7841c63136
git-svn-id: http://skia.googlecode.com/svn/trunk@8693 2bbb7eff-a529-9590-31e7-b0007b416f81
228 lines
9.0 KiB
C
228 lines
9.0 KiB
C
|
|
/*
|
|
* Copyright 2006 The Android Open Source Project
|
|
*
|
|
* Use of this source code is governed by a BSD-style license that can be
|
|
* found in the LICENSE file.
|
|
*/
|
|
|
|
|
|
#ifndef SkGeometry_DEFINED
|
|
#define SkGeometry_DEFINED
|
|
|
|
#include "SkMatrix.h"
|
|
|
|
/** An XRay is a half-line that runs from the specific point/origin to
|
|
+infinity in the X direction. e.g. XRay(3,5) is the half-line
|
|
(3,5)....(infinity, 5)
|
|
*/
|
|
typedef SkPoint SkXRay;
|
|
|
|
/** Given a line segment from pts[0] to pts[1], and an xray, return true if
|
|
they intersect. Optional outgoing "ambiguous" argument indicates
|
|
whether the answer is ambiguous because the query occurred exactly at
|
|
one of the endpoints' y coordinates, indicating that another query y
|
|
coordinate is preferred for robustness.
|
|
*/
|
|
bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2],
|
|
bool* ambiguous = NULL);
|
|
|
|
/** Given a quadratic equation Ax^2 + Bx + C = 0, return 0, 1, 2 roots for the
|
|
equation.
|
|
*/
|
|
int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]);
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
|
|
/** Set pt to the point on the src quadratic specified by t. t must be
|
|
0 <= t <= 1.0
|
|
*/
|
|
void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt,
|
|
SkVector* tangent = NULL);
|
|
void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt,
|
|
SkVector* tangent = NULL);
|
|
|
|
/** Given a src quadratic bezier, chop it at the specified t value,
|
|
where 0 < t < 1, and return the two new quadratics in dst:
|
|
dst[0..2] and dst[2..4]
|
|
*/
|
|
void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t);
|
|
|
|
/** Given a src quadratic bezier, chop it at the specified t == 1/2,
|
|
The new quads are returned in dst[0..2] and dst[2..4]
|
|
*/
|
|
void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]);
|
|
|
|
/** Given the 3 coefficients for a quadratic bezier (either X or Y values), look
|
|
for extrema, and return the number of t-values that are found that represent
|
|
these extrema. If the quadratic has no extrema betwee (0..1) exclusive, the
|
|
function returns 0.
|
|
Returned count tValues[]
|
|
0 ignored
|
|
1 0 < tValues[0] < 1
|
|
*/
|
|
int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValues[1]);
|
|
|
|
/** Given 3 points on a quadratic bezier, chop it into 1, 2 beziers such that
|
|
the resulting beziers are monotonic in Y. This is called by the scan converter.
|
|
Depending on what is returned, dst[] is treated as follows
|
|
0 dst[0..2] is the original quad
|
|
1 dst[0..2] and dst[2..4] are the two new quads
|
|
*/
|
|
int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]);
|
|
int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]);
|
|
|
|
/** Given 3 points on a quadratic bezier, divide it into 2 quadratics
|
|
if the point of maximum curvature exists on the quad segment.
|
|
Depending on what is returned, dst[] is treated as follows
|
|
1 dst[0..2] is the original quad
|
|
2 dst[0..2] and dst[2..4] are the two new quads
|
|
If dst == null, it is ignored and only the count is returned.
|
|
*/
|
|
int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]);
|
|
|
|
/** Given 3 points on a quadratic bezier, use degree elevation to
|
|
convert it into the cubic fitting the same curve. The new cubic
|
|
curve is returned in dst[0..3].
|
|
*/
|
|
SK_API void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]);
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
|
|
/** Convert from parametric from (pts) to polynomial coefficients
|
|
coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3]
|
|
*/
|
|
void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]);
|
|
|
|
/** Set pt to the point on the src cubic specified by t. t must be
|
|
0 <= t <= 1.0
|
|
*/
|
|
void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* locOrNull,
|
|
SkVector* tangentOrNull, SkVector* curvatureOrNull);
|
|
|
|
/** Given a src cubic bezier, chop it at the specified t value,
|
|
where 0 < t < 1, and return the two new cubics in dst:
|
|
dst[0..3] and dst[3..6]
|
|
*/
|
|
void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t);
|
|
/** Given a src cubic bezier, chop it at the specified t values,
|
|
where 0 < t < 1, and return the new cubics in dst:
|
|
dst[0..3],dst[3..6],...,dst[3*t_count..3*(t_count+1)]
|
|
*/
|
|
void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar t[],
|
|
int t_count);
|
|
|
|
/** Given a src cubic bezier, chop it at the specified t == 1/2,
|
|
The new cubics are returned in dst[0..3] and dst[3..6]
|
|
*/
|
|
void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]);
|
|
|
|
/** Given the 4 coefficients for a cubic bezier (either X or Y values), look
|
|
for extrema, and return the number of t-values that are found that represent
|
|
these extrema. If the cubic has no extrema betwee (0..1) exclusive, the
|
|
function returns 0.
|
|
Returned count tValues[]
|
|
0 ignored
|
|
1 0 < tValues[0] < 1
|
|
2 0 < tValues[0] < tValues[1] < 1
|
|
*/
|
|
int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
|
|
SkScalar tValues[2]);
|
|
|
|
/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
|
|
the resulting beziers are monotonic in Y. This is called by the scan converter.
|
|
Depending on what is returned, dst[] is treated as follows
|
|
0 dst[0..3] is the original cubic
|
|
1 dst[0..3] and dst[3..6] are the two new cubics
|
|
2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics
|
|
If dst == null, it is ignored and only the count is returned.
|
|
*/
|
|
int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]);
|
|
int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]);
|
|
|
|
/** Given a cubic bezier, return 0, 1, or 2 t-values that represent the
|
|
inflection points.
|
|
*/
|
|
int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[2]);
|
|
|
|
/** Return 1 for no chop, 2 for having chopped the cubic at a single
|
|
inflection point, 3 for having chopped at 2 inflection points.
|
|
dst will hold the resulting 1, 2, or 3 cubics.
|
|
*/
|
|
int SkChopCubicAtInflections(const SkPoint src[4], SkPoint dst[10]);
|
|
|
|
int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]);
|
|
int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
|
|
SkScalar tValues[3] = NULL);
|
|
|
|
/** Given a monotonic cubic bezier, determine whether an xray intersects the
|
|
cubic.
|
|
By definition the cubic is open at the starting point; in other
|
|
words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
|
|
left of the curve, the line is not considered to cross the curve,
|
|
but if it is equal to cubic[3].fY then it is considered to
|
|
cross.
|
|
Optional outgoing "ambiguous" argument indicates whether the answer is
|
|
ambiguous because the query occurred exactly at one of the endpoints' y
|
|
coordinates, indicating that another query y coordinate is preferred
|
|
for robustness.
|
|
*/
|
|
bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
|
|
bool* ambiguous = NULL);
|
|
|
|
/** Given an arbitrary cubic bezier, return the number of times an xray crosses
|
|
the cubic. Valid return values are [0..3]
|
|
By definition the cubic is open at the starting point; in other
|
|
words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
|
|
left of the curve, the line is not considered to cross the curve,
|
|
but if it is equal to cubic[3].fY then it is considered to
|
|
cross.
|
|
Optional outgoing "ambiguous" argument indicates whether the answer is
|
|
ambiguous because the query occurred exactly at one of the endpoints' y
|
|
coordinates or at a tangent point, indicating that another query y
|
|
coordinate is preferred for robustness.
|
|
*/
|
|
int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4],
|
|
bool* ambiguous = NULL);
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
|
|
enum SkRotationDirection {
|
|
kCW_SkRotationDirection,
|
|
kCCW_SkRotationDirection
|
|
};
|
|
|
|
/** Maximum number of points needed in the quadPoints[] parameter for
|
|
SkBuildQuadArc()
|
|
*/
|
|
#define kSkBuildQuadArcStorage 17
|
|
|
|
/** Given 2 unit vectors and a rotation direction, fill out the specified
|
|
array of points with quadratic segments. Return is the number of points
|
|
written to, which will be { 0, 3, 5, 7, ... kSkBuildQuadArcStorage }
|
|
|
|
matrix, if not null, is appled to the points before they are returned.
|
|
*/
|
|
int SkBuildQuadArc(const SkVector& unitStart, const SkVector& unitStop,
|
|
SkRotationDirection, const SkMatrix*, SkPoint quadPoints[]);
|
|
|
|
// experimental
|
|
struct SkRationalQuad {
|
|
SkPoint fPts[3];
|
|
SkScalar fW;
|
|
|
|
void set(const SkPoint pts[3], SkScalar w) {
|
|
memcpy(fPts, pts, 3 * sizeof(SkPoint));
|
|
fW = w;
|
|
}
|
|
|
|
void evalAt(SkScalar t, SkPoint* pt) const;
|
|
void chopAt(SkScalar t, SkRationalQuad dst[2]) const;
|
|
void chop(SkRationalQuad dst[2]) const;
|
|
|
|
int computeQuadPOW2(SkScalar tol) const;
|
|
int chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;
|
|
};
|
|
|
|
#endif
|