/* libs/graphics/sgl/SkGeometry.h
**
** Copyright 2006, The Android Open Source Project
**
** Licensed under the Apache License, Version 2.0 (the "License");
** you may not use this file except in compliance with the License.
** You may obtain a copy of the License at
**
** http://www.apache.org/licenses/LICENSE-2.0
**
** Unless required by applicable law or agreed to in writing, software
** distributed under the License is distributed on an "AS IS" BASIS,
** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
** See the License for the specific language governing permissions and
** limitations under the License.
*/
#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 ax xray, return true if
they intersect.
*/
bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2]);
/** 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].
*/
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);
void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], 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, or 2 for having chopped the cubic at its
inflection point.
*/
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.
*/
bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4]);
/** 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.
*/
int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4]);
///////////////////////////////////////////////////////////////////////////////////////////
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* matrix, SkPoint quadPoints[]);
#endif