/*
* 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"
#include "SkNx.h"
static inline Sk2s from_point(const SkPoint& point) {
return Sk2s::Load(&point);
}
static inline SkPoint to_point(const Sk2s& x) {
SkPoint point;
x.store(&point);
return point;
}
static Sk2s times_2(const Sk2s& value) {
return value + value;
}
/** 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]);
///////////////////////////////////////////////////////////////////////////////
SkPoint SkEvalQuadAt(const SkPoint src[3], SkScalar t);
SkPoint SkEvalQuadTangentAt(const SkPoint src[3], SkScalar t);
/** 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 = nullptr);
/** 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.
*/
SkScalar 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]);
///////////////////////////////////////////////////////////////////////////////
/** 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] = nullptr);
bool SkChopMonoCubicAtX(SkPoint src[4], SkScalar y, SkPoint dst[7]);
bool SkChopMonoCubicAtY(SkPoint src[4], SkScalar x, SkPoint dst[7]);
enum class SkCubicType {
kSerpentine,
kLoop,
kLocalCusp, // Cusp at a non-infinite parameter value with an inflection at t=infinity.
kCuspAtInfinity, // Cusp with a cusp at t=infinity and a local inflection.
kQuadratic,
kLineOrPoint
};
static inline bool SkCubicIsDegenerate(SkCubicType type) {
switch (type) {
case SkCubicType::kSerpentine:
case SkCubicType::kLoop:
case SkCubicType::kLocalCusp:
case SkCubicType::kCuspAtInfinity:
return false;
case SkCubicType::kQuadratic:
case SkCubicType::kLineOrPoint:
return true;
}
SK_ABORT("Invalid SkCubicType");
return true;
}
static inline const char* SkCubicTypeName(SkCubicType type) {
switch (type) {
case SkCubicType::kSerpentine: return "kSerpentine";
case SkCubicType::kLoop: return "kLoop";
case SkCubicType::kLocalCusp: return "kLocalCusp";
case SkCubicType::kCuspAtInfinity: return "kCuspAtInfinity";
case SkCubicType::kQuadratic: return "kQuadratic";
case SkCubicType::kLineOrPoint: return "kLineOrPoint";
}
SK_ABORT("Invalid SkCubicType");
return "";
}
/** Returns the cubic classification.
t[],s[] are set to the two homogeneous parameter values at which points the lines L & M
intersect with K, sorted from smallest to largest and oriented so positive values of the
implicit are on the "left" side. For a serpentine curve they are the inflection points. For a
loop they are the double point. For a local cusp, they are both equal and denote the cusp point.
For a cusp at an infinite parameter value, one will be the local inflection point and the other
+inf (t,s = 1,0). If the curve is degenerate (i.e. quadratic or linear) they are both set to a
parameter value of +inf (t,s = 1,0).
d[] is filled with the cubic inflection function coefficients. See "Resolution Independent
Curve Rendering using Programmable Graphics Hardware", 4.2 Curve Categorization:
If the input points contain infinities or NaN, the return values are undefined.
https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf
*/
SkCubicType SkClassifyCubic(const SkPoint p[4], double t[2] = nullptr, double s[2] = nullptr,
double d[4] = nullptr);
///////////////////////////////////////////////////////////////////////////////
enum SkRotationDirection {
kCW_SkRotationDirection,
kCCW_SkRotationDirection
};
struct SkConic {
SkConic() {}
SkConic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, SkScalar w) {
fPts[0] = p0;
fPts[1] = p1;
fPts[2] = p2;
fW = w;
}
SkConic(const SkPoint pts[3], SkScalar w) {
memcpy(fPts, pts, sizeof(fPts));
fW = w;
}
SkPoint fPts[3];
SkScalar fW;
void set(const SkPoint pts[3], SkScalar w) {
memcpy(fPts, pts, 3 * sizeof(SkPoint));
fW = w;
}
void set(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, SkScalar w) {
fPts[0] = p0;
fPts[1] = p1;
fPts[2] = p2;
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 = nullptr) const;
bool SK_WARN_UNUSED_RESULT chopAt(SkScalar t, SkConic dst[2]) const;
void chopAt(SkScalar t1, SkScalar t2, SkConic* dst) const;
void chop(SkConic dst[2]) const;
SkPoint evalAt(SkScalar t) const;
SkVector evalTangentAt(SkScalar t) 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 SK_API 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 SK_API SK_WARN_UNUSED_RESULT 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; // unimplemented
static SkScalar TransformW(const SkPoint[3], SkScalar w, const SkMatrix&);
enum {
kMaxConicsForArc = 5
};
static int BuildUnitArc(const SkVector& start, const SkVector& stop, SkRotationDirection,
const SkMatrix*, SkConic conics[kMaxConicsForArc]);
};
// inline helpers are contained in a namespace to avoid external leakage to fragile SkNx members
namespace {
/**
* use for : eval(t) == A * t^2 + B * t + C
*/
struct SkQuadCoeff {
SkQuadCoeff() {}
SkQuadCoeff(const Sk2s& A, const Sk2s& B, const Sk2s& C)
: fA(A)
, fB(B)
, fC(C)
{
}
SkQuadCoeff(const SkPoint src[3]) {
fC = from_point(src[0]);
Sk2s P1 = from_point(src[1]);
Sk2s P2 = from_point(src[2]);
fB = times_2(P1 - fC);
fA = P2 - times_2(P1) + fC;
}
Sk2s eval(SkScalar t) {
Sk2s tt(t);
return eval(tt);
}
Sk2s eval(const Sk2s& tt) {
return (fA * tt + fB) * tt + fC;
}
Sk2s fA;
Sk2s fB;
Sk2s fC;
};
struct SkConicCoeff {
SkConicCoeff(const SkConic& conic) {
Sk2s p0 = from_point(conic.fPts[0]);
Sk2s p1 = from_point(conic.fPts[1]);
Sk2s p2 = from_point(conic.fPts[2]);
Sk2s ww(conic.fW);
Sk2s p1w = p1 * ww;
fNumer.fC = p0;
fNumer.fA = p2 - times_2(p1w) + p0;
fNumer.fB = times_2(p1w - p0);
fDenom.fC = Sk2s(1);
fDenom.fB = times_2(ww - fDenom.fC);
fDenom.fA = Sk2s(0) - fDenom.fB;
}
Sk2s eval(SkScalar t) {
Sk2s tt(t);
Sk2s numer = fNumer.eval(tt);
Sk2s denom = fDenom.eval(tt);
return numer / denom;
}
SkQuadCoeff fNumer;
SkQuadCoeff fDenom;
};
struct SkCubicCoeff {
SkCubicCoeff(const SkPoint src[4]) {
Sk2s P0 = from_point(src[0]);
Sk2s P1 = from_point(src[1]);
Sk2s P2 = from_point(src[2]);
Sk2s P3 = from_point(src[3]);
Sk2s three(3);
fA = P3 + three * (P1 - P2) - P0;
fB = three * (P2 - times_2(P1) + P0);
fC = three * (P1 - P0);
fD = P0;
}
Sk2s eval(SkScalar t) {
Sk2s tt(t);
return eval(tt);
}
Sk2s eval(const Sk2s& t) {
return ((fA * t + fB) * t + fC) * t + fD;
}
Sk2s fA;
Sk2s fB;
Sk2s fC;
Sk2s fD;
};
}
#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);
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