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OpenSubdiv/examples/common/simple_math.h
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//
// Copyright (C) Pixar. All rights reserved.
//
// This license governs use of the accompanying software. If you
// use the software, you accept this license. If you do not accept
// the license, do not use the software.
//
// 1. Definitions
// The terms "reproduce," "reproduction," "derivative works," and
// "distribution" have the same meaning here as under U.S.
// copyright law. A "contribution" is the original software, or
// any additions or changes to the software.
// A "contributor" is any person or entity that distributes its
// contribution under this license.
// "Licensed patents" are a contributor's patent claims that read
// directly on its contribution.
//
// 2. Grant of Rights
// (A) Copyright Grant- Subject to the terms of this license,
// including the license conditions and limitations in section 3,
// each contributor grants you a non-exclusive, worldwide,
// royalty-free copyright license to reproduce its contribution,
// prepare derivative works of its contribution, and distribute
// its contribution or any derivative works that you create.
// (B) Patent Grant- Subject to the terms of this license,
// including the license conditions and limitations in section 3,
// each contributor grants you a non-exclusive, worldwide,
// royalty-free license under its licensed patents to make, have
// made, use, sell, offer for sale, import, and/or otherwise
// dispose of its contribution in the software or derivative works
// of the contribution in the software.
//
// 3. Conditions and Limitations
// (A) No Trademark License- This license does not grant you
// rights to use any contributor's name, logo, or trademarks.
// (B) If you bring a patent claim against any contributor over
// patents that you claim are infringed by the software, your
// patent license from such contributor to the software ends
// automatically.
// (C) If you distribute any portion of the software, you must
// retain all copyright, patent, trademark, and attribution
// notices that are present in the software.
// (D) If you distribute any portion of the software in source
// code form, you may do so only under this license by including a
// complete copy of this license with your distribution. If you
// distribute any portion of the software in compiled or object
// code form, you may only do so under a license that complies
// with this license.
// (E) The software is licensed "as-is." You bear the risk of
// using it. The contributors give no express warranties,
// guarantees or conditions. You may have additional consumer
// rights under your local laws which this license cannot change.
// To the extent permitted under your local laws, the contributors
// exclude the implied warranties of merchantability, fitness for
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//
#ifndef SIMPLE_MATH_H
#define SIMPLE_MATH_H
#include <cmath>
inline void
cross(float *n, const float *p0, const float *p1, const float *p2) {
float a[3] = { p1[0]-p0[0], p1[1]-p0[1], p1[2]-p0[2] };
float b[3] = { p2[0]-p0[0], p2[1]-p0[1], p2[2]-p0[2] };
n[0] = a[1]*b[2]-a[2]*b[1];
n[1] = a[2]*b[0]-a[0]*b[2];
n[2] = a[0]*b[1]-a[1]*b[0];
float rn = 1.0f/sqrtf(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
n[0] *= rn;
n[1] *= rn;
n[2] *= rn;
}
inline void
normalize(float * p) {
float dist = sqrtf( p[0]*p[0] + p[1]*p[1] + p[2]*p[2] );
p[0]/=dist;
p[1]/=dist;
p[2]/=dist;
}
inline void
multMatrix(float *d, const float *a, const float *b) {
for (int i=0; i<4; ++i)
{
for (int j=0; j<4; ++j)
{
d[i*4 + j] =
a[i*4 + 0] * b[0*4 + j] +
a[i*4 + 1] * b[1*4 + j] +
a[i*4 + 2] * b[2*4 + j] +
a[i*4 + 3] * b[3*4 + j];
}
}
}
inline void
inverseMatrix(float *d, const float *m) {
d[0] = m[ 5]*m[10]*m[15] - m[ 5]*m[11]*m[14] -
m[ 9]*m[ 6]*m[15] + m[ 9]*m[ 7]*m[14] +
m[13]*m[ 6]*m[11] - m[13]*m[ 7]*m[10];
d[1] = -m[ 1]*m[10]*m[15] + m[ 1]*m[11]*m[14] +
m[ 9]*m[ 2]*m[15] - m[ 9]*m[ 3]*m[14] -
m[13]*m[ 2]*m[11] + m[13]*m[ 3]*m[10];
d[2] = m[ 1]*m[ 6]*m[15] - m[ 1]*m[ 7]*m[14] -
m[ 5]*m[ 2]*m[15] + m[ 5]*m[ 3]*m[14] +
m[13]*m[ 2]*m[ 7] - m[13]*m[ 3]*m[ 6];
d[3] = -m[ 1]*m[ 6]*m[11] + m[ 1]*m[ 7]*m[10] +
m[ 5]*m[ 2]*m[11] - m[ 5]*m[ 3]*m[10] -
m[ 9]*m[ 2]*m[ 7] + m[ 9]*m[ 3]*m[ 6];
d[4] = -m[ 4]*m[10]*m[15] + m[ 4]*m[11]*m[14] +
m[ 8]*m[ 6]*m[15] - m[ 8]*m[ 7]*m[14] -
m[12]*m[ 6]*m[11] + m[12]*m[ 7]*m[10];
d[5] = m[ 0]*m[10]*m[15] - m[ 0]*m[11]*m[14] -
m[ 8]*m[ 2]*m[15] + m[ 8]*m[ 3]*m[14] +
m[12]*m[ 2]*m[11] - m[12]*m[ 3]*m[10];
d[6] = -m[ 0]*m[ 6]*m[15] + m[ 0]*m[ 7]*m[14] +
m[ 4]*m[ 2]*m[15] - m[ 4]*m[ 3]*m[14] -
m[12]*m[ 2]*m[ 7] + m[12]*m[ 3]*m[ 6];
d[7] = m[ 0]*m[ 6]*m[11] - m[ 0]*m[ 7]*m[10] -
m[ 4]*m[ 2]*m[11] + m[ 4]*m[ 3]*m[10] +
m[ 8]*m[ 2]*m[ 7] - m[ 8]*m[ 3]*m[ 6];
d[8] = m[ 4]*m[ 9]*m[15] - m[ 4]*m[11]*m[13] -
m[ 8]*m[ 5]*m[15] + m[ 8]*m[ 7]*m[13] +
m[12]*m[ 5]*m[11] - m[12]*m[ 7]*m[ 9];
d[9] = -m[ 0]*m[ 9]*m[15] + m[ 0]*m[11]*m[13] +
m[ 8]*m[ 1]*m[15] - m[ 8]*m[ 3]*m[13] -
m[12]*m[ 1]*m[11] + m[12]*m[ 3]*m[ 9];
d[10] = m[ 0]*m[ 5]*m[15] - m[ 0]*m[ 7]*m[13] -
m[ 4]*m[ 1]*m[15] + m[ 4]*m[ 3]*m[13] +
m[12]*m[ 1]*m[ 7] - m[12]*m[ 3]*m[ 5];
d[11] = -m[ 0]*m[ 5]*m[11] + m[ 0]*m[ 7]*m[ 9] +
m[ 4]*m[ 1]*m[11] - m[ 4]*m[ 3]*m[ 9] -
m[ 8]*m[ 1]*m[ 7] + m[ 8]*m[ 3]*m[ 5];
d[12] = -m[ 4]*m[ 9]*m[14] + m[ 4]*m[10]*m[13] +
m[ 8]*m[ 5]*m[14] - m[ 8]*m[ 6]*m[13] -
m[12]*m[ 5]*m[10] + m[12]*m[ 6]*m[ 9];
d[13] = m[ 0]*m[ 9]*m[14] - m[ 0]*m[10]*m[13] -
m[ 8]*m[ 1]*m[14] + m[ 8]*m[ 2]*m[13] +
m[12]*m[ 1]*m[10] - m[12]*m[ 2]*m[ 9];
d[14] = -m[ 0]*m[ 5]*m[14] + m[ 0]*m[ 6]*m[13] +
m[ 4]*m[ 1]*m[14] - m[ 4]*m[ 2]*m[13] -
m[12]*m[ 1]*m[ 6] + m[12]*m[ 2]*m[ 5];
d[15] = m[ 0]*m[ 5]*m[10] - m[ 0]*m[ 6]*m[ 9] -
m[ 4]*m[ 1]*m[10] + m[ 4]*m[ 2]*m[ 9] +
m[ 8]*m[ 1]*m[ 6] - m[ 8]*m[ 2]*m[ 5];
float det = m[0] * d[0] + m[1] * d[4] + m[2] * d[8] + m[3] * d[12];
if (det == 0) return;
det = 1.0f / det;
for (int i = 0; i < 16; i++)
d[i] = d[i] * det;
}
inline void
perspective(float *m, float fovy, float aspect, float znear, float zfar)
{
float r = 2 * (float)M_PI * fovy / 360.0F;
float t = 1.0f / tan(r*0.5f);
m[0] = t/aspect;
m[1] = m[2] = m[3] = 0.0;
m[4] = 0.0;
m[5] = t;
m[6] = m[7] = 0.0;
m[8] = m[9] = 0.0;
m[10] = (zfar + znear) / (znear - zfar);
m[11] = -1;
m[12] = m[13] = 0.0;
m[14] = (2*zfar*znear)/(znear - zfar);
m[15] = 0.0;
}
inline void
identity(float *m)
{
m[0] = 1; m[1] = 0; m[2] = 0; m[3] = 0;
m[4] = 0; m[5] = 1; m[6] = 0; m[7] = 0;
m[8] = 0; m[9] = 0; m[10] = 1; m[11] = 0;
m[12] = 0; m[13] = 0; m[14] = 0; m[15] = 1;
}
inline void
translate(float *m, float x, float y, float z)
{
float t[16];
identity(t);
t[12] = x;
t[13] = y;
t[14] = z;
float o[16];
for(int i = 0; i < 16; i++) o[i] = m[i];
multMatrix(m, t, o);
}
inline void
ortho(float *m, float left, float top, float right, float bottom)
{
identity(m);
m[0] = 2.0f / (right - left);
m[5] = 2.0f / (top - bottom);
m[10] = -1;
m[12] = -(right+left)/(right-left);
m[13] = -(top+bottom)/(top-bottom);
}
inline void
rotate(float *m, float angle, float x, float y, float z)
{
float r = 2 * (float) M_PI * angle/360.0f;
float c = cos(r);
float s = sin(r);
float t[16];
t[0] = x*x*(1-c)+c;
t[1] = y*x*(1-c)+z*s;
t[2] = x*z*(1-c)-y*s;
t[3] = 0;
t[4] = x*y*(1-c)-z*s;
t[5] = y*y*(1-c)+c;
t[6] = y*z*(1-c)+x*s;
t[7] = 0;
t[8] = x*z*(1-c)+y*s;
t[9] = y*z*(1-c)-x*s;
t[10] = z*z*(1-c)+c;
t[11] = 0;
t[12] = t[13] = t[14] = 0;
t[15] = 1;
float o[16];
for(int i = 0; i < 16; i++) o[i] = m[i];
multMatrix(m, t, o);
}
inline void
transpose(float *m)
{
std::swap(m[1], m[4]);
std::swap(m[2], m[8]);
std::swap(m[3], m[12]);
std::swap(m[6], m[9]);
std::swap(m[7], m[13]);
std::swap(m[11],m[14]);
}
#endif // SIMPLE_MATH_H
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