/*
* 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, if the point of maximum
curvature exists on the segment, returns the t value for this
point along the curve. Otherwise it will return a value of 0.
*/
float SkFindQuadMaxCurvature(const SkPoint src[3]);
/** 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 SkConic {
SkPoint fPts[3];
SkScalar fW;
void set(const SkPoint pts[3], SkScalar w) {
memcpy(fPts, pts, 3 * sizeof(SkPoint));
fW = w;
}
/**
* Given a t-value [0...1] return its position and/or tangent.
* If pos is not null, return its position at the t-value.
* If tangent is not null, return its tangent at the t-value. NOTE the
* tangent value's length is arbitrary, and only its direction should
* be used.
*/
void evalAt(SkScalar t, SkPoint* pos, SkVector* tangent = NULL) const;
void chopAt(SkScalar t, SkConic dst[2]) const;
void chop(SkConic dst[2]) const;
void computeAsQuadError(SkVector* err) const;
bool asQuadTol(SkScalar tol) const;
/**
* return the power-of-2 number of quads needed to approximate this conic
* with a sequence of quads. Will be >= 0.
*/
int computeQuadPOW2(SkScalar tol) const;
/**
* Chop this conic into N quads, stored continguously in pts[], where
* N = 1 << pow2. The amount of storage needed is (1 + 2 * N)
*/
int chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;
bool findXExtrema(SkScalar* t) const;
bool findYExtrema(SkScalar* t) const;
bool chopAtXExtrema(SkConic dst[2]) const;
bool chopAtYExtrema(SkConic dst[2]) const;
void computeTightBounds(SkRect* bounds) const;
void computeFastBounds(SkRect* bounds) const;
/** Find the parameter value where the conic takes on its maximum curvature.
*
* @param t output scalar for max curvature. Will be unchanged if
* max curvature outside 0..1 range.
*
* @return true if max curvature found inside 0..1 range, false otherwise
*/
bool findMaxCurvature(SkScalar* t) const;
};
#include "SkTemplates.h"
/**
* Help class to allocate storage for approximating a conic with N quads.
*/
class SkAutoConicToQuads {
public:
SkAutoConicToQuads() : fQuadCount(0) {}
/**
* Given a conic and a tolerance, return the array of points for the
* approximating quad(s). Call countQuads() to know the number of quads
* represented in these points.
*
* The quads are allocated to share end-points. e.g. if there are 4 quads,
* there will be 9 points allocated as follows
* quad[0] == pts[0..2]
* quad[1] == pts[2..4]
* quad[2] == pts[4..6]
* quad[3] == pts[6..8]
*/
const SkPoint* computeQuads(const SkConic& conic, SkScalar tol) {
int pow2 = conic.computeQuadPOW2(tol);
fQuadCount = 1 << pow2;
SkPoint* pts = fStorage.reset(1 + 2 * fQuadCount);
conic.chopIntoQuadsPOW2(pts, pow2);
return pts;
}
const SkPoint* computeQuads(const SkPoint pts[3], SkScalar weight,
SkScalar tol) {
SkConic conic;
conic.set(pts, weight);
return computeQuads(conic, tol);
}
int countQuads() const { return fQuadCount; }
private:
enum {
kQuadCount = 8, // should handle most conics
kPointCount = 1 + 2 * kQuadCount,
};
SkAutoSTMalloc<kPointCount, SkPoint> fStorage;
int fQuadCount; // #quads for current usage
};
#endif