_XMNegativeOne.v );
        R.r[1] = XMVectorMultiply( R.r[1], g_XMNegativeOne.v );
        R.r[2] = XMVectorMultiply( R.r[2], g_XMNegativeOne.v );
    }

    // Get the rotation quaternion from the matrix.
    XMVECTOR vOrientation = XMQuaternionRotationMatrix( R );

    // Make sure it is normal (in case the vectors are slightly non-orthogonal).
    vOrientation = XMQuaternionNormalize( vOrientation );

    // Rebuild the rotation matrix from the quaternion.
    R = XMMatrixRotationQuaternion( vOrientation );

    // Build the rotation into the rotated space.
    XMMATRIX InverseR = XMMatrixTranspose( R );

    // Find the minimum OBB using the eigenvectors as the axes.
    XMVECTOR vMin, vMax;

    vMin = vMax = XMVector3TransformNormal( XMLoadFloat3( pPoints ), InverseR );

    for( size_t i = 1; i < Count; ++i )
    {
        XMVECTOR Point = XMVector3TransformNormal( XMLoadFloat3( reinterpret_cast<const XMFLOAT3*>( reinterpret_cast<const uint8_t*>(pPoints) + i * Stride ) ),
                                                   InverseR );

        vMin = XMVectorMin( vMin, Point );
        vMax = XMVectorMax( vMax, Point );
    }

    // Rotate the center into world space.
    XMVECTOR vCenter = XMVectorScale( XMVectorAdd( vMin, vMax ), 0.5f );
    vCenter = XMVector3TransformNormal( vCenter, R );

    // Store center, extents, and orientation.
    XMStoreFloat3( &Out.Center, vCenter );
    XMStoreFloat3( &Out.Extents, XMVectorScale( XMVectorSubtract( vMax, vMin ), 0.5f ) );
    XMStoreFloat4( &Out.Orientation, vOrientation );
}


/****************************************************************************
 *
 * BoundingFrustum
 *
 ****************************************************************************/

//-----------------------------------------------------------------------------
// Transform a frustum by an angle preserving transform.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV BoundingFrustum::Transform( BoundingFrustum& Out, FXMMATRIX M ) const
{
    // Load the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Composite the frustum rotation and the transform rotation
    XMMATRIX nM;
    nM.r[0] = XMVector3Normalize( M.r[0] );
    nM.r[1] = XMVector3Normalize( M.r[1] );
    nM.r[2] = XMVector3Normalize( M.r[2] );
    nM.r[3] = g_XMIdentityR3;
    XMVECTOR Rotation = XMQuaternionRotationMatrix( nM );
    vOrientation = XMQuaternionMultiply( vOrientation, Rotation );

    // Transform the center.
    vOrigin = XMVector3Transform( vOrigin, M );

    // Store the frustum.
    XMStoreFloat3( &Out.Origin, vOrigin );
    XMStoreFloat4( &Out.Orientation, vOrientation );

    // Scale the near and far distances (the slopes remain the same).
    XMVECTOR dX = XMVector3Dot( M.r[0], M.r[0] );
    XMVECTOR dY = XMVector3Dot( M.r[1], M.r[1] );
    XMVECTOR dZ = XMVector3Dot( M.r[2], M.r[2] );

    XMVECTOR d = XMVectorMax( dX, XMVectorMax( dY, dZ ) );
    float Scale = sqrtf( XMVectorGetX(d) );

    Out.Near = Near * Scale;
    Out.Far = Far * Scale;

    // Copy the slopes.
    Out.RightSlope = RightSlope;
    Out.LeftSlope = LeftSlope;
    Out.TopSlope = TopSlope;
    Out.BottomSlope = BottomSlope;
}

_Use_decl_annotations_
inline void XM_CALLCONV BoundingFrustum::Transform( BoundingFrustum& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation ) const
{
    assert( DirectX::Internal::XMQuaternionIsUnit( Rotation ) );

    // Load the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Composite the frustum rotation and the transform rotation.
    vOrientation = XMQuaternionMultiply( vOrientation, Rotation );

    // Transform the origin.
    vOrigin = XMVectorAdd( XMVector3Rotate( XMVectorScale( vOrigin, Scale ), Rotation ), Translation );

    // Store the frustum.
    XMStoreFloat3( &Out.Origin, vOrigin );
    XMStoreFloat4( &Out.Orientation, vOrientation );

    // Scale the near and far distances (the slopes remain the same).
    Out.Near = Near * Scale;
    Out.Far = Far * Scale;

    // Copy the slopes.
    Out.RightSlope = RightSlope;
    Out.LeftSlope = LeftSlope;
    Out.TopSlope = TopSlope;
    Out.BottomSlope = BottomSlope;
}


//-----------------------------------------------------------------------------
// Get the corner points of the frustum
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingFrustum::GetCorners( XMFLOAT3* Corners ) const
{
    assert( Corners != 0 );

    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Build the corners of the frustum.
    XMVECTOR vRightTop = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vRightBottom = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vLeftTop = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vLeftBottom = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &Far );

    // Returns 8 corners position of bounding frustum.
    //     Near    Far
    //    0----1  4----5
    //    |    |  |    |
    //    |    |  |    |
    //    3----2  7----6

    XMVECTOR vCorners[CORNER_COUNT];
    vCorners[0] = XMVectorMultiply( vLeftTop, vNear );
    vCorners[1] = XMVectorMultiply( vRightTop, vNear );
    vCorners[2] = XMVectorMultiply( vRightBottom, vNear );
    vCorners[3] = XMVectorMultiply( vLeftBottom, vNear );
    vCorners[4] = XMVectorMultiply( vLeftTop, vFar );
    vCorners[5] = XMVectorMultiply( vRightTop, vFar );
    vCorners[6] = XMVectorMultiply( vRightBottom, vFar );
    vCorners[7] = XMVectorMultiply( vLeftBottom, vFar );

    for( size_t i=0; i < CORNER_COUNT; ++i )
    {
        XMVECTOR C = XMVectorAdd( XMVector3Rotate( vCorners[i], vOrientation ), vOrigin );
        XMStoreFloat3( &Corners[i], C );
    }
}


//-----------------------------------------------------------------------------
// Point in frustum test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingFrustum::Contains( FXMVECTOR Point ) const
{
    // Build frustum planes.
    XMVECTOR Planes[6];
    Planes[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    Planes[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    Planes[2] = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    Planes[3] = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    Planes[4] = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    Planes[5] = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );

    // Load origin and orientation.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Transform point into local space of frustum.
    XMVECTOR TPoint = XMVector3InverseRotate( XMVectorSubtract( Point, vOrigin ), vOrientation );

    // Set w to one.
    TPoint = XMVectorInsert<0, 0, 0, 0, 1>( TPoint, XMVectorSplatOne() );

    XMVECTOR Zero = XMVectorZero();
    XMVECTOR Outside = Zero;

    // Test point against each plane of the frustum.
    for( size_t i = 0; i < 6; ++i )
    {
        XMVECTOR Dot = XMVector4Dot( TPoint, Planes[i] );
        Outside = XMVectorOrInt( Outside, XMVectorGreater( Dot, Zero ) );
    }

    return XMVector4NotEqualInt( Outside, XMVectorTrueInt() ) ? CONTAINS : DISJOINT;
}


//-----------------------------------------------------------------------------
// Triangle vs frustum test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingFrustum::Contains( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Create 6 planes (do it inline to encourage use of registers)
    XMVECTOR NearPlane = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    NearPlane = DirectX::Internal::XMPlaneTransform( NearPlane, vOrientation, vOrigin );
    NearPlane = XMPlaneNormalize( NearPlane );

    XMVECTOR FarPlane = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    FarPlane = DirectX::Internal::XMPlaneTransform( FarPlane, vOrientation, vOrigin );
    FarPlane = XMPlaneNormalize( FarPlane );

    XMVECTOR RightPlane = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    RightPlane = DirectX::Internal::XMPlaneTransform( RightPlane, vOrientation, vOrigin );
    RightPlane = XMPlaneNormalize( RightPlane );

    XMVECTOR LeftPlane = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    LeftPlane = DirectX::Internal::XMPlaneTransform( LeftPlane, vOrientation, vOrigin );
    LeftPlane = XMPlaneNormalize( LeftPlane );
    
    XMVECTOR TopPlane = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    TopPlane = DirectX::Internal::XMPlaneTransform( TopPlane, vOrientation, vOrigin );
    TopPlane = XMPlaneNormalize( TopPlane );

    XMVECTOR BottomPlane = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );
    BottomPlane = DirectX::Internal::XMPlaneTransform( BottomPlane, vOrientation, vOrigin );
    BottomPlane = XMPlaneNormalize( BottomPlane );

    return TriangleTests::ContainedBy( V0, V1, V2, NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane );
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingFrustum::Contains( const BoundingSphere& sh ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Create 6 planes (do it inline to encourage use of registers)
    XMVECTOR NearPlane = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    NearPlane = DirectX::Internal::XMPlaneTransform( NearPlane, vOrientation, vOrigin );
    NearPlane = XMPlaneNormalize( NearPlane );

    XMVECTOR FarPlane = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    FarPlane = DirectX::Internal::XMPlaneTransform( FarPlane, vOrientation, vOrigin );
    FarPlane = XMPlaneNormalize( FarPlane );

    XMVECTOR RightPlane = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    RightPlane = DirectX::Internal::XMPlaneTransform( RightPlane, vOrientation, vOrigin );
    RightPlane = XMPlaneNormalize( RightPlane );

    XMVECTOR LeftPlane = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    LeftPlane = DirectX::Internal::XMPlaneTransform( LeftPlane, vOrientation, vOrigin );
    LeftPlane = XMPlaneNormalize( LeftPlane );
    
    XMVECTOR TopPlane = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    TopPlane = DirectX::Internal::XMPlaneTransform( TopPlane, vOrientation, vOrigin );
    TopPlane = XMPlaneNormalize( TopPlane );

    XMVECTOR BottomPlane = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );
    BottomPlane = DirectX::Internal::XMPlaneTransform( BottomPlane, vOrientation, vOrigin );
    BottomPlane = XMPlaneNormalize( BottomPlane );

    return sh.ContainedBy( NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane );
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingFrustum::Contains( const BoundingBox& box ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Create 6 planes (do it inline to encourage use of registers)
    XMVECTOR NearPlane = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    NearPlane = DirectX::Internal::XMPlaneTransform( NearPlane, vOrientation, vOrigin );
    NearPlane = XMPlaneNormalize( NearPlane );

    XMVECTOR FarPlane = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    FarPlane = DirectX::Internal::XMPlaneTransform( FarPlane, vOrientation, vOrigin );
    FarPlane = XMPlaneNormalize( FarPlane );

    XMVECTOR RightPlane = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    RightPlane = DirectX::Internal::XMPlaneTransform( RightPlane, vOrientation, vOrigin );
    RightPlane = XMPlaneNormalize( RightPlane );

    XMVECTOR LeftPlane = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    LeftPlane = DirectX::Internal::XMPlaneTransform( LeftPlane, vOrientation, vOrigin );
    LeftPlane = XMPlaneNormalize( LeftPlane );
    
    XMVECTOR TopPlane = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    TopPlane = DirectX::Internal::XMPlaneTransform( TopPlane, vOrientation, vOrigin );
    TopPlane = XMPlaneNormalize( TopPlane );

    XMVECTOR BottomPlane = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );
    BottomPlane = DirectX::Internal::XMPlaneTransform( BottomPlane, vOrientation, vOrigin );
    BottomPlane = XMPlaneNormalize( BottomPlane );

    return box.ContainedBy( NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane );
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingFrustum::Contains( const BoundingOrientedBox& box ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Create 6 planes (do it inline to encourage use of registers)
    XMVECTOR NearPlane = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    NearPlane = DirectX::Internal::XMPlaneTransform( NearPlane, vOrientation, vOrigin );
    NearPlane = XMPlaneNormalize( NearPlane );

    XMVECTOR FarPlane = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    FarPlane = DirectX::Internal::XMPlaneTransform( FarPlane, vOrientation, vOrigin );
    FarPlane = XMPlaneNormalize( FarPlane );

    XMVECTOR RightPlane = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    RightPlane = DirectX::Internal::XMPlaneTransform( RightPlane, vOrientation, vOrigin );
    RightPlane = XMPlaneNormalize( RightPlane );

    XMVECTOR LeftPlane = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    LeftPlane = DirectX::Internal::XMPlaneTransform( LeftPlane, vOrientation, vOrigin );
    LeftPlane = XMPlaneNormalize( LeftPlane );
    
    XMVECTOR TopPlane = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    TopPlane = DirectX::Internal::XMPlaneTransform( TopPlane, vOrientation, vOrigin );
    TopPlane = XMPlaneNormalize( TopPlane );

    XMVECTOR BottomPlane = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );
    BottomPlane = DirectX::Internal::XMPlaneTransform( BottomPlane, vOrientation, vOrigin );
    BottomPlane = XMPlaneNormalize( BottomPlane );

    return box.ContainedBy( NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane );
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType BoundingFrustum::Contains( const BoundingFrustum& fr ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    // Create 6 planes (do it inline to encourage use of registers)
    XMVECTOR NearPlane = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    NearPlane = DirectX::Internal::XMPlaneTransform( NearPlane, vOrientation, vOrigin );
    NearPlane = XMPlaneNormalize( NearPlane );

    XMVECTOR FarPlane = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    FarPlane = DirectX::Internal::XMPlaneTransform( FarPlane, vOrientation, vOrigin );
    FarPlane = XMPlaneNormalize( FarPlane );

    XMVECTOR RightPlane = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    RightPlane = DirectX::Internal::XMPlaneTransform( RightPlane, vOrientation, vOrigin );
    RightPlane = XMPlaneNormalize( RightPlane );

    XMVECTOR LeftPlane = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    LeftPlane = DirectX::Internal::XMPlaneTransform( LeftPlane, vOrientation, vOrigin );
    LeftPlane = XMPlaneNormalize( LeftPlane );
    
    XMVECTOR TopPlane = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    TopPlane = DirectX::Internal::XMPlaneTransform( TopPlane, vOrientation, vOrigin );
    TopPlane = XMPlaneNormalize( TopPlane );

    XMVECTOR BottomPlane = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );
    BottomPlane = DirectX::Internal::XMPlaneTransform( BottomPlane, vOrientation, vOrigin );
    BottomPlane = XMPlaneNormalize( BottomPlane );

    return fr.ContainedBy( NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane );
}


//-----------------------------------------------------------------------------
// Exact sphere vs frustum test.  The algorithm first checks the sphere against
// the planes of the frustum, then if the plane checks were indeterminate finds
// the nearest feature (plane, line, point) on the frustum to the center of the
// sphere and compares the distance to the nearest feature to the radius of the 
// sphere
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingFrustum::Intersects( const BoundingSphere& sh ) const
{
    XMVECTOR Zero = XMVectorZero();

    // Build the frustum planes.
    XMVECTOR Planes[6];
    Planes[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    Planes[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    Planes[2] = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    Planes[3] = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    Planes[4] = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    Planes[5] = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );

    // Normalize the planes so we can compare to the sphere radius.
    Planes[2] = XMVector3Normalize( Planes[2] );
    Planes[3] = XMVector3Normalize( Planes[3] );
    Planes[4] = XMVector3Normalize( Planes[4] );
    Planes[5] = XMVector3Normalize( Planes[5] );

    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Load the sphere.
    XMVECTOR vCenter = XMLoadFloat3( &sh.Center );
    XMVECTOR vRadius = XMVectorReplicatePtr( &sh.Radius );

    // Transform the center of the sphere into the local space of frustum.
    vCenter = XMVector3InverseRotate( XMVectorSubtract( vCenter, vOrigin ), vOrientation );

    // Set w of the center to one so we can dot4 with the plane.
    vCenter = XMVectorInsert<0, 0, 0, 0, 1>( vCenter, XMVectorSplatOne() );

    // Check against each plane of the frustum.
    XMVECTOR Outside = XMVectorFalseInt();
    XMVECTOR InsideAll = XMVectorTrueInt();
    XMVECTOR CenterInsideAll = XMVectorTrueInt();

    XMVECTOR Dist[6];

    for( size_t i = 0; i < 6; ++i )
    {
        Dist[i] = XMVector4Dot( vCenter, Planes[i] );

        // Outside the plane?
        Outside = XMVectorOrInt( Outside, XMVectorGreater( Dist[i], vRadius ) );

        // Fully inside the plane?
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( Dist[i], XMVectorNegate( vRadius ) ) );

        // Check if the center is inside the plane.
        CenterInsideAll = XMVectorAndInt( CenterInsideAll, XMVectorLessOrEqual( Dist[i], Zero ) );
    }

    // If the sphere is outside any of the planes it is outside. 
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If the sphere is inside all planes it is fully inside.
    if ( XMVector4EqualInt( InsideAll, XMVectorTrueInt() ) )
        return true;

    // If the center of the sphere is inside all planes and the sphere intersects 
    // one or more planes then it must intersect.
    if ( XMVector4EqualInt( CenterInsideAll, XMVectorTrueInt() ) )
        return true;

    // The sphere may be outside the frustum or intersecting the frustum.
    // Find the nearest feature (face, edge, or corner) on the frustum 
    // to the sphere.

    // The faces adjacent to each face are:
    static const size_t adjacent_faces[6][4] =
    {
        { 2, 3, 4, 5 },    // 0
        { 2, 3, 4, 5 },    // 1
        { 0, 1, 4, 5 },    // 2
        { 0, 1, 4, 5 },    // 3
        { 0, 1, 2, 3 },    // 4
        { 0, 1, 2, 3 }
    };  // 5

    XMVECTOR Intersects = XMVectorFalseInt();

    // Check to see if the nearest feature is one of the planes.
    for( size_t i = 0; i < 6; ++i )
    {
        // Find the nearest point on the plane to the center of the sphere.
        XMVECTOR Point = XMVectorNegativeMultiplySubtract( Planes[i], Dist[i], vCenter );

        // Set w of the point to one.
        Point = XMVectorInsert<0, 0, 0, 0, 1>( Point, XMVectorSplatOne() );
        
        // If the point is inside the face (inside the adjacent planes) then
        // this plane is the nearest feature.
        XMVECTOR InsideFace = XMVectorTrueInt();
        
        for ( size_t j = 0; j < 4; j++ )
        {
            size_t plane_index = adjacent_faces[i][j];

            InsideFace = XMVectorAndInt( InsideFace,
                           XMVectorLessOrEqual( XMVector4Dot( Point, Planes[plane_index] ), Zero ) );
        }
     
        // Since we have already checked distance from the plane we know that the
        // sphere must intersect if this plane is the nearest feature.
        Intersects = XMVectorOrInt( Intersects, 
                                    XMVectorAndInt( XMVectorGreater( Dist[i], Zero ), InsideFace ) );
    }

    if ( XMVector4EqualInt( Intersects, XMVectorTrueInt() ) )
        return true;

    // Build the corners of the frustum.
    XMVECTOR vRightTop = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vRightBottom = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vLeftTop = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vLeftBottom = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &Far );

    XMVECTOR Corners[CORNER_COUNT];
    Corners[0] = XMVectorMultiply( vRightTop, vNear );
    Corners[1] = XMVectorMultiply( vRightBottom, vNear );
    Corners[2] = XMVectorMultiply( vLeftTop, vNear );
    Corners[3] = XMVectorMultiply( vLeftBottom, vNear );
    Corners[4] = XMVectorMultiply( vRightTop, vFar );
    Corners[5] = XMVectorMultiply( vRightBottom, vFar );
    Corners[6] = XMVectorMultiply( vLeftTop, vFar );
    Corners[7] = XMVectorMultiply( vLeftBottom, vFar );

    // The Edges are:
    static const size_t edges[12][2] =
    {
        { 0, 1 }, { 2, 3 }, { 0, 2 }, { 1, 3 },    // Near plane
        { 4, 5 }, { 6, 7 }, { 4, 6 }, { 5, 7 },    // Far plane
        { 0, 4 }, { 1, 5 }, { 2, 6 }, { 3, 7 },
    }; // Near to far

    XMVECTOR RadiusSq = XMVectorMultiply( vRadius, vRadius );

    // Check to see if the nearest feature is one of the edges (or corners).
    for( size_t i = 0; i < 12; ++i )
    {
        size_t ei0 = edges[i][0];
        size_t ei1 = edges[i][1];

        // Find the nearest point on the edge to the center of the sphere.
        // The corners of the frustum are included as the endpoints of the edges.
        XMVECTOR Point = DirectX::Internal::PointOnLineSegmentNearestPoint( Corners[ei0], Corners[ei1], vCenter );

        XMVECTOR Delta = XMVectorSubtract( vCenter, Point );

        XMVECTOR DistSq = XMVector3Dot( Delta, Delta );

        // If the distance to the center of the sphere to the point is less than 
        // the radius of the sphere then it must intersect.
        Intersects = XMVectorOrInt( Intersects, XMVectorLessOrEqual( DistSq, RadiusSq ) );
    }

    if ( XMVector4EqualInt( Intersects, XMVectorTrueInt() ) )
        return true;

    // The sphere must be outside the frustum.
    return false;
}


//-----------------------------------------------------------------------------
// Exact axis aligned box vs frustum test.  Constructs an oriented box and uses
// the oriented box vs frustum test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingFrustum::Intersects( const BoundingBox& box ) const
{
    // Make the axis aligned box oriented and do an OBB vs frustum test.
    BoundingOrientedBox obox( box.Center, box.Extents, XMFLOAT4( 0.f, 0.f, 0.f, 1.f ) );
    return Intersects( obox );
}


//-----------------------------------------------------------------------------
// Exact oriented box vs frustum test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingFrustum::Intersects( const BoundingOrientedBox& box ) const
{
    static const XMVECTORU32 SelectY =
    {
        XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0
    };
    static const XMVECTORU32 SelectZ =
    {
        XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0
    };

    XMVECTOR Zero = XMVectorZero();

    // Build the frustum planes.
    XMVECTOR Planes[6];
    Planes[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    Planes[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    Planes[2] = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    Planes[3] = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    Planes[4] = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    Planes[5] = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );

    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR FrustumOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( FrustumOrientation ) );

    // Load the box.
    XMVECTOR Center = XMLoadFloat3( &box.Center );
    XMVECTOR Extents = XMLoadFloat3( &box.Extents );
    XMVECTOR BoxOrientation = XMLoadFloat4( &box.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( BoxOrientation ) );

    // Transform the oriented box into the space of the frustum in order to 
    // minimize the number of transforms we have to do.
    Center = XMVector3InverseRotate( XMVectorSubtract( Center, vOrigin ), FrustumOrientation );
    BoxOrientation = XMQuaternionMultiply( BoxOrientation, XMQuaternionConjugate( FrustumOrientation ) );

    // Set w of the center to one so we can dot4 with the plane.
    Center = XMVectorInsert<0, 0, 0, 0, 1>( Center, XMVectorSplatOne() );

    // Build the 3x3 rotation matrix that defines the box axes.
    XMMATRIX R = XMMatrixRotationQuaternion( BoxOrientation );

    // Check against each plane of the frustum.
    XMVECTOR Outside = XMVectorFalseInt();
    XMVECTOR InsideAll = XMVectorTrueInt();
    XMVECTOR CenterInsideAll = XMVectorTrueInt();

    for( size_t i = 0; i < 6; ++i )
    {
        // Compute the distance to the center of the box.
        XMVECTOR Dist = XMVector4Dot( Center, Planes[i] );

        // Project the axes of the box onto the normal of the plane.  Half the
        // length of the projection (sometime called the "radius") is equal to
        // h(u) * abs(n dot b(u))) + h(v) * abs(n dot b(v)) + h(w) * abs(n dot b(w))
        // where h(i) are extents of the box, n is the plane normal, and b(i) are the 
        // axes of the box.
        XMVECTOR Radius = XMVector3Dot( Planes[i], R.r[0] );
        Radius = XMVectorSelect( Radius, XMVector3Dot( Planes[i], R.r[1] ), SelectY );
        Radius = XMVectorSelect( Radius, XMVector3Dot( Planes[i], R.r[2] ), SelectZ );
        Radius = XMVector3Dot( Extents, XMVectorAbs( Radius ) );

        // Outside the plane?
        Outside = XMVectorOrInt( Outside, XMVectorGreater( Dist, Radius ) );

        // Fully inside the plane?
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( Dist, XMVectorNegate( Radius ) ) );

        // Check if the center is inside the plane.
        CenterInsideAll = XMVectorAndInt( CenterInsideAll, XMVectorLessOrEqual( Dist, Zero ) );
    }

    // If the box is outside any of the planes it is outside. 
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If the box is inside all planes it is fully inside.
    if ( XMVector4EqualInt( InsideAll, XMVectorTrueInt() ) )
        return true;

    // If the center of the box is inside all planes and the box intersects 
    // one or more planes then it must intersect.
    if ( XMVector4EqualInt( CenterInsideAll, XMVectorTrueInt() ) )
        return true;

    // Build the corners of the frustum.
    XMVECTOR vRightTop = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vRightBottom = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vLeftTop = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vLeftBottom = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &Far );

    XMVECTOR Corners[CORNER_COUNT];
    Corners[0] = XMVectorMultiply( vRightTop, vNear );
    Corners[1] = XMVectorMultiply( vRightBottom, vNear );
    Corners[2] = XMVectorMultiply( vLeftTop, vNear );
    Corners[3] = XMVectorMultiply( vLeftBottom, vNear );
    Corners[4] = XMVectorMultiply( vRightTop, vFar );
    Corners[5] = XMVectorMultiply( vRightBottom, vFar );
    Corners[6] = XMVectorMultiply( vLeftTop, vFar );
    Corners[7] = XMVectorMultiply( vLeftBottom, vFar );

    // Test against box axes (3)
    {
        // Find the min/max values of the projection of the frustum onto each axis.
        XMVECTOR FrustumMin, FrustumMax;

        FrustumMin = XMVector3Dot( Corners[0], R.r[0] );
        FrustumMin = XMVectorSelect( FrustumMin, XMVector3Dot( Corners[0], R.r[1] ), SelectY );
        FrustumMin = XMVectorSelect( FrustumMin, XMVector3Dot( Corners[0], R.r[2] ), SelectZ );
        FrustumMax = FrustumMin;

        for( size_t i = 1; i < BoundingOrientedBox::CORNER_COUNT; ++i )
        {
            XMVECTOR Temp = XMVector3Dot( Corners[i], R.r[0] );
            Temp = XMVectorSelect( Temp, XMVector3Dot( Corners[i], R.r[1] ), SelectY );
            Temp = XMVectorSelect( Temp, XMVector3Dot( Corners[i], R.r[2] ), SelectZ );

            FrustumMin = XMVectorMin( FrustumMin, Temp );
            FrustumMax = XMVectorMax( FrustumMax, Temp );
        }

        // Project the center of the box onto the axes.
        XMVECTOR BoxDist = XMVector3Dot( Center, R.r[0] );
        BoxDist = XMVectorSelect( BoxDist, XMVector3Dot( Center, R.r[1] ), SelectY );
        BoxDist = XMVectorSelect( BoxDist, XMVector3Dot( Center, R.r[2] ), SelectZ );

        // The projection of the box onto the axis is just its Center and Extents.
        // if (min > box_max || max < box_min) reject;
        XMVECTOR Result = XMVectorOrInt( XMVectorGreater( FrustumMin, XMVectorAdd( BoxDist, Extents ) ),
                                          XMVectorLess( FrustumMax, XMVectorSubtract( BoxDist, Extents ) ) );

        if( DirectX::Internal::XMVector3AnyTrue( Result ) )
            return false;
    }

    // Test against edge/edge axes (3*6).
    XMVECTOR FrustumEdgeAxis[6];

    FrustumEdgeAxis[0] = vRightTop;
    FrustumEdgeAxis[1] = vRightBottom;
    FrustumEdgeAxis[2] = vLeftTop;
    FrustumEdgeAxis[3] = vLeftBottom;
    FrustumEdgeAxis[4] = XMVectorSubtract( vRightTop, vLeftTop );
    FrustumEdgeAxis[5] = XMVectorSubtract( vLeftBottom, vLeftTop );

    for( size_t i = 0; i < 3; ++i )
    {
        for( size_t j = 0; j < 6; j++ )
        {
            // Compute the axis we are going to test.
            XMVECTOR Axis = XMVector3Cross( R.r[i], FrustumEdgeAxis[j] );

            // Find the min/max values of the projection of the frustum onto the axis.
            XMVECTOR FrustumMin, FrustumMax;

            FrustumMin = FrustumMax = XMVector3Dot( Axis, Corners[0] );

            for( size_t k = 1; k < CORNER_COUNT; k++ )
            {
                XMVECTOR Temp = XMVector3Dot( Axis, Corners[k] );
                FrustumMin = XMVectorMin( FrustumMin, Temp );
                FrustumMax = XMVectorMax( FrustumMax, Temp );
            }

            // Project the center of the box onto the axis.
            XMVECTOR Dist = XMVector3Dot( Center, Axis );

            // Project the axes of the box onto the axis to find the "radius" of the box.
            XMVECTOR Radius = XMVector3Dot( Axis, R.r[0] );
            Radius = XMVectorSelect( Radius, XMVector3Dot( Axis, R.r[1] ), SelectY );
            Radius = XMVectorSelect( Radius, XMVector3Dot( Axis, R.r[2] ), SelectZ );
            Radius = XMVector3Dot( Extents, XMVectorAbs( Radius ) );

            // if (center > max + radius || center < min - radius) reject;
            Outside = XMVectorOrInt( Outside, XMVectorGreater( Dist, XMVectorAdd( FrustumMax, Radius ) ) );
            Outside = XMVectorOrInt( Outside, XMVectorLess( Dist, XMVectorSubtract( FrustumMin, Radius ) ) );
        }
    }

    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If we did not find a separating plane then the box must intersect the frustum.
    return true;
}


//-----------------------------------------------------------------------------
// Exact frustum vs frustum test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool BoundingFrustum::Intersects( const BoundingFrustum& fr ) const
{
    // Load origin and orientation of frustum B.
    XMVECTOR OriginB = XMLoadFloat3( &Origin );
    XMVECTOR OrientationB = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( OrientationB ) );

    // Build the planes of frustum B.
    XMVECTOR AxisB[6];
    AxisB[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, 0.0f );
    AxisB[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, 0.0f );
    AxisB[2] = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    AxisB[3] = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    AxisB[4] = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    AxisB[5] = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );

    XMVECTOR PlaneDistB[6];
    PlaneDistB[0] = XMVectorNegate( XMVectorReplicatePtr( &Near ) );
    PlaneDistB[1] = XMVectorReplicatePtr( &Far );
    PlaneDistB[2] = XMVectorZero();
    PlaneDistB[3] = XMVectorZero();
    PlaneDistB[4] = XMVectorZero();
    PlaneDistB[5] = XMVectorZero();

    // Load origin and orientation of frustum A.
    XMVECTOR OriginA = XMLoadFloat3( &fr.Origin );
    XMVECTOR OrientationA = XMLoadFloat4( &fr.Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( OrientationA ) );

    // Transform frustum A into the space of the frustum B in order to 
    // minimize the number of transforms we have to do.
    OriginA = XMVector3InverseRotate( XMVectorSubtract( OriginA, OriginB ), OrientationB );
    OrientationA = XMQuaternionMultiply( OrientationA, XMQuaternionConjugate( OrientationB ) );

    // Build the corners of frustum A (in the local space of B).
    XMVECTOR RightTopA = XMVectorSet( fr.RightSlope, fr.TopSlope, 1.0f, 0.0f );
    XMVECTOR RightBottomA = XMVectorSet( fr.RightSlope, fr.BottomSlope, 1.0f, 0.0f );
    XMVECTOR LeftTopA = XMVectorSet(fr.LeftSlope,fr.TopSlope, 1.0f, 0.0f );
    XMVECTOR LeftBottomA = XMVectorSet( fr.LeftSlope, fr.BottomSlope, 1.0f, 0.0f );
    XMVECTOR NearA = XMVectorReplicatePtr( &fr.Near );
    XMVECTOR FarA = XMVectorReplicatePtr( &fr.Far );

    RightTopA = XMVector3Rotate( RightTopA, OrientationA );
    RightBottomA = XMVector3Rotate( RightBottomA, OrientationA );
    LeftTopA = XMVector3Rotate( LeftTopA, OrientationA );
    LeftBottomA = XMVector3Rotate( LeftBottomA, OrientationA );

    XMVECTOR CornersA[CORNER_COUNT];
    CornersA[0] = XMVectorMultiplyAdd( RightTopA, NearA, OriginA );
    CornersA[1] = XMVectorMultiplyAdd( RightBottomA, NearA, OriginA );
    CornersA[2] = XMVectorMultiplyAdd( LeftTopA, NearA, OriginA );
    CornersA[3] = XMVectorMultiplyAdd( LeftBottomA, NearA, OriginA );
    CornersA[4] = XMVectorMultiplyAdd( RightTopA, FarA, OriginA );
    CornersA[5] = XMVectorMultiplyAdd( RightBottomA, FarA, OriginA );
    CornersA[6] = XMVectorMultiplyAdd( LeftTopA, FarA, OriginA );
    CornersA[7] = XMVectorMultiplyAdd( LeftBottomA, FarA, OriginA );

    // Check frustum A against each plane of frustum B.
    XMVECTOR Outside = XMVectorFalseInt();
    XMVECTOR InsideAll = XMVectorTrueInt();

    for( size_t i = 0; i < 6; ++i )
    {
        // Find the min/max projection of the frustum onto the plane normal.
        XMVECTOR Min, Max;

        Min = Max = XMVector3Dot( AxisB[i], CornersA[0] );

        for( size_t j = 1; j < CORNER_COUNT; j++ )
        {
            XMVECTOR Temp = XMVector3Dot( AxisB[i], CornersA[j] );
            Min = XMVectorMin( Min, Temp );
            Max = XMVectorMax( Max, Temp );
        }

        // Outside the plane?
        Outside = XMVectorOrInt( Outside, XMVectorGreater( Min, PlaneDistB[i] ) );

        // Fully inside the plane?
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( Max, PlaneDistB[i] ) );
    }

    // If the frustum A is outside any of the planes of frustum B it is outside. 
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If frustum A is inside all planes of frustum B it is fully inside.
    if ( XMVector4EqualInt( InsideAll, XMVectorTrueInt() ) )
        return true;

    // Build the corners of frustum B.
    XMVECTOR RightTopB = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR RightBottomB = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR LeftTopB = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR LeftBottomB = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR NearB = XMVectorReplicatePtr( &Near );
    XMVECTOR FarB = XMVectorReplicatePtr( &Far );

    XMVECTOR CornersB[BoundingFrustum::CORNER_COUNT];
    CornersB[0] = XMVectorMultiply( RightTopB, NearB );
    CornersB[1] = XMVectorMultiply( RightBottomB, NearB );
    CornersB[2] = XMVectorMultiply( LeftTopB, NearB );
    CornersB[3] = XMVectorMultiply( LeftBottomB, NearB );
    CornersB[4] = XMVectorMultiply( RightTopB, FarB );
    CornersB[5] = XMVectorMultiply( RightBottomB, FarB );
    CornersB[6] = XMVectorMultiply( LeftTopB, FarB );
    CornersB[7] = XMVectorMultiply( LeftBottomB, FarB );

    // Build the planes of frustum A (in the local space of B).
    XMVECTOR AxisA[6];
    XMVECTOR PlaneDistA[6];

    AxisA[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, 0.0f );
    AxisA[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, 0.0f );
    AxisA[2] = XMVectorSet( 1.0f, 0.0f, -fr.RightSlope, 0.0f );
    AxisA[3] = XMVectorSet( -1.0f, 0.0f, fr.LeftSlope, 0.0f );
    AxisA[4] = XMVectorSet( 0.0f, 1.0f, -fr.TopSlope, 0.0f );
    AxisA[5] = XMVectorSet( 0.0f, -1.0f, fr.BottomSlope, 0.0f );

    AxisA[0] = XMVector3Rotate( AxisA[0], OrientationA );
    AxisA[1] = XMVectorNegate( AxisA[0] );
    AxisA[2] = XMVector3Rotate( AxisA[2], OrientationA );
    AxisA[3] = XMVector3Rotate( AxisA[3], OrientationA );
    AxisA[4] = XMVector3Rotate( AxisA[4], OrientationA );
    AxisA[5] = XMVector3Rotate( AxisA[5], OrientationA );

    PlaneDistA[0] = XMVector3Dot( AxisA[0], CornersA[0] );  // Re-use corner on near plane.
    PlaneDistA[1] = XMVector3Dot( AxisA[1], CornersA[4] );  // Re-use corner on far plane.
    PlaneDistA[2] = XMVector3Dot( AxisA[2], OriginA );
    PlaneDistA[3] = XMVector3Dot( AxisA[3], OriginA );
    PlaneDistA[4] = XMVector3Dot( AxisA[4], OriginA );
    PlaneDistA[5] = XMVector3Dot( AxisA[5], OriginA );

    // Check each axis of frustum A for a seperating plane (5).
    for( size_t i = 0; i < 6; ++i )
    {
        // Find the minimum projection of the frustum onto the plane normal.
        XMVECTOR Min;

        Min = XMVector3Dot( AxisA[i], CornersB[0] );

        for( size_t j = 1; j < CORNER_COUNT; j++ )
        {
            XMVECTOR Temp = XMVector3Dot( AxisA[i], CornersB[j] );
            Min = XMVectorMin( Min, Temp );
        }

        // Outside the plane?
        Outside = XMVectorOrInt( Outside, XMVectorGreater( Min, PlaneDistA[i] ) );
    }

    // If the frustum B is outside any of the planes of frustum A it is outside. 
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // Check edge/edge axes (6 * 6).
    XMVECTOR FrustumEdgeAxisA[6];
    FrustumEdgeAxisA[0] = RightTopA;
    FrustumEdgeAxisA[1] = RightBottomA;
    FrustumEdgeAxisA[2] = LeftTopA;
    FrustumEdgeAxisA[3] = LeftBottomA;
    FrustumEdgeAxisA[4] = XMVectorSubtract( RightTopA, LeftTopA );
    FrustumEdgeAxisA[5] = XMVectorSubtract( LeftBottomA, LeftTopA );

    XMVECTOR FrustumEdgeAxisB[6];
    FrustumEdgeAxisB[0] = RightTopB;
    FrustumEdgeAxisB[1] = RightBottomB;
    FrustumEdgeAxisB[2] = LeftTopB;
    FrustumEdgeAxisB[3] = LeftBottomB;
    FrustumEdgeAxisB[4] = XMVectorSubtract( RightTopB, LeftTopB );
    FrustumEdgeAxisB[5] = XMVectorSubtract( LeftBottomB, LeftTopB );

    for( size_t i = 0; i < 6; ++i )
    {
        for( size_t j = 0; j < 6; j++ )
        {
            // Compute the axis we are going to test.
            XMVECTOR Axis = XMVector3Cross( FrustumEdgeAxisA[i], FrustumEdgeAxisB[j] );

            // Find the min/max values of the projection of both frustums onto the axis.
            XMVECTOR MinA, MaxA;
            XMVECTOR MinB, MaxB;

            MinA = MaxA = XMVector3Dot( Axis, CornersA[0] );
            MinB = MaxB = XMVector3Dot( Axis, CornersB[0] );

            for( size_t k = 1; k < CORNER_COUNT; k++ )
            {
                XMVECTOR TempA = XMVector3Dot( Axis, CornersA[k] );
                MinA = XMVectorMin( MinA, TempA );
                MaxA = XMVectorMax( MaxA, TempA );

                XMVECTOR TempB = XMVector3Dot( Axis, CornersB[k] );
                MinB = XMVectorMin( MinB, TempB );
                MaxB = XMVectorMax( MaxB, TempB );
            }

            // if (MinA > MaxB || MinB > MaxA) reject
            Outside = XMVectorOrInt( Outside, XMVectorGreater( MinA, MaxB ) );
            Outside = XMVectorOrInt( Outside, XMVectorGreater( MinB, MaxA ) );
        }
    }

    // If there is a seperating plane, then the frustums do not intersect.
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If we did not find a separating plane then the frustums intersect.
    return true;
}


//-----------------------------------------------------------------------------
// Triangle vs frustum test.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingFrustum::Intersects( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2 ) const
{
    // Build the frustum planes (NOTE: D is negated from the usual).
    XMVECTOR Planes[6];
    Planes[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, -Near );
    Planes[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, Far );
    Planes[2] = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    Planes[3] = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    Planes[4] = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    Planes[5] = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );

    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Transform triangle into the local space of frustum.
    XMVECTOR TV0 = XMVector3InverseRotate( XMVectorSubtract( V0, vOrigin ), vOrientation );
    XMVECTOR TV1 = XMVector3InverseRotate( XMVectorSubtract( V1, vOrigin ), vOrientation );
    XMVECTOR TV2 = XMVector3InverseRotate( XMVectorSubtract( V2, vOrigin ), vOrientation );

    // Test each vertex of the triangle against the frustum planes.
    XMVECTOR Outside = XMVectorFalseInt();
    XMVECTOR InsideAll = XMVectorTrueInt();

    for( size_t i = 0; i < 6; ++i )
    {
        XMVECTOR Dist0 = XMVector3Dot( TV0, Planes[i] );
        XMVECTOR Dist1 = XMVector3Dot( TV1, Planes[i] );
        XMVECTOR Dist2 = XMVector3Dot( TV2, Planes[i] );

        XMVECTOR MinDist = XMVectorMin( Dist0, Dist1 );
        MinDist = XMVectorMin( MinDist, Dist2 );
        XMVECTOR MaxDist = XMVectorMax( Dist0, Dist1 );
        MaxDist = XMVectorMax( MaxDist, Dist2 );

        XMVECTOR PlaneDist = XMVectorSplatW( Planes[i] );

        // Outside the plane?
        Outside = XMVectorOrInt( Outside, XMVectorGreater( MinDist, PlaneDist ) );

        // Fully inside the plane?
        InsideAll = XMVectorAndInt( InsideAll, XMVectorLessOrEqual( MaxDist, PlaneDist ) );
    }

    // If the triangle is outside any of the planes it is outside. 
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If the triangle is inside all planes it is fully inside.
    if ( XMVector4EqualInt( InsideAll, XMVectorTrueInt() ) )
        return true;

    // Build the corners of the frustum.
    XMVECTOR vRightTop = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vRightBottom = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vLeftTop = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR vLeftBottom = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &Far );

    XMVECTOR Corners[CORNER_COUNT];
    Corners[0] = XMVectorMultiply( vRightTop, vNear );
    Corners[1] = XMVectorMultiply( vRightBottom, vNear );
    Corners[2] = XMVectorMultiply( vLeftTop, vNear );
    Corners[3] = XMVectorMultiply( vLeftBottom, vNear );
    Corners[4] = XMVectorMultiply( vRightTop, vFar );
    Corners[5] = XMVectorMultiply( vRightBottom, vFar );
    Corners[6] = XMVectorMultiply( vLeftTop, vFar );
    Corners[7] = XMVectorMultiply( vLeftBottom, vFar );

    // Test the plane of the triangle.
    XMVECTOR Normal = XMVector3Cross( XMVectorSubtract( V1, V0 ), XMVectorSubtract( V2, V0 ) );
    XMVECTOR Dist = XMVector3Dot( Normal, V0 );

    XMVECTOR MinDist, MaxDist;
    MinDist = MaxDist = XMVector3Dot( Corners[0], Normal );
    for( size_t i = 1; i < CORNER_COUNT; ++i )
    {
        XMVECTOR Temp = XMVector3Dot( Corners[i], Normal );
        MinDist = XMVectorMin( MinDist, Temp );
        MaxDist = XMVectorMax( MaxDist, Temp );
    }

    Outside = XMVectorOrInt( XMVectorGreater( MinDist, Dist ), XMVectorLess( MaxDist, Dist ) );   
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // Check the edge/edge axes (3*6).
    XMVECTOR TriangleEdgeAxis[3];
    TriangleEdgeAxis[0] = XMVectorSubtract( V1, V0 );
    TriangleEdgeAxis[1] = XMVectorSubtract( V2, V1 );
    TriangleEdgeAxis[2] = XMVectorSubtract( V0, V2 );

    XMVECTOR FrustumEdgeAxis[6];
    FrustumEdgeAxis[0] = vRightTop;
    FrustumEdgeAxis[1] = vRightBottom;
    FrustumEdgeAxis[2] = vLeftTop;
    FrustumEdgeAxis[3] = vLeftBottom;
    FrustumEdgeAxis[4] = XMVectorSubtract( vRightTop, vLeftTop );
    FrustumEdgeAxis[5] = XMVectorSubtract( vLeftBottom, vLeftTop );

    for( size_t i = 0; i < 3; ++i )
    {
        for( size_t j = 0; j < 6; j++ )
        {
            // Compute the axis we are going to test.
            XMVECTOR Axis = XMVector3Cross( TriangleEdgeAxis[i], FrustumEdgeAxis[j] );

            // Find the min/max of the projection of the triangle onto the axis.
            XMVECTOR MinA, MaxA;

            XMVECTOR Dist0 = XMVector3Dot( V0, Axis );
            XMVECTOR Dist1 = XMVector3Dot( V1, Axis );
            XMVECTOR Dist2 = XMVector3Dot( V2, Axis );

            MinA = XMVectorMin( Dist0, Dist1 );
            MinA = XMVectorMin( MinA, Dist2 );
            MaxA = XMVectorMax( Dist0, Dist1 );
            MaxA = XMVectorMax( MaxA, Dist2 );

            // Find the min/max of the projection of the frustum onto the axis.
            XMVECTOR MinB, MaxB;

            MinB = MaxB = XMVector3Dot( Axis, Corners[0] );

            for( size_t k = 1; k < CORNER_COUNT; k++ )
            {
                XMVECTOR Temp = XMVector3Dot( Axis, Corners[k] );
                MinB = XMVectorMin( MinB, Temp );
                MaxB = XMVectorMax( MaxB, Temp );
            }

            // if (MinA > MaxB || MinB > MaxA) reject;
            Outside = XMVectorOrInt( Outside, XMVectorGreater( MinA, MaxB ) );
            Outside = XMVectorOrInt( Outside, XMVectorGreater( MinB, MaxA ) );
        }
    }

    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return false;

    // If we did not find a separating plane then the triangle must intersect the frustum.
    return true;
}


//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline PlaneIntersectionType XM_CALLCONV BoundingFrustum::Intersects( FXMVECTOR Plane ) const
{
    assert( DirectX::Internal::XMPlaneIsUnit( Plane ) );

    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Set w of the origin to one so we can dot4 with a plane.
    vOrigin = XMVectorInsert<0, 0, 0, 0, 1>( vOrigin, XMVectorSplatOne() );

    // Build the corners of the frustum (in world space).
    XMVECTOR RightTop = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR RightBottom = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR LeftTop = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR LeftBottom = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &Far );

    RightTop = XMVector3Rotate( RightTop, vOrientation );
    RightBottom = XMVector3Rotate( RightBottom, vOrientation );
    LeftTop = XMVector3Rotate( LeftTop, vOrientation );
    LeftBottom = XMVector3Rotate( LeftBottom, vOrientation );

    XMVECTOR Corners0 = XMVectorMultiplyAdd( RightTop, vNear, vOrigin );
    XMVECTOR Corners1 = XMVectorMultiplyAdd( RightBottom, vNear, vOrigin );
    XMVECTOR Corners2 = XMVectorMultiplyAdd( LeftTop, vNear, vOrigin );
    XMVECTOR Corners3 = XMVectorMultiplyAdd( LeftBottom, vNear, vOrigin );
    XMVECTOR Corners4 = XMVectorMultiplyAdd( RightTop, vFar, vOrigin );
    XMVECTOR Corners5 = XMVectorMultiplyAdd( RightBottom, vFar, vOrigin );
    XMVECTOR Corners6 = XMVectorMultiplyAdd( LeftTop, vFar, vOrigin );
    XMVECTOR Corners7 = XMVectorMultiplyAdd( LeftBottom, vFar, vOrigin );

    XMVECTOR Outside, Inside;
    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane, Outside, Inside );

    // If the frustum is outside any plane it is outside.
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return FRONT;

    // If the frustum is inside all planes it is inside.
    if ( XMVector4EqualInt( Inside, XMVectorTrueInt() ) )
        return BACK;

    // The frustum is not inside all planes or outside a plane it intersects.
    return INTERSECTING;
}


//-----------------------------------------------------------------------------
// Ray vs. frustum test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV BoundingFrustum::Intersects( FXMVECTOR rayOrigin, FXMVECTOR Direction, float& Dist ) const
{
    // If ray starts inside the frustum, return a distance of 0 for the hit
    if ( Contains(rayOrigin) == CONTAINS )
    {
        Dist = 0.0f;
        return true;
    }

    // Build the frustum planes.
    XMVECTOR Planes[6];
    Planes[0] = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
    Planes[1] = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
    Planes[2] = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
    Planes[3] = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
    Planes[4] = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
    Planes[5] = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );

    // Load origin and orientation of the frustum.
    XMVECTOR frOrigin = XMLoadFloat3( &Origin );
    XMVECTOR frOrientation = XMLoadFloat4( &Orientation );

    // This algorithm based on "Fast Ray-Convex Polyhedron Intersectin," in James Arvo, ed., Graphics Gems II pp. 247-250
    float tnear = -FLT_MAX;
    float tfar = FLT_MAX;

    for( size_t i=0; i < 6; ++i )
    {
        XMVECTOR Plane = DirectX::Internal::XMPlaneTransform( Planes[i], frOrientation, frOrigin );
        Plane = XMPlaneNormalize( Plane );

        XMVECTOR AxisDotOrigin = XMPlaneDotCoord( Plane, rayOrigin );
        XMVECTOR AxisDotDirection = XMVector3Dot( Plane, Direction );

        if ( XMVector3LessOrEqual( XMVectorAbs( AxisDotDirection ), g_RayEpsilon ) )
        {
            // Ray is parallel to plane - check if ray origin is inside plane's
            if ( XMVector3Greater( AxisDotOrigin, g_XMZero ) )
            {
                // Ray origin is outside half-space.
                Dist = 0.f;
                return false;
            }
        }
        else
        {
            // Ray not parallel - get distance to plane.
            float vd = XMVectorGetX( AxisDotDirection );
            float vn = XMVectorGetX( AxisDotOrigin );
            float t = -vn / vd;
            if (vd < 0.0f)
            {
                // Front face - T is a near point.
                if (t > tfar)
                {
                    Dist = 0.f;
                    return false;
                }
                if (t > tnear)
                {
                    // Hit near face.
                    tnear = t;
                }
            }
            else
            {
                // back face - T is far point.
                if (t < tnear)
                {
                    Dist = 0.f;
                    return false;
                }
                if (t < tfar)
                {
                    // Hit far face.
                    tfar = t;
                }
            }
        }
    }

    // Survived all tests.
    // Note: if ray originates on polyhedron, may want to change 0.0f to some
    // epsilon to avoid intersecting the originating face.
    float distance = ( tnear >= 0.0f ) ? tnear : tfar;
    if (distance >= 0.0f)
    {
        Dist = distance;
        return true;
    }    

    Dist = 0.f;
    return false;
}


//-----------------------------------------------------------------------------
// Test a frustum vs 6 planes (typically forming another frustum).
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV BoundingFrustum::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2,
                                                                 GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5 ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    assert( DirectX::Internal::XMQuaternionIsUnit( vOrientation ) );

    // Set w of the origin to one so we can dot4 with a plane.
    vOrigin = XMVectorInsert<0, 0, 0, 0, 1>( vOrigin, XMVectorSplatOne() );

    // Build the corners of the frustum (in world space).
    XMVECTOR RightTop = XMVectorSet( RightSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR RightBottom = XMVectorSet( RightSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR LeftTop = XMVectorSet( LeftSlope, TopSlope, 1.0f, 0.0f );
    XMVECTOR LeftBottom = XMVectorSet( LeftSlope, BottomSlope, 1.0f, 0.0f );
    XMVECTOR vNear = XMVectorReplicatePtr( &Near );
    XMVECTOR vFar = XMVectorReplicatePtr( &Far );

    RightTop = XMVector3Rotate( RightTop, vOrientation );
    RightBottom = XMVector3Rotate( RightBottom, vOrientation );
    LeftTop = XMVector3Rotate( LeftTop, vOrientation );
    LeftBottom = XMVector3Rotate( LeftBottom, vOrientation );

    XMVECTOR Corners0 = XMVectorMultiplyAdd( RightTop, vNear, vOrigin );
    XMVECTOR Corners1 = XMVectorMultiplyAdd( RightBottom, vNear, vOrigin );
    XMVECTOR Corners2 = XMVectorMultiplyAdd( LeftTop, vNear, vOrigin );
    XMVECTOR Corners3 = XMVectorMultiplyAdd( LeftBottom, vNear, vOrigin );
    XMVECTOR Corners4 = XMVectorMultiplyAdd( RightTop, vFar, vOrigin );
    XMVECTOR Corners5 = XMVectorMultiplyAdd( RightBottom, vFar, vOrigin );
    XMVECTOR Corners6 = XMVectorMultiplyAdd( LeftTop, vFar, vOrigin );
    XMVECTOR Corners7 = XMVectorMultiplyAdd( LeftBottom, vFar, vOrigin );

    XMVECTOR Outside, Inside;

    // Test against each plane.
    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane0, Outside, Inside );

    XMVECTOR AnyOutside = Outside;
    XMVECTOR AllInside = Inside;

    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane1, Outside, Inside );

    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane2, Outside, Inside );

    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane3, Outside, Inside );

    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane4, Outside, Inside );

    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectFrustumPlane( Corners0, Corners1, Corners2, Corners3, 
                                                  Corners4, Corners5, Corners6, Corners7, 
                                                  Plane5, Outside, Inside );

    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    // If the frustum is outside any plane it is outside.
    if ( XMVector4EqualInt( AnyOutside, XMVectorTrueInt() ) )
        return DISJOINT;

    // If the frustum is inside all planes it is inside.
    if ( XMVector4EqualInt( AllInside, XMVectorTrueInt() ) )
        return CONTAINS;

    // The frustum is not inside all planes or outside a plane, it may intersect.
    return INTERSECTS;
}


//-----------------------------------------------------------------------------
// Build the 6 frustum planes from a frustum.
//
// The intended use for these routines is for fast culling to a view frustum.  
// When the volume being tested against a view frustum is small relative to the
// view frustum it is usually either inside all six planes of the frustum
// (CONTAINS) or outside one of the planes of the frustum (DISJOINT). If neither
// of these cases is true then it may or may not be intersecting the frustum
// (INTERSECTS)
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void BoundingFrustum::GetPlanes( XMVECTOR* NearPlane, XMVECTOR* FarPlane, XMVECTOR* RightPlane,
                                        XMVECTOR* LeftPlane, XMVECTOR* TopPlane, XMVECTOR* BottomPlane ) const
{
    // Load origin and orientation of the frustum.
    XMVECTOR vOrigin = XMLoadFloat3( &Origin );
    XMVECTOR vOrientation = XMLoadFloat4( &Orientation );

    if (NearPlane)
    {
        XMVECTOR vNearPlane = XMVectorSet( 0.0f, 0.0f, -1.0f, Near );
        vNearPlane = DirectX::Internal::XMPlaneTransform( vNearPlane, vOrientation, vOrigin );
        *NearPlane = XMPlaneNormalize( vNearPlane );
    }

    if (FarPlane)
    {
        XMVECTOR vFarPlane = XMVectorSet( 0.0f, 0.0f, 1.0f, -Far );
        vFarPlane = DirectX::Internal::XMPlaneTransform( vFarPlane, vOrientation, vOrigin );
        *FarPlane = XMPlaneNormalize( vFarPlane );
    }

    if (RightPlane)
    {
        XMVECTOR vRightPlane = XMVectorSet( 1.0f, 0.0f, -RightSlope, 0.0f );
        vRightPlane = DirectX::Internal::XMPlaneTransform( vRightPlane, vOrientation, vOrigin );
        *RightPlane = XMPlaneNormalize( vRightPlane );
    }

    if (LeftPlane)
    {
        XMVECTOR vLeftPlane = XMVectorSet( -1.0f, 0.0f, LeftSlope, 0.0f );
        vLeftPlane = DirectX::Internal::XMPlaneTransform( vLeftPlane, vOrientation, vOrigin );
        *LeftPlane = XMPlaneNormalize( vLeftPlane );
    }

    if (TopPlane)
    {
        XMVECTOR vTopPlane = XMVectorSet( 0.0f, 1.0f, -TopSlope, 0.0f );
        vTopPlane = DirectX::Internal::XMPlaneTransform( vTopPlane, vOrientation, vOrigin );
        *TopPlane = XMPlaneNormalize( vTopPlane );
    }

    if (BottomPlane)
    {
        XMVECTOR vBottomPlane = XMVectorSet( 0.0f, -1.0f, BottomSlope, 0.0f );
        vBottomPlane = DirectX::Internal::XMPlaneTransform( vBottomPlane, vOrientation, vOrigin );
        *BottomPlane = XMPlaneNormalize( vBottomPlane );
    }
}


//-----------------------------------------------------------------------------
// Build a frustum from a persepective projection matrix.  The matrix may only
// contain a projection; any rotation, translation or scale will cause the
// constructed frustum to be incorrect.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV BoundingFrustum::CreateFromMatrix( BoundingFrustum& Out, FXMMATRIX Projection )
{
    // Corners of the projection frustum in homogenous space.
    static XMVECTORF32 HomogenousPoints[6] =
    {
        {  1.0f,  0.0f, 1.0f, 1.0f },   // right (at far plane)
        { -1.0f,  0.0f, 1.0f, 1.0f },   // left
        {  0.0f,  1.0f, 1.0f, 1.0f },   // top
        {  0.0f, -1.0f, 1.0f, 1.0f },   // bottom

        { 0.0f, 0.0f, 0.0f, 1.0f },     // near
        { 0.0f, 0.0f, 1.0f, 1.0f }      // far
    };

    XMVECTOR Determinant;
    XMMATRIX matInverse = XMMatrixInverse( &Determinant, Projection );

    // Compute the frustum corners in world space.
    XMVECTOR Points[6];

    for( size_t i = 0; i < 6; ++i )
    {
        // Transform point.
        Points[i] = XMVector4Transform( HomogenousPoints[i], matInverse );
    }

    Out.Origin = XMFLOAT3( 0.0f, 0.0f, 0.0f );
    Out.Orientation = XMFLOAT4( 0.0f, 0.0f, 0.0f, 1.0f );

    // Compute the slopes.
    Points[0] = XMVectorMultiply( Points[0], XMVectorReciprocal( XMVectorSplatZ( Points[0] ) ) );
    Points[1] = XMVectorMultiply( Points[1], XMVectorReciprocal( XMVectorSplatZ( Points[1] ) ) );
    Points[2] = XMVectorMultiply( Points[2], XMVectorReciprocal( XMVectorSplatZ( Points[2] ) ) );
    Points[3] = XMVectorMultiply( Points[3], XMVectorReciprocal( XMVectorSplatZ( Points[3] ) ) );

    Out.RightSlope = XMVectorGetX( Points[0] );
    Out.LeftSlope = XMVectorGetX( Points[1] );
    Out.TopSlope = XMVectorGetY( Points[2] );
    Out.BottomSlope = XMVectorGetY( Points[3] );

    // Compute near and far.
    Points[4] = XMVectorMultiply( Points[4], XMVectorReciprocal( XMVectorSplatW( Points[4] ) ) );
    Points[5] = XMVectorMultiply( Points[5], XMVectorReciprocal( XMVectorSplatW( Points[5] ) ) );

    Out.Near = XMVectorGetZ( Points[4] );
    Out.Far = XMVectorGetZ( Points[5] );
}


/****************************************************************************
 *
 * TriangleTests
 *
 ****************************************************************************/

namespace TriangleTests
{

//-----------------------------------------------------------------------------
// Compute the intersection of a ray (Origin, Direction) with a triangle 
// (V0, V1, V2).  Return true if there is an intersection and also set *pDist 
// to the distance along the ray to the intersection.
// 
// The algorithm is based on Moller, Tomas and Trumbore, "Fast, Minimum Storage 
// Ray-Triangle Intersection", Journal of Graphics Tools, vol. 2, no. 1, 
// pp 21-28, 1997.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV Intersects( FXMVECTOR Origin, FXMVECTOR Direction, FXMVECTOR V0, GXMVECTOR V1, HXMVECTOR V2, float& Dist )
{
    assert( DirectX::Internal::XMVector3IsUnit( Direction ) );

    XMVECTOR Zero = XMVectorZero();

    XMVECTOR e1 = XMVectorSubtract( V1, V0 );
    XMVECTOR e2 = XMVectorSubtract( V2, V0 );

    // p = Direction ^ e2;
    XMVECTOR p = XMVector3Cross( Direction, e2 );

    // det = e1 * p;
    XMVECTOR det = XMVector3Dot( e1, p );

    XMVECTOR u, v, t;

    if( XMVector3GreaterOrEqual( det, g_RayEpsilon ) )
    {
        // Determinate is positive (front side of the triangle).
        XMVECTOR s = XMVectorSubtract( Origin, V0 );

        // u = s * p;
        u = XMVector3Dot( s, p );

        XMVECTOR NoIntersection = XMVectorLess( u, Zero );
        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( u, det ) );

        // q = s ^ e1;
        XMVECTOR q = XMVector3Cross( s, e1 );

        // v = Direction * q;
        v = XMVector3Dot( Direction, q );

        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( v, Zero ) );
        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( XMVectorAdd( u, v ), det ) );

        // t = e2 * q;
        t = XMVector3Dot( e2, q );

        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( t, Zero ) );

        if( XMVector4EqualInt( NoIntersection, XMVectorTrueInt() ) )
        {
            Dist = 0.f;
            return false;
        }
    }
    else if( XMVector3LessOrEqual( det, g_RayNegEpsilon ) )
    {
        // Determinate is negative (back side of the triangle).
        XMVECTOR s = XMVectorSubtract( Origin, V0 );

        // u = s * p;
        u = XMVector3Dot( s, p );

        XMVECTOR NoIntersection = XMVectorGreater( u, Zero );
        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( u, det ) );

        // q = s ^ e1;
        XMVECTOR q = XMVector3Cross( s, e1 );

        // v = Direction * q;
        v = XMVector3Dot( Direction, q );

        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( v, Zero ) );
        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorLess( XMVectorAdd( u, v ), det ) );

        // t = e2 * q;
        t = XMVector3Dot( e2, q );

        NoIntersection = XMVectorOrInt( NoIntersection, XMVectorGreater( t, Zero ) );

        if ( XMVector4EqualInt( NoIntersection, XMVectorTrueInt() ) )
        {
            Dist = 0.f;
            return false;
        }
    }
    else
    {
        // Parallel ray.
        Dist = 0.f;
        return false;
    }

    t = XMVectorDivide ( t, det );

    // (u / det) and (v / dev) are the barycentric cooridinates of the intersection.

    // Store the x-component to *pDist
    XMStoreFloat( &Dist, t );

    return true;
}


//-----------------------------------------------------------------------------
// Test if two triangles intersect.
//
// The final test of algorithm is based on Shen, Heng, and Tang, "A Fast 
// Triangle-Triangle Overlap Test Using Signed Distances", Journal of Graphics 
// Tools, vol. 8, no. 1, pp 17-23, 2003 and Guigue and Devillers, "Fast and 
// Robust Triangle-Triangle Overlap Test Using Orientation Predicates", Journal 
// of Graphics Tools, vol. 8, no. 1, pp 25-32, 2003.
//
// The final test could be considered an edge-edge separating plane test with
// the 9 possible cases narrowed down to the only two pairs of edges that can 
// actaully result in a seperation.
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline bool XM_CALLCONV Intersects( FXMVECTOR A0, FXMVECTOR A1, FXMVECTOR A2, GXMVECTOR B0, HXMVECTOR B1, HXMVECTOR B2 )
{
    static const XMVECTORU32 SelectY =
    {
        XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0
    };
    static const XMVECTORU32 SelectZ =
    {
        XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0
    };
    static const XMVECTORU32 Select0111 =
    {
        XM_SELECT_0, XM_SELECT_1, XM_SELECT_1, XM_SELECT_1
    };
    static const XMVECTORU32 Select1011 =
    {
        XM_SELECT_1, XM_SELECT_0, XM_SELECT_1, XM_SELECT_1
    };
    static const XMVECTORU32 Select1101 =
    {
        XM_SELECT_1, XM_SELECT_1, XM_SELECT_0, XM_SELECT_1
    };

    XMVECTOR Zero = XMVectorZero();

    // Compute the normal of triangle A.
    XMVECTOR N1 = XMVector3Cross( XMVectorSubtract( A1, A0 ), XMVectorSubtract( A2, A0 ) );

    // Assert that the triangle is not degenerate.
    assert( !XMVector3Equal( N1, Zero ) );

    // Test points of B against the plane of A.
    XMVECTOR BDist = XMVector3Dot( N1, XMVectorSubtract( B0, A0 ) );
    BDist = XMVectorSelect( BDist, XMVector3Dot( N1, XMVectorSubtract( B1, A0 ) ), SelectY );
    BDist = XMVectorSelect( BDist, XMVector3Dot( N1, XMVectorSubtract( B2, A0 ) ), SelectZ );

    // Ensure robustness with co-planar triangles by zeroing small distances.
    uint32_t BDistIsZeroCR;
    XMVECTOR BDistIsZero = XMVectorGreaterR( &BDistIsZeroCR, g_RayEpsilon, XMVectorAbs( BDist ) );
    BDist = XMVectorSelect( BDist, Zero, BDistIsZero );

    uint32_t BDistIsLessCR;
    XMVECTOR BDistIsLess = XMVectorGreaterR( &BDistIsLessCR, Zero, BDist );

    uint32_t BDistIsGreaterCR;
    XMVECTOR BDistIsGreater = XMVectorGreaterR( &BDistIsGreaterCR, BDist, Zero );

    // If all the points are on the same side we don't intersect.
    if( XMComparisonAllTrue( BDistIsLessCR ) || XMComparisonAllTrue( BDistIsGreaterCR ) )
        return false;

    // Compute the normal of triangle B.
    XMVECTOR N2 = XMVector3Cross( XMVectorSubtract( B1, B0 ), XMVectorSubtract( B2, B0 ) );

    // Assert that the triangle is not degenerate.
    assert( !XMVector3Equal( N2, Zero ) );

    // Test points of A against the plane of B.
    XMVECTOR ADist = XMVector3Dot( N2, XMVectorSubtract( A0, B0 ) );
    ADist = XMVectorSelect( ADist, XMVector3Dot( N2, XMVectorSubtract( A1, B0 ) ), SelectY );
    ADist = XMVectorSelect( ADist, XMVector3Dot( N2, XMVectorSubtract( A2, B0 ) ), SelectZ );

    // Ensure robustness with co-planar triangles by zeroing small distances.
    uint32_t ADistIsZeroCR;
    XMVECTOR ADistIsZero = XMVectorGreaterR( &ADistIsZeroCR, g_RayEpsilon, XMVectorAbs( BDist ) );
    ADist = XMVectorSelect( ADist, Zero, ADistIsZero );

    uint32_t ADistIsLessCR;
    XMVECTOR ADistIsLess = XMVectorGreaterR( &ADistIsLessCR, Zero, ADist );

    uint32_t ADistIsGreaterCR;
    XMVECTOR ADistIsGreater = XMVectorGreaterR( &ADistIsGreaterCR, ADist, Zero );

    // If all the points are on the same side we don't intersect.
    if( XMComparisonAllTrue( ADistIsLessCR ) || XMComparisonAllTrue( ADistIsGreaterCR ) )
        return false;

    // Special case for co-planar triangles.
    if( XMComparisonAllTrue( ADistIsZeroCR ) || XMComparisonAllTrue( BDistIsZeroCR ) )
    {
        XMVECTOR Axis, Dist, MinDist;

        // Compute an axis perpindicular to the edge (points out).
        Axis = XMVector3Cross( N1, XMVectorSubtract( A1, A0 ) );
        Dist = XMVector3Dot( Axis, A0 );

        // Test points of B against the axis.
        MinDist = XMVector3Dot( B0, Axis );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( B1, Axis ) );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( B2, Axis ) );
        if( XMVector4GreaterOrEqual( MinDist, Dist ) )
            return false;

        // Edge (A1, A2)
        Axis = XMVector3Cross( N1, XMVectorSubtract( A2, A1 ) );
        Dist = XMVector3Dot( Axis, A1 );

        MinDist = XMVector3Dot( B0, Axis );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( B1, Axis ) );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( B2, Axis ) );
        if( XMVector4GreaterOrEqual( MinDist, Dist ) )
            return false;

        // Edge (A2, A0)
        Axis = XMVector3Cross( N1, XMVectorSubtract( A0, A2 ) );
        Dist = XMVector3Dot( Axis, A2 );

        MinDist = XMVector3Dot( B0, Axis );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( B1, Axis ) );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( B2, Axis ) );
        if( XMVector4GreaterOrEqual( MinDist, Dist ) )
            return false;

        // Edge (B0, B1)
        Axis = XMVector3Cross( N2, XMVectorSubtract( B1, B0 ) );
        Dist = XMVector3Dot( Axis, B0 );

        MinDist = XMVector3Dot( A0, Axis );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( A1, Axis ) );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( A2, Axis ) );
        if( XMVector4GreaterOrEqual( MinDist, Dist ) )
            return false;

        // Edge (B1, B2)
        Axis = XMVector3Cross( N2, XMVectorSubtract( B2, B1 ) );
        Dist = XMVector3Dot( Axis, B1 );

        MinDist = XMVector3Dot( A0, Axis );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( A1, Axis ) );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( A2, Axis ) );
        if( XMVector4GreaterOrEqual( MinDist, Dist ) )
            return false;

        // Edge (B2,B0)
        Axis = XMVector3Cross( N2, XMVectorSubtract( B0, B2 ) );
        Dist = XMVector3Dot( Axis, B2 );

        MinDist = XMVector3Dot( A0, Axis );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( A1, Axis ) );
        MinDist = XMVectorMin( MinDist, XMVector3Dot( A2, Axis ) );
        if( XMVector4GreaterOrEqual( MinDist, Dist ) )
            return false;

        return true;
    }

    //
    // Find the single vertex of A and B (ie the vertex on the opposite side
    // of the plane from the other two) and reorder the edges so we can compute 
    // the signed edge/edge distances.
    //
    // if ( (V0 >= 0 && V1 <  0 && V2 <  0) ||
    //      (V0 >  0 && V1 <= 0 && V2 <= 0) ||
    //      (V0 <= 0 && V1 >  0 && V2 >  0) ||
    //      (V0 <  0 && V1 >= 0 && V2 >= 0) ) then V0 is singular;
    //
    // If our singular vertex is not on the positive side of the plane we reverse
    // the triangle winding so that the overlap comparisons will compare the 
    // correct edges with the correct signs.
    //
    XMVECTOR ADistIsLessEqual = XMVectorOrInt( ADistIsLess, ADistIsZero );
    XMVECTOR ADistIsGreaterEqual = XMVectorOrInt( ADistIsGreater, ADistIsZero );

    XMVECTOR AA0, AA1, AA2;
    bool bPositiveA;

    if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsGreaterEqual, ADistIsLess, Select0111 ) ) ||
        DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsGreater, ADistIsLessEqual, Select0111 ) ) )
    {
        // A0 is singular, crossing from positive to negative.
        AA0 = A0; AA1 = A1; AA2 = A2;
        bPositiveA = true;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsLessEqual, ADistIsGreater, Select0111 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsLess, ADistIsGreaterEqual, Select0111 ) ) )
    {
        // A0 is singular, crossing from negative to positive.
        AA0 = A0; AA1 = A2; AA2 = A1;
        bPositiveA = false;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsGreaterEqual, ADistIsLess, Select1011 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsGreater, ADistIsLessEqual, Select1011 ) ) )
    {
        // A1 is singular, crossing from positive to negative.
        AA0 = A1; AA1 = A2; AA2 = A0;
        bPositiveA = true;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsLessEqual, ADistIsGreater, Select1011 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsLess, ADistIsGreaterEqual, Select1011 ) ) )
    {
        // A1 is singular, crossing from negative to positive.
        AA0 = A1; AA1 = A0; AA2 = A2;
        bPositiveA = false;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsGreaterEqual, ADistIsLess, Select1101 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsGreater, ADistIsLessEqual, Select1101 ) ) )
    {
        // A2 is singular, crossing from positive to negative.
        AA0 = A2; AA1 = A0; AA2 = A1;
        bPositiveA = true;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsLessEqual, ADistIsGreater, Select1101 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( ADistIsLess, ADistIsGreaterEqual, Select1101 ) ) )
    {
        // A2 is singular, crossing from negative to positive.
        AA0 = A2; AA1 = A1; AA2 = A0;
        bPositiveA = false;
    }
    else
    {
        assert( false );
        return false;
    }

    XMVECTOR BDistIsLessEqual = XMVectorOrInt( BDistIsLess, BDistIsZero );
    XMVECTOR BDistIsGreaterEqual = XMVectorOrInt( BDistIsGreater, BDistIsZero );

    XMVECTOR BB0, BB1, BB2;
    bool bPositiveB;

    if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsGreaterEqual, BDistIsLess, Select0111 ) ) ||
        DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsGreater, BDistIsLessEqual, Select0111 ) ) )
    {
        // B0 is singular, crossing from positive to negative.
        BB0 = B0; BB1 = B1; BB2 = B2;
        bPositiveB = true;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsLessEqual, BDistIsGreater, Select0111 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsLess, BDistIsGreaterEqual, Select0111 ) ) )
    {
        // B0 is singular, crossing from negative to positive.
        BB0 = B0; BB1 = B2; BB2 = B1;
        bPositiveB = false;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsGreaterEqual, BDistIsLess, Select1011 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsGreater, BDistIsLessEqual, Select1011 ) ) )
    {
        // B1 is singular, crossing from positive to negative.
        BB0 = B1; BB1 = B2; BB2 = B0;
        bPositiveB = true;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsLessEqual, BDistIsGreater, Select1011 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsLess, BDistIsGreaterEqual, Select1011 ) ) )
    {
        // B1 is singular, crossing from negative to positive.
        BB0 = B1; BB1 = B0; BB2 = B2;
        bPositiveB = false;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsGreaterEqual, BDistIsLess, Select1101 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsGreater, BDistIsLessEqual, Select1101 ) ) )
    {
        // B2 is singular, crossing from positive to negative.
        BB0 = B2; BB1 = B0; BB2 = B1;
        bPositiveB = true;
    }
    else if( DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsLessEqual, BDistIsGreater, Select1101 ) ) ||
             DirectX::Internal::XMVector3AllTrue( XMVectorSelect( BDistIsLess, BDistIsGreaterEqual, Select1101 ) ) )
    {
        // B2 is singular, crossing from negative to positive.
        BB0 = B2; BB1 = B1; BB2 = B0;
        bPositiveB = false;
    }
    else
    {
        assert( false );
        return false;
    }

    XMVECTOR Delta0, Delta1;

    // Reverse the direction of the test depending on whether the singular vertices are
    // the same sign or different signs.
    if( bPositiveA ^ bPositiveB )
    {
        Delta0 = XMVectorSubtract( BB0, AA0 );
        Delta1 = XMVectorSubtract( AA0, BB0 );
    }
    else
    {
        Delta0 = XMVectorSubtract( AA0, BB0 );
        Delta1 = XMVectorSubtract( BB0, AA0 );
    }

    // Check if the triangles overlap on the line of intersection between the
    // planes of the two triangles by finding the signed line distances.
    XMVECTOR Dist0 = XMVector3Dot( Delta0, XMVector3Cross( XMVectorSubtract( BB2, BB0 ), XMVectorSubtract( AA2, AA0 ) ) );
    if( XMVector4Greater( Dist0, Zero ) )
        return false;

    XMVECTOR Dist1 = XMVector3Dot( Delta1, XMVector3Cross( XMVectorSubtract( BB1, BB0 ), XMVectorSubtract( AA1, AA0 ) ) );
    if( XMVector4Greater( Dist1, Zero ) )
        return false;

    return true;
}


//-----------------------------------------------------------------------------
// Ray-triangle test
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline PlaneIntersectionType XM_CALLCONV Intersects( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2, GXMVECTOR Plane )
{
    XMVECTOR One = XMVectorSplatOne();

    assert( DirectX::Internal::XMPlaneIsUnit( Plane ) );

    // Set w of the points to one so we can dot4 with a plane.
    XMVECTOR TV0 = XMVectorInsert<0, 0, 0, 0, 1>(V0, One);
    XMVECTOR TV1 = XMVectorInsert<0, 0, 0, 0, 1>(V1, One);
    XMVECTOR TV2 = XMVectorInsert<0, 0, 0, 0, 1>(V2, One);

    XMVECTOR Outside, Inside;
    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane, Outside, Inside );

    // If the triangle is outside any plane it is outside.
    if ( XMVector4EqualInt( Outside, XMVectorTrueInt() ) )
        return FRONT;

    // If the triangle is inside all planes it is inside.
    if ( XMVector4EqualInt( Inside, XMVectorTrueInt() ) )
        return BACK;

    // The triangle is not inside all planes or outside a plane it intersects.
    return INTERSECTING;
}


//-----------------------------------------------------------------------------
// Test a triangle vs 6 planes (typically forming a frustum).
//-----------------------------------------------------------------------------
_Use_decl_annotations_
inline ContainmentType XM_CALLCONV ContainedBy( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2,
                                                GXMVECTOR Plane0, HXMVECTOR Plane1, HXMVECTOR Plane2,
                                                CXMVECTOR Plane3, CXMVECTOR Plane4, CXMVECTOR Plane5 )
{
    XMVECTOR One = XMVectorSplatOne();

    // Set w of the points to one so we can dot4 with a plane.
    XMVECTOR TV0 = XMVectorInsert<0, 0, 0, 0, 1>(V0, One);
    XMVECTOR TV1 = XMVectorInsert<0, 0, 0, 0, 1>(V1, One);
    XMVECTOR TV2 = XMVectorInsert<0, 0, 0, 0, 1>(V2, One);

    XMVECTOR Outside, Inside;

    // Test against each plane.
    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane0, Outside, Inside );

    XMVECTOR AnyOutside = Outside;
    XMVECTOR AllInside = Inside;

    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane1, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane2, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane3, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane4, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    DirectX::Internal::FastIntersectTrianglePlane( TV0, TV1, TV2, Plane5, Outside, Inside );
    AnyOutside = XMVectorOrInt( AnyOutside, Outside );
    AllInside = XMVectorAndInt( AllInside, Inside );

    // If the triangle is outside any plane it is outside.
    if ( XMVector4EqualInt( AnyOutside, XMVectorTrueInt() ) )
        return DISJOINT;

    // If the triangle is inside all planes it is inside.
    if ( XMVector4EqualInt( AllInside, XMVectorTrueInt() ) )
        return CONTAINS;

    // The triangle is not inside all planes or outside a plane, it may intersect.
    return INTERSECTS;
}

}; // namespace TriangleTests