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gerrit-public.fairphone.software / platform / external / skia / d1dc920097194e3342355185528c84408a9929c8 / . / experimental / Intersection / Simplify.cpp
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/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "Simplify.h"
#undef SkASSERT
#define SkASSERT(cond) while (!(cond)) { sk_throw(); }
// Terminology:
// A Path contains one of more Contours
// A Contour is made up of Segment array
// A Segment is described by a Verb and a Point array with 2, 3, or 4 points
// A Verb is one of Line, Quad(ratic), or Cubic
// A Segment contains a Span array
// A Span is describes a portion of a Segment using starting and ending T
// T values range from 0 to 1, where 0 is the first Point in the Segment
// FIXME: remove once debugging is complete
#if 0 // set to 1 for no debugging whatsoever
//const bool gxRunTestsInOneThread = false;
#define DEBUG_ADD_INTERSECTING_TS 0
#define DEBUG_BRIDGE 0
#define DEBUG_CROSS 0
#define DEBUG_DUMP 0
#define DEBUG_PATH_CONSTRUCTION 0
#define DEBUG_WINDING 0
#define DEBUG_UNUSED 0 // set to expose unused functions
#define DEBUG_MARK_DONE 0
#else
//const bool gRunTestsInOneThread = true;
#define DEBUG_ADD_INTERSECTING_TS 0
#define DEBUG_BRIDGE 1
#define DEBUG_CROSS 1
#define DEBUG_DUMP 1
#define DEBUG_PATH_CONSTRUCTION 1
#define DEBUG_WINDING 0
#define DEBUG_UNUSED 0 // set to expose unused functions
#define DEBUG_MARK_DONE 0
#endif
#if DEBUG_DUMP
static const char* kLVerbStr[] = {"", "line", "quad", "cubic"};
// static const char* kUVerbStr[] = {"", "Line", "Quad", "Cubic"};
static int gContourID;
static int gSegmentID;
#endif
#ifndef DEBUG_TEST
#define DEBUG_TEST 0
#endif
static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
Intersections& intersections) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
return intersect(aLine, bLine, intersections.fT[0], intersections.fT[1]);
}
static int QuadLineIntersect(const SkPoint a[3], const SkPoint b[2],
Intersections& intersections) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
intersect(aQuad, bLine, intersections);
return intersections.fUsed;
}
static int CubicLineIntersect(const SkPoint a[2], const SkPoint b[3],
Intersections& intersections) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
}
static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
Intersections& intersections) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
const Quadratic bQuad = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY}};
intersect(aQuad, bQuad, intersections);
return intersections.fUsed;
}
static int CubicIntersect(const SkPoint a[4], const SkPoint b[4],
Intersections& intersections) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
const Cubic bCubic = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY},
{b[3].fX, b[3].fY}};
intersect(aCubic, bCubic, intersections);
return intersections.fUsed;
}
static int HLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
SkScalar y, bool flipped, Intersections& intersections) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
return horizontalIntersect(aLine, left, right, y, flipped, intersections);
}
static int HQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
SkScalar y, bool flipped, Intersections& intersections) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
return horizontalIntersect(aQuad, left, right, y, flipped, intersections);
}
static int HCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
SkScalar y, bool flipped, Intersections& intersections) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
return horizontalIntersect(aCubic, left, right, y, flipped, intersections);
}
static int VLineIntersect(const SkPoint a[2], SkScalar top, SkScalar bottom,
SkScalar x, bool flipped, Intersections& intersections) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
return verticalIntersect(aLine, top, bottom, x, flipped, intersections);
}
static int VQuadIntersect(const SkPoint a[3], SkScalar top, SkScalar bottom,
SkScalar x, bool flipped, Intersections& intersections) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
return verticalIntersect(aQuad, top, bottom, x, flipped, intersections);
}
static int VCubicIntersect(const SkPoint a[4], SkScalar top, SkScalar bottom,
SkScalar x, bool flipped, Intersections& intersections) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
return verticalIntersect(aCubic, top, bottom, x, flipped, intersections);
}
static int (* const VSegmentIntersect[])(const SkPoint [], SkScalar ,
SkScalar , SkScalar , bool , Intersections& ) = {
NULL,
VLineIntersect,
VQuadIntersect,
VCubicIntersect
};
static void LineXYAtT(const SkPoint a[2], double t, SkPoint* out) {
const _Line line = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
double x, y;
xy_at_t(line, t, x, y);
out->fX = SkDoubleToScalar(x);
out->fY = SkDoubleToScalar(y);
}
static void QuadXYAtT(const SkPoint a[3], double t, SkPoint* out) {
const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
double x, y;
xy_at_t(quad, t, x, y);
out->fX = SkDoubleToScalar(x);
out->fY = SkDoubleToScalar(y);
}
static void CubicXYAtT(const SkPoint a[4], double t, SkPoint* out) {
const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
double x, y;
xy_at_t(cubic, t, x, y);
out->fX = SkDoubleToScalar(x);
out->fY = SkDoubleToScalar(y);
}
static void (* const SegmentXYAtT[])(const SkPoint [], double , SkPoint* ) = {
NULL,
LineXYAtT,
QuadXYAtT,
CubicXYAtT
};
static SkScalar LineXAtT(const SkPoint a[2], double t) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
double x;
xy_at_t(aLine, t, x, *(double*) 0);
return SkDoubleToScalar(x);
}
static SkScalar QuadXAtT(const SkPoint a[3], double t) {
const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
double x;
xy_at_t(quad, t, x, *(double*) 0);
return SkDoubleToScalar(x);
}
static SkScalar CubicXAtT(const SkPoint a[4], double t) {
const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
double x;
xy_at_t(cubic, t, x, *(double*) 0);
return SkDoubleToScalar(x);
}
static SkScalar (* const SegmentXAtT[])(const SkPoint [], double ) = {
NULL,
LineXAtT,
QuadXAtT,
CubicXAtT
};
static SkScalar LineYAtT(const SkPoint a[2], double t) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
double y;
xy_at_t(aLine, t, *(double*) 0, y);
return SkDoubleToScalar(y);
}
static SkScalar QuadYAtT(const SkPoint a[3], double t) {
const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
double y;
xy_at_t(quad, t, *(double*) 0, y);
return SkDoubleToScalar(y);
}
static SkScalar CubicYAtT(const SkPoint a[4], double t) {
const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
double y;
xy_at_t(cubic, t, *(double*) 0, y);
return SkDoubleToScalar(y);
}
static SkScalar (* const SegmentYAtT[])(const SkPoint [], double ) = {
NULL,
LineYAtT,
QuadYAtT,
CubicYAtT
};
static SkScalar LineDXAtT(const SkPoint a[2], double ) {
return a[1].fX - a[0].fX;
}
static SkScalar QuadDXAtT(const SkPoint a[3], double t) {
const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
double x;
dxdy_at_t(quad, t, x, *(double*) 0);
return SkDoubleToScalar(x);
}
static SkScalar CubicDXAtT(const SkPoint a[4], double t) {
const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
{a[3].fX, a[3].fY}};
double x;
dxdy_at_t(cubic, t, x, *(double*) 0);
return SkDoubleToScalar(x);
}
static SkScalar (* const SegmentDXAtT[])(const SkPoint [], double ) = {
NULL,
LineDXAtT,
QuadDXAtT,
CubicDXAtT
};
static void LineSubDivide(const SkPoint a[2], double startT, double endT,
SkPoint sub[2]) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
_Line dst;
sub_divide(aLine, startT, endT, dst);
sub[0].fX = SkDoubleToScalar(dst[0].x);
sub[0].fY = SkDoubleToScalar(dst[0].y);
sub[1].fX = SkDoubleToScalar(dst[1].x);
sub[1].fY = SkDoubleToScalar(dst[1].y);
}
static void QuadSubDivide(const SkPoint a[3], double startT, double endT,
SkPoint sub[3]) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}};
Quadratic dst;
sub_divide(aQuad, startT, endT, dst);
sub[0].fX = SkDoubleToScalar(dst[0].x);
sub[0].fY = SkDoubleToScalar(dst[0].y);
sub[1].fX = SkDoubleToScalar(dst[1].x);
sub[1].fY = SkDoubleToScalar(dst[1].y);
sub[2].fX = SkDoubleToScalar(dst[2].x);
sub[2].fY = SkDoubleToScalar(dst[2].y);
}
static void CubicSubDivide(const SkPoint a[4], double startT, double endT,
SkPoint sub[4]) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
Cubic dst;
sub_divide(aCubic, startT, endT, dst);
sub[0].fX = SkDoubleToScalar(dst[0].x);
sub[0].fY = SkDoubleToScalar(dst[0].y);
sub[1].fX = SkDoubleToScalar(dst[1].x);
sub[1].fY = SkDoubleToScalar(dst[1].y);
sub[2].fX = SkDoubleToScalar(dst[2].x);
sub[2].fY = SkDoubleToScalar(dst[2].y);
sub[3].fX = SkDoubleToScalar(dst[3].x);
sub[3].fY = SkDoubleToScalar(dst[3].y);
}
static void (* const SegmentSubDivide[])(const SkPoint [], double , double ,
SkPoint []) = {
NULL,
LineSubDivide,
QuadSubDivide,
CubicSubDivide
};
#if DEBUG_UNUSED
static void QuadSubBounds(const SkPoint a[3], double startT, double endT,
SkRect& bounds) {
SkPoint dst[3];
QuadSubDivide(a, startT, endT, dst);
bounds.fLeft = bounds.fRight = dst[0].fX;
bounds.fTop = bounds.fBottom = dst[0].fY;
for (int index = 1; index < 3; ++index) {
bounds.growToInclude(dst[index].fX, dst[index].fY);
}
}
static void CubicSubBounds(const SkPoint a[4], double startT, double endT,
SkRect& bounds) {
SkPoint dst[4];
CubicSubDivide(a, startT, endT, dst);
bounds.fLeft = bounds.fRight = dst[0].fX;
bounds.fTop = bounds.fBottom = dst[0].fY;
for (int index = 1; index < 4; ++index) {
bounds.growToInclude(dst[index].fX, dst[index].fY);
}
}
#endif
static SkPath::Verb QuadReduceOrder(const SkPoint a[3],
SkTDArray<SkPoint>& reducePts) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}};
Quadratic dst;
int order = reduceOrder(aQuad, dst);
if (order == 3) {
return SkPath::kQuad_Verb;
}
for (int index = 0; index < order; ++index) {
SkPoint* pt = reducePts.append();
pt->fX = SkDoubleToScalar(dst[index].x);
pt->fY = SkDoubleToScalar(dst[index].y);
}
return (SkPath::Verb) (order - 1);
}
static SkPath::Verb CubicReduceOrder(const SkPoint a[4],
SkTDArray<SkPoint>& reducePts) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
Cubic dst;
int order = reduceOrder(aCubic, dst, kReduceOrder_QuadraticsAllowed);
if (order == 4) {
return SkPath::kCubic_Verb;
}
for (int index = 0; index < order; ++index) {
SkPoint* pt = reducePts.append();
pt->fX = SkDoubleToScalar(dst[index].x);
pt->fY = SkDoubleToScalar(dst[index].y);
}
return (SkPath::Verb) (order - 1);
}
static bool QuadIsLinear(const SkPoint a[3]) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}};
return isLinear(aQuad, 0, 2);
}
static bool CubicIsLinear(const SkPoint a[4]) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
return isLinear(aCubic, 0, 3);
}
static SkScalar LineLeftMost(const SkPoint a[2], double startT, double endT) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
double x[2];
xy_at_t(aLine, startT, x[0], *(double*) 0);
xy_at_t(aLine, endT, x[1], *(double*) 0);
return SkMinScalar((float) x[0], (float) x[1]);
}
static SkScalar QuadLeftMost(const SkPoint a[3], double startT, double endT) {
const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}};
return (float) leftMostT(aQuad, startT, endT);
}
static SkScalar CubicLeftMost(const SkPoint a[4], double startT, double endT) {
const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
return (float) leftMostT(aCubic, startT, endT);
}
static SkScalar (* const SegmentLeftMost[])(const SkPoint [], double , double) = {
NULL,
LineLeftMost,
QuadLeftMost,
CubicLeftMost
};
#if DEBUG_UNUSED
static bool IsCoincident(const SkPoint a[2], const SkPoint& above,
const SkPoint& below) {
const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
const _Line bLine = {{above.fX, above.fY}, {below.fX, below.fY}};
return implicit_matches_ulps(aLine, bLine, 32);
}
#endif
class Segment;
// sorting angles
// given angles of {dx dy ddx ddy dddx dddy} sort them
class Angle {
public:
// FIXME: this is bogus for quads and cubics
// if the quads and cubics' line from end pt to ctrl pt are coincident,
// there's no obvious way to determine the curve ordering from the
// derivatives alone. In particular, if one quadratic's coincident tangent
// is longer than the other curve, the final control point can place the
// longer curve on either side of the shorter one.
// Using Bezier curve focus http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf
// may provide some help, but nothing has been figured out yet.
bool operator<(const Angle& rh) const {
if ((fDy < 0) ^ (rh.fDy < 0)) {
return fDy < 0;
}
if (fDy == 0 && rh.fDy == 0 && fDx != rh.fDx) {
return fDx < rh.fDx;
}
SkScalar cmp = fDx * rh.fDy - rh.fDx * fDy;
if (cmp) {
return cmp < 0;
}
if ((fDDy < 0) ^ (rh.fDDy < 0)) {
return fDDy < 0;
}
if (fDDy == 0 && rh.fDDy == 0 && fDDx != rh.fDDx) {
return fDDx < rh.fDDx;
}
cmp = fDDx * rh.fDDy - rh.fDDx * fDDy;
if (cmp) {
return cmp < 0;
}
if ((fDDDy < 0) ^ (rh.fDDDy < 0)) {
return fDDDy < 0;
}
if (fDDDy == 0 && rh.fDDDy == 0) {
return fDDDx < rh.fDDDx;
}
return fDDDx * rh.fDDDy < rh.fDDDx * fDDDy;
}
int end() const {
return fEnd;
}
bool isHorizontal() const {
return fDy == 0 && fDDy == 0 && fDDDy == 0;
}
// since all angles share a point, this needs to know which point
// is the common origin, i.e., whether the center is at pts[0] or pts[verb]
// practically, this should only be called by addAngle
void set(const SkPoint* pts, SkPath::Verb verb, const Segment* segment,
int start, int end) {
SkASSERT(start != end);
fSegment = segment;
fStart = start;
fEnd = end;
fDx = pts[1].fX - pts[0].fX; // b - a
fDy = pts[1].fY - pts[0].fY;
if (verb == SkPath::kLine_Verb) {
fDDx = fDDy = fDDDx = fDDDy = 0;
return;
}
fDDx = pts[2].fX - pts[1].fX - fDx; // a - 2b + c
fDDy = pts[2].fY - pts[1].fY - fDy;
if (verb == SkPath::kQuad_Verb) {
fDDDx = fDDDy = 0;
return;
}
fDDDx = pts[3].fX + 3 * (pts[1].fX - pts[2].fX) - pts[0].fX;
fDDDy = pts[3].fY + 3 * (pts[1].fY - pts[2].fY) - pts[0].fY;
}
// noncoincident quads/cubics may have the same initial angle
// as lines, so must sort by derivatives as well
// if flatness turns out to be a reasonable way to sort, use the below:
void setFlat(const SkPoint* pts, SkPath::Verb verb, Segment* segment,
int start, int end) {
fSegment = segment;
fStart = start;
fEnd = end;
fDx = pts[1].fX - pts[0].fX; // b - a
fDy = pts[1].fY - pts[0].fY;
if (verb == SkPath::kLine_Verb) {
fDDx = fDDy = fDDDx = fDDDy = 0;
return;
}
if (verb == SkPath::kQuad_Verb) {
int uplsX = FloatAsInt(pts[2].fX - pts[1].fY - fDx);
int uplsY = FloatAsInt(pts[2].fY - pts[1].fY - fDy);
int larger = std::max(abs(uplsX), abs(uplsY));
int shift = 0;
double flatT;
SkPoint ddPt; // FIXME: get rid of copy (change fDD_ to point)
LineParameters implicitLine;
_Line tangent = {{pts[0].fX, pts[0].fY}, {pts[1].fX, pts[1].fY}};
implicitLine.lineEndPoints(tangent);
implicitLine.normalize();
while (larger > UlpsEpsilon * 1024) {
larger >>= 2;
++shift;
flatT = 0.5 / (1 << shift);
QuadXYAtT(pts, flatT, &ddPt);
_Point _pt = {ddPt.fX, ddPt.fY};
double distance = implicitLine.pointDistance(_pt);
if (approximately_zero(distance)) {
SkDebugf("%s ulps too small %1.9g\n", __FUNCTION__, distance);
break;
}
}
flatT = 0.5 / (1 << shift);
QuadXYAtT(pts, flatT, &ddPt);
fDDx = ddPt.fX - pts[0].fX;
fDDy = ddPt.fY - pts[0].fY;
SkASSERT(fDDx != 0 || fDDy != 0);
fDDDx = fDDDy = 0;
return;
}
SkASSERT(0); // FIXME: add cubic case
}
Segment* segment() const {
return const_cast<Segment*>(fSegment);
}
int sign() const {
return SkSign32(fStart - fEnd);
}
int start() const {
return fStart;
}
private:
SkScalar fDx;
SkScalar fDy;
SkScalar fDDx;
SkScalar fDDy;
SkScalar fDDDx;
SkScalar fDDDy;
const Segment* fSegment;
int fStart;
int fEnd;
};
static void sortAngles(SkTDArray<Angle>& angles, SkTDArray<Angle*>& angleList) {
int angleCount = angles.count();
int angleIndex;
angleList.setReserve(angleCount);
for (angleIndex = 0; angleIndex < angleCount; ++angleIndex) {
*angleList.append() = &angles[angleIndex];
}
QSort<Angle>(angleList.begin(), angleList.end() - 1);
}
// Bounds, unlike Rect, does not consider a line to be empty.
struct Bounds : public SkRect {
static bool Intersects(const Bounds& a, const Bounds& b) {
return a.fLeft <= b.fRight && b.fLeft <= a.fRight &&
a.fTop <= b.fBottom && b.fTop <= a.fBottom;
}
void add(SkScalar left, SkScalar top, SkScalar right, SkScalar bottom) {
if (left < fLeft) {
fLeft = left;
}
if (top < fTop) {
fTop = top;
}
if (right > fRight) {
fRight = right;
}
if (bottom > fBottom) {
fBottom = bottom;
}
}
void add(const Bounds& toAdd) {
add(toAdd.fLeft, toAdd.fTop, toAdd.fRight, toAdd.fBottom);
}
bool isEmpty() {
return fLeft > fRight || fTop > fBottom
|| fLeft == fRight && fTop == fBottom
|| isnan(fLeft) || isnan(fRight)
|| isnan(fTop) || isnan(fBottom);
}
void setCubicBounds(const SkPoint a[4]) {
_Rect dRect;
Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}, {a[3].fX, a[3].fY}};
dRect.setBounds(cubic);
set((float) dRect.left, (float) dRect.top, (float) dRect.right,
(float) dRect.bottom);
}
void setQuadBounds(const SkPoint a[3]) {
const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
{a[2].fX, a[2].fY}};
_Rect dRect;
dRect.setBounds(quad);
set((float) dRect.left, (float) dRect.top, (float) dRect.right,
(float) dRect.bottom);
}
};
struct Span {
Segment* fOther;
mutable SkPoint const* fPt; // lazily computed as needed
double fT;
double fOtherT; // value at fOther[fOtherIndex].fT
int fOtherIndex; // can't be used during intersection
int fWindSum; // accumulated from contours surrounding this one
int fWindValue; // 0 == canceled; 1 == normal; >1 == coincident
bool fDone; // if set, this span to next higher T has been processed
};
class Segment {
public:
Segment() {
#if DEBUG_DUMP
fID = ++gSegmentID;
#endif
}
SkScalar activeTop() const {
SkASSERT(!done());
int count = fTs.count();
SkScalar result = SK_ScalarMax;
bool lastDone = true;
for (int index = 0; index < count; ++index) {
bool done = fTs[index].fDone;
if (!done || !lastDone) {
SkScalar y = yAtT(index);
if (result > y) {
result = y;
}
}
lastDone = done;
}
SkASSERT(result < SK_ScalarMax);
return result;
}
void addAngle(SkTDArray<Angle>& angles, int start, int end) const {
SkASSERT(start != end);
SkPoint edge[4];
(*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
Angle* angle = angles.append();
angle->set(edge, fVerb, this, start, end);
}
void addCubic(const SkPoint pts[4]) {
init(pts, SkPath::kCubic_Verb);
fBounds.setCubicBounds(pts);
}
// FIXME: this needs to defer add for aligned consecutive line segments
SkPoint addCurveTo(int start, int end, SkPath& path, bool active) {
SkPoint edge[4];
// OPTIMIZE? if not active, skip remainder and return xy_at_t(end)
(*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
if (active) {
#if DEBUG_PATH_CONSTRUCTION
SkDebugf("%s %s (%1.9g,%1.9g)", __FUNCTION__,
kLVerbStr[fVerb], edge[1].fX, edge[1].fY);
if (fVerb > 1) {
SkDebugf(" (%1.9g,%1.9g)", edge[2].fX, edge[2].fY);
}
if (fVerb > 2) {
SkDebugf(" (%1.9g,%1.9g)", edge[3].fX, edge[3].fY);
}
SkDebugf("\n");
#endif
switch (fVerb) {
case SkPath::kLine_Verb:
path.lineTo(edge[1].fX, edge[1].fY);
break;
case SkPath::kQuad_Verb:
path.quadTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY);
break;
case SkPath::kCubic_Verb:
path.cubicTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY,
edge[3].fX, edge[3].fY);
break;
}
}
return edge[fVerb];
}
void addLine(const SkPoint pts[2]) {
init(pts, SkPath::kLine_Verb);
fBounds.set(pts, 2);
}
const SkPoint& addMoveTo(int tIndex, SkPath& path, bool active) {
const SkPoint& pt = xyAtT(tIndex);
if (active) {
#if DEBUG_PATH_CONSTRUCTION
SkDebugf("%s (%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY);
#endif
path.moveTo(pt.fX, pt.fY);
}
return pt;
}
// add 2 to edge or out of range values to get T extremes
void addOtherT(int index, double otherT, int otherIndex) {
Span& span = fTs[index];
span.fOtherT = otherT;
span.fOtherIndex = otherIndex;
}
void addQuad(const SkPoint pts[3]) {
init(pts, SkPath::kQuad_Verb);
fBounds.setQuadBounds(pts);
}
// Defer all coincident edge processing until
// after normal intersections have been computed
// no need to be tricky; insert in normal T order
// resolve overlapping ts when considering coincidence later
// add non-coincident intersection. Resulting edges are sorted in T.
int addT(double newT, Segment* other) {
// FIXME: in the pathological case where there is a ton of intercepts,
// binary search?
int insertedAt = -1;
size_t tCount = fTs.count();
for (size_t index = 0; index < tCount; ++index) {
// OPTIMIZATION: if there are three or more identical Ts, then
// the fourth and following could be further insertion-sorted so
// that all the edges are clockwise or counterclockwise.
// This could later limit segment tests to the two adjacent
// neighbors, although it doesn't help with determining which
// circular direction to go in.
if (newT < fTs[index].fT) {
insertedAt = index;
break;
}
}
Span* span;
if (insertedAt >= 0) {
span = fTs.insert(insertedAt);
} else {
insertedAt = tCount;
span = fTs.append();
}
span->fT = newT;
span->fOther = other;
span->fPt = NULL;
span->fWindSum = SK_MinS32;
span->fWindValue = 1;
if ((span->fDone = newT == 1)) {
++fDoneSpans;
}
return insertedAt;
}
// set spans from start to end to decrement by one
// note this walks other backwards
// FIMXE: there's probably an edge case that can be constructed where
// two span in one segment are separated by float epsilon on one span but
// not the other, if one segment is very small. For this
// case the counts asserted below may or may not be enough to separate the
// spans. Even if the counts work out, what if the spanw aren't correctly
// sorted? It feels better in such a case to match the span's other span
// pointer since both coincident segments must contain the same spans.
void addTCancel(double startT, double endT, Segment& other,
double oStartT, double oEndT) {
SkASSERT(endT - startT >= FLT_EPSILON);
SkASSERT(oEndT - oStartT >= FLT_EPSILON);
int index = 0;
while (startT - fTs[index].fT >= FLT_EPSILON) {
++index;
}
int oIndex = other.fTs.count();
while (other.fTs[--oIndex].fT - oEndT > -FLT_EPSILON)
;
Span* test = &fTs[index];
Span* oTest = &other.fTs[oIndex];
do {
bool decrement = test->fWindValue && oTest->fWindValue;
Span* end = test;
do {
if (decrement) {
SkASSERT(end->fWindValue > 0);
if (--(end->fWindValue) == 0) {
end->fDone = true;
++fDoneSpans;
}
}
end = &fTs[++index];
} while (end->fT - test->fT < FLT_EPSILON);
Span* oTestStart = oTest;
do {
if (decrement) {
SkASSERT(oTestStart->fWindValue > 0);
if (--(oTestStart->fWindValue) == 0) {
oTestStart->fDone = true;
++other.fDoneSpans;
}
}
if (!oIndex) {
break;
}
oTestStart = &other.fTs[--oIndex];
} while (oTest->fT - oTestStart->fT < FLT_EPSILON);
test = end;
oTest = oTestStart;
} while (test->fT < endT - FLT_EPSILON);
SkASSERT(!oIndex || oTest->fT <= oStartT - FLT_EPSILON);
}
// set spans from start to end to increment the greater by one and decrement
// the lesser
void addTCoincident(double startT, double endT, Segment& other,
double oStartT, double oEndT) {
SkASSERT(endT - startT >= FLT_EPSILON);
SkASSERT(oEndT - oStartT >= FLT_EPSILON);
int index = 0;
while (startT - fTs[index].fT >= FLT_EPSILON) {
++index;
}
int oIndex = 0;
while (oStartT - other.fTs[oIndex].fT >= FLT_EPSILON) {
++oIndex;
}
Span* test = &fTs[index];
Span* oTest = &other.fTs[oIndex];
SkTDArray<double> outsideTs;
SkTDArray<double> oOutsideTs;
do {
bool transfer = test->fWindValue && oTest->fWindValue;
bool decrementOther = test->fWindValue >= oTest->fWindValue;
Span* end = test;
double startT = end->fT;
double oStartT = oTest->fT;
do {
if (transfer) {
if (decrementOther) {
++(end->fWindValue);
} else {
SkASSERT(end->fWindValue > 0);
if (--(end->fWindValue) == 0) {
end->fDone = true;
++fDoneSpans;
int outCount = outsideTs.count();
if (outCount == 0 || end->fT - outsideTs[outCount - 2]
>= FLT_EPSILON) {
*outsideTs.append() = end->fT;
*outsideTs.append() = oStartT;
}
}
}
}
end = &fTs[++index];
} while (end->fT - test->fT < FLT_EPSILON);
Span* oEnd = oTest;
do {
if (transfer) {
if (decrementOther) {
SkASSERT(oEnd->fWindValue > 0);
if (--(oEnd->fWindValue) == 0) {
oEnd->fDone = true;
++other.fDoneSpans;
int oOutCount = oOutsideTs.count();
if (oOutCount == 0 || oEnd->fT
- oOutsideTs[oOutCount - 2] >= FLT_EPSILON) {
*oOutsideTs.append() = oEnd->fT;
*oOutsideTs.append() = startT;
}
}
} else {
++(oEnd->fWindValue);
}
}
oEnd = &other.fTs[++oIndex];
} while (oEnd->fT - oTest->fT < FLT_EPSILON);
test = end;
oTest = oEnd;
} while (test->fT < endT - FLT_EPSILON);
SkASSERT(oTest->fT < oEndT + FLT_EPSILON);
SkASSERT(oTest->fT > oEndT - FLT_EPSILON);
if (!done() && outsideTs.count()) {
addTOutsides(outsideTs, other, oEndT);
}
if (!other.done() && oOutsideTs.count()) {
other.addTOutsides(oOutsideTs, *this, endT);
}
}
void addTOutsides(const SkTDArray<double>& outsideTs, Segment& other,
double otherEnd) {
int count = outsideTs.count();
double endT = 0;
int endSpan = 0;
for (int index = 0; index < count; index += 2) {
double t = outsideTs[index];
double otherT = outsideTs[index + 1];
if (t > 1 - FLT_EPSILON) {
return;
}
if (t - endT > FLT_EPSILON) {
endSpan = addTPair(t, other, otherT);
}
do {
endT = fTs[++endSpan].fT;
} while (endT - t < FLT_EPSILON);
}
addTPair(endT, other, otherEnd);
}
int addTPair(double t, Segment& other, double otherT) {
int insertedAt = addT(t, &other);
int otherInsertedAt = other.addT(otherT, this);
addOtherT(insertedAt, otherT, otherInsertedAt);
other.addOtherT(otherInsertedAt, t, insertedAt);
return insertedAt;
}
void addTwoAngles(int start, int end, SkTDArray<Angle>& angles) const {
// add edge leading into junction
if (fTs[SkMin32(end, start)].fWindValue > 0) {
addAngle(angles, end, start);
}
// add edge leading away from junction
int step = SkSign32(end - start);
int tIndex = nextSpan(end, step);
if (tIndex >= 0 && fTs[SkMin32(end, tIndex)].fWindValue > 0) {
addAngle(angles, end, tIndex);
}
}
const Bounds& bounds() const {
return fBounds;
}
void buildAngles(int index, SkTDArray<Angle>& angles) const {
double referenceT = fTs[index].fT;
int lesser = index;
while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
buildAnglesInner(lesser, angles);
}
do {
buildAnglesInner(index, angles);
} while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
}
void buildAnglesInner(int index, SkTDArray<Angle>& angles) const {
Span* span = &fTs[index];
Segment* other = span->fOther;
// if there is only one live crossing, and no coincidence, continue
// in the same direction
// if there is coincidence, the only choice may be to reverse direction
// find edge on either side of intersection
int oIndex = span->fOtherIndex;
// if done == -1, prior span has already been processed
int step = 1;
int next = other->nextSpan(oIndex, step);
if (next < 0) {
step = -step;
next = other->nextSpan(oIndex, step);
}
// add candidate into and away from junction
other->addTwoAngles(next, oIndex, angles);
}
bool cancels(const Segment& other) const {
SkASSERT(fVerb == SkPath::kLine_Verb);
SkASSERT(other.fVerb == SkPath::kLine_Verb);
SkPoint dxy = fPts[0] - fPts[1];
SkPoint odxy = other.fPts[0] - other.fPts[1];
return dxy.fX * odxy.fX < 0 || dxy.fY * odxy.fY < 0;
}
// figure out if the segment's ascending T goes clockwise or not
// not enough context to write this as shown
// instead, add all segments meeting at the top
// sort them using buildAngleList
// find the first in the sort
// see if ascendingT goes to top
bool clockwise(int /* tIndex */) const {
SkASSERT(0); // incomplete
return false;
}
int crossedSpan(const SkPoint& basePt, SkScalar& bestY, double& hitT) const {
int start = 0;
int bestT = -1;
SkScalar top = bounds().fTop;
SkScalar bottom = bounds().fBottom;
int end;
do {
end = nextSpan(start, 1);
SkPoint edge[4];
// OPTIMIZE: wrap this so that if start==0 end==fTCount-1 we can
// work with the original data directly
(*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
// start here; intersect ray starting at basePt with edge
Intersections intersections;
int pts = (*VSegmentIntersect[fVerb])(edge, top, bottom, basePt.fX,
false, intersections);
if (pts == 0) {
continue;
}
if (pts > 1 && fVerb == SkPath::kLine_Verb) {
// if the intersection is edge on, wait for another one
continue;
}
SkASSERT(pts == 1); // FIXME: more code required to disambiguate
SkPoint pt;
double foundT = intersections.fT[0][0];
(*SegmentXYAtT[fVerb])(fPts, foundT, &pt);
if (bestY < pt.fY) {
bestY = pt.fY;
bestT = foundT < 1 ? start : end;
hitT = foundT;
}
start = end;
} while (fTs[end].fT != 1);
return bestT;
}
bool done() const {
SkASSERT(fDoneSpans <= fTs.count());
return fDoneSpans == fTs.count();
}
// so the span needs to contain the pairing info found here
// this should include the winding computed for the edge, and
// what edge it connects to, and whether it is discarded
// (maybe discarded == abs(winding) > 1) ?
// only need derivatives for duration of sorting, add a new struct
// for pairings, remove extra spans that have zero length and
// reference an unused other
// for coincident, the last span on the other may be marked done
// (always?)
// if loop is exhausted, contour may be closed.
// FIXME: pass in close point so we can check for closure
// given a segment, and a sense of where 'inside' is, return the next
// segment. If this segment has an intersection, or ends in multiple
// segments, find the mate that continues the outside.
// note that if there are multiples, but no coincidence, we can limit
// choices to connections in the correct direction
// mark found segments as done
// start is the index of the beginning T of this edge
// it is guaranteed to have an end which describes a non-zero length (?)
// winding -1 means ccw, 1 means cw
// firstFind allows coincident edges to be treated differently
Segment* findNext(int winding, const int startIndex, const int endIndex,
int& nextStart, int& nextEnd, bool firstFind) {
SkASSERT(startIndex != endIndex);
int count = fTs.count();
SkASSERT(startIndex < endIndex ? startIndex < count - 1
: startIndex > 0);
int step = SkSign32(endIndex - startIndex);
int end = nextSpan(startIndex, step);
SkASSERT(end >= 0);
Span* endSpan = &fTs[end];
Segment* other;
if (isSimple(end)) {
// mark the smaller of startIndex, endIndex done, and all adjacent
// spans with the same T value (but not 'other' spans)
markDone(SkMin32(startIndex, endIndex), winding);
other = endSpan->fOther;
nextStart = endSpan->fOtherIndex;
nextEnd = nextStart + step;
SkASSERT(step < 0 ? nextEnd >= 0 : nextEnd < other->fTs.count());
return other;
}
// more than one viable candidate -- measure angles to find best
SkTDArray<Angle> angles;
SkASSERT(startIndex - endIndex != 0);
SkASSERT((startIndex - endIndex < 0) ^ (step < 0));
addTwoAngles(startIndex, end, angles);
buildAngles(end, angles);
SkTDArray<Angle*> sorted;
sortAngles(angles, sorted);
// find the starting edge
int firstIndex = -1;
int angleCount = angles.count();
int angleIndex;
const Angle* angle;
for (angleIndex = 0; angleIndex < angleCount; ++angleIndex) {
angle = sorted[angleIndex];
if (angle->segment() == this && angle->start() == end &&
angle->end() == startIndex) {
firstIndex = angleIndex;
break;
}
}
// back up if prior edge is coincident with firstIndex
// adjustFirst(sorted, firstIndex, winding, firstFind);
SkASSERT(firstIndex >= 0);
int startWinding = winding;
int nextIndex = firstIndex + 1;
int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
const Angle* foundAngle = NULL;
// bool alreadyMarked = angle->segment()->fTs[SkMin32(angle->start(),
// angle->end())].fDone;
// iterate through the angle, and compute everyone's winding
bool firstEdge = true;
do {
if (nextIndex == angleCount) {
nextIndex = 0;
}
const Angle* nextAngle = sorted[nextIndex];
int maxWinding = winding;
Segment* nextSegment = nextAngle->segment();
int windValue = nextSegment->windValue(nextAngle);
SkASSERT(windValue > 0);
winding -= nextAngle->sign() * windValue;
firstEdge = false;
if (!winding) {
if (!foundAngle) {
foundAngle = nextAngle;
}
goto doNext;
}
if (nextSegment->done()) {
goto doNext;
}
// if the winding is non-zero, nextAngle does not connect to
// current chain. If we haven't done so already, mark the angle
// as done, record the winding value, and mark connected unambiguous
// segments as well.
if (nextSegment->winding(nextAngle) == SK_MinS32) {
if (abs(maxWinding) < abs(winding)) {
maxWinding = winding;
}
if (foundAngle) {
nextSegment->markAndChaseWinding(nextAngle, maxWinding);
} else {
nextSegment->markAndChaseDone(nextAngle, maxWinding);
}
}
doNext:
angle = nextAngle;
} while (++nextIndex != lastIndex);
// if (!alreadyMarked) {
sorted[firstIndex]->segment()->
markDone(SkMin32(startIndex, endIndex), startWinding);
// }
if (!foundAngle) {
return NULL;
}
nextStart = foundAngle->start();
nextEnd = foundAngle->end();
return foundAngle->segment();
}
// FIXME: this is tricky code; needs its own unit test
void findTooCloseToCall(int /* winding */ ) { // FIXME: winding should be considered
int count = fTs.count();
if (count < 3) { // require t=0, x, 1 at minimum
return;
}
int matchIndex = 0;
int moCount;
Span* match;
Segment* mOther;
do {
match = &fTs[matchIndex];
mOther = match->fOther;
moCount = mOther->fTs.count();
if (moCount >= 3) {
break;
}
if (++matchIndex >= count) {
return;
}
} while (true); // require t=0, x, 1 at minimum
// OPTIMIZATION: defer matchPt until qualifying toCount is found?
const SkPoint* matchPt = &xyAtT(match);
// look for a pair of nearby T values that map to the same (x,y) value
// if found, see if the pair of other segments share a common point. If
// so, the span from here to there is coincident.
for (int index = matchIndex + 1; index < count; ++index) {
Span* test = &fTs[index];
if (test->fDone) {
continue;
}
Segment* tOther = test->fOther;
int toCount = tOther->fTs.count();
if (toCount < 3) { // require t=0, x, 1 at minimum
continue;
}
const SkPoint* testPt = &xyAtT(test);
if (*matchPt != *testPt) {
matchIndex = index;
moCount = toCount;
match = test;
mOther = tOther;
matchPt = testPt;
continue;
}
int moStart = -1;
int moEnd = -1;
double moStartT, moEndT;
for (int moIndex = 0; moIndex < moCount; ++moIndex) {
Span& moSpan = mOther->fTs[moIndex];
if (moSpan.fDone) {
continue;
}
if (moSpan.fOther == this) {
if (moSpan.fOtherT == match->fT) {
moStart = moIndex;
moStartT = moSpan.fT;
}
continue;
}
if (moSpan.fOther == tOther) {
SkASSERT(moEnd == -1);
moEnd = moIndex;
moEndT = moSpan.fT;
}
}
if (moStart < 0 || moEnd < 0) {
continue;
}
// FIXME: if moStartT, moEndT are initialized to NaN, can skip this test
if (moStartT == moEndT) {
continue;
}
int toStart = -1;
int toEnd = -1;
double toStartT, toEndT;
for (int toIndex = 0; toIndex < toCount; ++toIndex) {
Span& toSpan = tOther->fTs[toIndex];
if (toSpan.fOther == this) {
if (toSpan.fOtherT == test->fT) {
toStart = toIndex;
toStartT = toSpan.fT;
}
continue;
}
if (toSpan.fOther == mOther && toSpan.fOtherT == moEndT) {
SkASSERT(toEnd == -1);
toEnd = toIndex;
toEndT = toSpan.fT;
}
}
// FIXME: if toStartT, toEndT are initialized to NaN, can skip this test
if (toStart <= 0 || toEnd <= 0) {
continue;
}
if (toStartT == toEndT) {
continue;
}
// test to see if the segment between there and here is linear
if (!mOther->isLinear(moStart, moEnd)
|| !tOther->isLinear(toStart, toEnd)) {
continue;
}
// FIXME: defer implementation until the rest works
// this may share code with regular coincident detection
SkASSERT(0);
#if 0
if (flipped) {
mOther->addTCancel(moStart, moEnd, tOther, tStart, tEnd);
} else {
mOther->addTCoincident(moStart, moEnd, tOther, tStart, tEnd);
}
#endif
}
}
// OPTIMIZATION : for a pair of lines, can we compute points at T (cached)
// and use more concise logic like the old edge walker code?
// FIXME: this needs to deal with coincident edges
Segment* findTop(int& tIndex, int& endIndex) {
// iterate through T intersections and return topmost
// topmost tangent from y-min to first pt is closer to horizontal
SkASSERT(!done());
int firstT;
int lastT;
SkPoint topPt;
topPt.fY = SK_ScalarMax;
int count = fTs.count();
// see if either end is not done since we want smaller Y of the pair
bool lastDone = true;
for (int index = 0; index < count; ++index) {
const Span& span = fTs[index];
if (!span.fDone || !lastDone) {
const SkPoint& intercept = xyAtT(&span);
if (topPt.fY > intercept.fY || (topPt.fY == intercept.fY
&& topPt.fX > intercept.fX)) {
topPt = intercept;
firstT = lastT = index;
} else if (topPt == intercept) {
lastT = index;
}
}
lastDone = span.fDone;
}
// sort the edges to find the leftmost
int step = 1;
int end = nextSpan(firstT, step);
if (end == -1) {
step = -1;
end = nextSpan(firstT, step);
SkASSERT(end != -1);
}
// if the topmost T is not on end, or is three-way or more, find left
// look for left-ness from tLeft to firstT (matching y of other)
SkTDArray<Angle> angles;
SkASSERT(firstT - end != 0);
addTwoAngles(end, firstT, angles);
buildAngles(firstT, angles);
SkTDArray<Angle*> sorted;
sortAngles(angles, sorted);
// skip edges that have already been processed
firstT = -1;
Segment* leftSegment;
do {
const Angle* angle = sorted[++firstT];
leftSegment = angle->segment();
tIndex = angle->end();
endIndex = angle->start();
} while (leftSegment->fTs[SkMin32(tIndex, endIndex)].fDone);
return leftSegment;
}
// FIXME: not crazy about this
// when the intersections are performed, the other index is into an
// incomplete array. as the array grows, the indices become incorrect
// while the following fixes the indices up again, it isn't smart about
// skipping segments whose indices are already correct
// assuming we leave the code that wrote the index in the first place
void fixOtherTIndex() {
int iCount = fTs.count();
for (int i = 0; i < iCount; ++i) {
Span& iSpan = fTs[i];
double oT = iSpan.fOtherT;
Segment* other = iSpan.fOther;
int oCount = other->fTs.count();
for (int o = 0; o < oCount; ++o) {
Span& oSpan = other->fTs[o];
if (oT == oSpan.fT && this == oSpan.fOther) {
iSpan.fOtherIndex = o;
break;
}
}
}
}
// OPTIMIZATION: uses tail recursion. Unwise?
void innerChaseDone(int index, int step, int winding) {
int end = nextSpan(index, step);
if (multipleSpans(end, step)) {
return;
}
const Span& endSpan = fTs[end];
Segment* other = endSpan.fOther;
index = endSpan.fOtherIndex;
int otherEnd = other->nextSpan(index, step);
other->innerChaseDone(index, step, winding);
other->markDone(SkMin32(index, otherEnd), winding);
}
void innerChaseWinding(int index, int step, int winding) {
int end = nextSpan(index, step);
if (multipleSpans(end, step)) {
return;
}
const Span& endSpan = fTs[end];
Segment* other = endSpan.fOther;
index = endSpan.fOtherIndex;
int otherEnd = other->nextSpan(index, step);
int min = SkMin32(index, otherEnd);
if (other->fTs[min].fWindSum != SK_MinS32) {
SkASSERT(other->fTs[index].fWindSum == winding);
return;
}
other->innerChaseWinding(index, step, winding);
other->markWinding(min, winding);
}
void init(const SkPoint pts[], SkPath::Verb verb) {
fPts = pts;
fVerb = verb;
fDoneSpans = 0;
}
bool intersected() const {
return fTs.count() > 0;
}
bool isLinear(int start, int end) const {
if (fVerb == SkPath::kLine_Verb) {
return true;
}
if (fVerb == SkPath::kQuad_Verb) {
SkPoint qPart[3];
QuadSubDivide(fPts, fTs[start].fT, fTs[end].fT, qPart);
return QuadIsLinear(qPart);
} else {
SkASSERT(fVerb == SkPath::kCubic_Verb);
SkPoint cPart[4];
CubicSubDivide(fPts, fTs[start].fT, fTs[end].fT, cPart);
return CubicIsLinear(cPart);
}
}
// OPTIMIZE: successive calls could start were the last leaves off
// or calls could specialize to walk forwards or backwards
bool isMissing(double startT) const {
size_t tCount = fTs.count();
for (size_t index = 0; index < tCount; ++index) {
if (fabs(startT - fTs[index].fT) < FLT_EPSILON) {
return false;
}
}
return true;
}
bool isSimple(int end) const {
int count = fTs.count();
if (count == 2) {
return true;
}
double t = fTs[end].fT;
if (t < FLT_EPSILON) {
return fTs[1].fT >= FLT_EPSILON;
}
if (t > 1 - FLT_EPSILON) {
return fTs[count - 2].fT <= 1 - FLT_EPSILON;
}
return false;
}
bool isHorizontal() const {
return fBounds.fTop == fBounds.fBottom;
}
bool isVertical() const {
return fBounds.fLeft == fBounds.fRight;
}
SkScalar leftMost(int start, int end) const {
return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
}
// this span is excluded by the winding rule -- chase the ends
// as long as they are unambiguous to mark connections as done
// and give them the same winding value
void markAndChaseDone(const Angle* angle, int winding) {
int index = angle->start();
int endIndex = angle->end();
int step = SkSign32(endIndex - index);
innerChaseDone(index, step, winding);
markDone(SkMin32(index, endIndex), winding);
}
void markAndChaseWinding(const Angle* angle, int winding) {
int index = angle->start();
int endIndex = angle->end();
int min = SkMin32(index, endIndex);
int step = SkSign32(endIndex - index);
innerChaseWinding(index, step, winding);
markWinding(min, winding);
}
// FIXME: this should also mark spans with equal (x,y)
// This may be called when the segment is already marked done. While this
// wastes time, it shouldn't do any more than spin through the T spans.
// OPTIMIZATION: abort on first done found (assuming that this code is
// always called to mark segments done).
void markDone(int index, int winding) {
// SkASSERT(!done());
double referenceT = fTs[index].fT;
int lesser = index;
while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
Span& span = fTs[lesser];
if (span.fDone) {
continue;
}
#if DEBUG_MARK_DONE
const SkPoint& pt = xyAtT(&span);
SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
__FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
#endif
span.fDone = true;
SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
span.fWindSum = winding;
fDoneSpans++;
}
do {
Span& span = fTs[index];
// SkASSERT(!span.fDone);
if (span.fDone) {
continue;
}
#if DEBUG_MARK_DONE
const SkPoint& pt = xyAtT(&span);
SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
__FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
#endif
span.fDone = true;
SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
span.fWindSum = winding;
fDoneSpans++;
} while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
}
void markWinding(int index, int winding) {
SkASSERT(!done());
double referenceT = fTs[index].fT;
int lesser = index;
while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
Span& span = fTs[lesser];
if (span.fDone) {
continue;
}
SkASSERT(span.fWindValue == 1 || winding == 0);
SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
#if DEBUG_MARK_DONE
const SkPoint& pt = xyAtT(&span);
SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
__FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
#endif
span.fWindSum = winding;
}
do {
Span& span = fTs[index];
// SkASSERT(!span.fDone || span.fCoincident);
if (span.fDone) {
continue;
}
SkASSERT(span.fWindValue == 1 || winding == 0);
SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
#if DEBUG_MARK_DONE
const SkPoint& pt = xyAtT(&span);
SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
__FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
#endif
span.fWindSum = winding;
} while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
}
bool multipleSpans(int end, int step) const {
return step > 0 ? ++end < fTs.count() : end > 0;
}
// This has callers for two different situations: one establishes the end
// of the current span, and one establishes the beginning of the next span
// (thus the name). When this is looking for the end of the current span,
// coincidence is found when the beginning Ts contain -step and the end
// contains step. When it is looking for the beginning of the next, the
// first Ts found can be ignored and the last Ts should contain -step.
// OPTIMIZATION: probably should split into two functions
int nextSpan(int from, int step) const {
const Span& fromSpan = fTs[from];
int count = fTs.count();
int to = from;
while (step > 0 ? ++to < count : --to >= 0) {
const Span& span = fTs[to];
if ((step > 0 ? span.fT - fromSpan.fT : fromSpan.fT - span.fT) < FLT_EPSILON) {
continue;
}
return to;
}
return -1;
}
const SkPoint* pts() const {
return fPts;
}
void reset() {
init(NULL, (SkPath::Verb) -1);
fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
fTs.reset();
}
// OPTIMIZATION: mark as debugging only if used solely by tests
const Span& span(int tIndex) const {
return fTs[tIndex];
}
int spanSign(int startIndex, int endIndex) const {
return startIndex < endIndex ? -fTs[startIndex].fWindValue :
fTs[endIndex].fWindValue;
}
// OPTIMIZATION: mark as debugging only if used solely by tests
double t(int tIndex) const {
return fTs[tIndex].fT;
}
void updatePts(const SkPoint pts[]) {
fPts = pts;
}
SkPath::Verb verb() const {
return fVerb;
}
// if the only remaining spans are small, ignore them, and mark done
bool virtuallyDone() {
int count = fTs.count();
double previous = 0;
bool previousDone = fTs[0].fDone;
for (int index = 1; index < count; ++index) {
Span& span = fTs[index];
double t = span.fT;
if (t - previous < FLT_EPSILON) {
if (span.fDone && !previousDone) {
int prior = --index;
int winding = span.fWindSum;
do {
Span& priorSpan = fTs[prior];
priorSpan.fDone = true;
priorSpan.fWindSum = winding;
fDoneSpans++;
} while (--prior >= 0 && t - fTs[prior].fT < FLT_EPSILON);
}
} else if (!previousDone) {
return false;
}
previous = t;
previousDone = span.fDone;
}
SkASSERT(done());
return true;
}
int winding(int tIndex) const {
return fTs[tIndex].fWindSum;
}
int winding(const Angle* angle) const {
int start = angle->start();
int end = angle->end();
int index = SkMin32(start, end);
return winding(index);
}
int windValue(int tIndex) const {
return fTs[tIndex].fWindValue;
}
int windValue(const Angle* angle) const {
int start = angle->start();
int end = angle->end();
int index = SkMin32(start, end);
return windValue(index);
}
SkScalar xAtT(const Span* span) const {
return xyAtT(span).fX;
}
const SkPoint& xyAtT(int index) const {
return xyAtT(&fTs[index]);
}
const SkPoint& xyAtT(const Span* span) const {
if (!span->fPt) {
if (span->fT == 0) {
span->fPt = &fPts[0];
} else if (span->fT == 1) {
span->fPt = &fPts[fVerb];
} else {
SkPoint* pt = fIntersections.append();
(*SegmentXYAtT[fVerb])(fPts, span->fT, pt);
span->fPt = pt;
}
}
return *span->fPt;
}
SkScalar yAtT(int index) const {
return yAtT(&fTs[index]);
}
SkScalar yAtT(const Span* span) const {
return xyAtT(span).fY;
}
#if DEBUG_DUMP
void dump() const {
const char className[] = "Segment";
const int tab = 4;
for (int i = 0; i < fTs.count(); ++i) {
SkPoint out;
(*SegmentXYAtT[fVerb])(fPts, t(i), &out);
SkDebugf("%*s [%d] %s.fTs[%d]=%1.9g (%1.9g,%1.9g) other=%d"
" otherT=%1.9g windSum=%d\n",
tab + sizeof(className), className, fID,
kLVerbStr[fVerb], i, fTs[i].fT, out.fX, out.fY,
fTs[i].fOther->fID, fTs[i].fOtherT, fTs[i].fWindSum);
}
SkDebugf("%*s [%d] fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)",
tab + sizeof(className), className, fID,
fBounds.fLeft, fBounds.fTop, fBounds.fRight, fBounds.fBottom);
}
#endif
private:
const SkPoint* fPts;
SkPath::Verb fVerb;
Bounds fBounds;
SkTDArray<Span> fTs; // two or more (always includes t=0 t=1)
// OPTIMIZATION:if intersections array is a pointer, the it could only
// be allocated as needed instead of always initialized -- though maybe
// the initialization is lightweight enough that it hardly matters
mutable SkTDArray<SkPoint> fIntersections;
int fDoneSpans; // used for quick check that segment is finished
#if DEBUG_DUMP
int fID;
#endif
};
class Contour;
struct Coincidence {
Contour* fContours[2];
int fSegments[2];
double fTs[2][2];
};
class Contour {
public:
Contour() {
reset();
#if DEBUG_DUMP
fID = ++gContourID;
#endif
}
bool operator<(const Contour& rh) const {
return fBounds.fTop == rh.fBounds.fTop
? fBounds.fLeft < rh.fBounds.fLeft
: fBounds.fTop < rh.fBounds.fTop;
}
void addCoincident(int index, Contour* other, int otherIndex,
const Intersections& ts, bool swap) {
Coincidence& coincidence = *fCoincidences.append();
coincidence.fContours[0] = this;
coincidence.fContours[1] = other;
coincidence.fSegments[0] = index;
coincidence.fSegments[1] = otherIndex;
coincidence.fTs[swap][0] = ts.fT[0][0];
coincidence.fTs[swap][1] = ts.fT[0][1];
coincidence.fTs[!swap][0] = ts.fT[1][0];
coincidence.fTs[!swap][1] = ts.fT[1][1];
}
void addCross(const Contour* crosser) {
#ifdef DEBUG_CROSS
for (int index = 0; index < fCrosses.count(); ++index) {
SkASSERT(fCrosses[index] != crosser);
}
#endif
*fCrosses.append() = crosser;
}
void addCubic(const SkPoint pts[4]) {
fSegments.push_back().addCubic(pts);
fContainsCurves = true;
}
int addLine(const SkPoint pts[2]) {
fSegments.push_back().addLine(pts);
return fSegments.count();
}
void addOtherT(int segIndex, int tIndex, double otherT, int otherIndex) {
fSegments[segIndex].addOtherT(tIndex, otherT, otherIndex);
}
int addQuad(const SkPoint pts[3]) {
fSegments.push_back().addQuad(pts);
fContainsCurves = true;
return fSegments.count();
}
int addT(int segIndex, double newT, Contour* other, int otherIndex) {
containsIntercepts();
return fSegments[segIndex].addT(newT, &other->fSegments[otherIndex]);
}
const Bounds& bounds() const {
return fBounds;
}
void complete() {
setBounds();
fContainsIntercepts = false;
}
void containsIntercepts() {
fContainsIntercepts = true;
}
const Segment* crossedSegment(const SkPoint& basePt, SkScalar& bestY,
int &tIndex, double& hitT) {
int segmentCount = fSegments.count();
const Segment* bestSegment = NULL;
for (int test = 0; test < segmentCount; ++test) {
Segment* testSegment = &fSegments[test];
const SkRect& bounds = testSegment->bounds();
if (bounds.fTop < bestY) {
continue;
}
if (bounds.fTop > basePt.fY) {
continue;
}
if (bounds.fLeft > basePt.fX) {
continue;
}
if (bounds.fRight < basePt.fX) {
continue;
}
double testHitT;
int testT = testSegment->crossedSpan(basePt, bestY, testHitT);
if (testT >= 0) {
bestSegment = testSegment;
tIndex = testT;
hitT = testHitT;
}
}
return bestSegment;
}
bool crosses(const Contour* crosser) const {
if (this == crosser) {
return true;
}
for (int index = 0; index < fCrosses.count(); ++index) {
if (fCrosses[index] == crosser) {
return true;
}
}
return false;
}
void findTooCloseToCall(int winding) {
int segmentCount = fSegments.count();
for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
fSegments[sIndex].findTooCloseToCall(winding);
}
}
void fixOtherTIndex() {
int segmentCount = fSegments.count();
for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
fSegments[sIndex].fixOtherTIndex();
}
}
void reset() {
fSegments.reset();
fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
fContainsCurves = fContainsIntercepts = false;
fWindingSum = SK_MinS32;
}
void resolveCoincidence(int winding) {
int count = fCoincidences.count();
for (int index = 0; index < count; ++index) {
Coincidence& coincidence = fCoincidences[index];
Contour* thisContour = coincidence.fContours[0];
Contour* otherContour = coincidence.fContours[1];
int thisIndex = coincidence.fSegments[0];
int otherIndex = coincidence.fSegments[1];
Segment& thisOne = thisContour->fSegments[thisIndex];
Segment& other = otherContour->fSegments[otherIndex];
double startT = coincidence.fTs[0][0];
double endT = coincidence.fTs[0][1];
if (startT > endT) {
SkTSwap<double>(startT, endT);
}
SkASSERT(endT - startT >= FLT_EPSILON);
double oStartT = coincidence.fTs[1][0];
double oEndT = coincidence.fTs[1][1];
if (oStartT > oEndT) {
SkTSwap<double>(oStartT, oEndT);
}
SkASSERT(oEndT - oStartT >= FLT_EPSILON);
if (winding > 0 || thisOne.cancels(other)) {
// make sure startT and endT have t entries
if (thisOne.isMissing(startT) || other.isMissing(oEndT)) {
thisOne.addTPair(startT, other, oEndT);
}
if (thisOne.isMissing(endT) || other.isMissing(oStartT)) {
other.addTPair(oStartT, thisOne, endT);
}
thisOne.addTCancel(startT, endT, other, oStartT, oEndT);
} else {
if (thisOne.isMissing(startT) || other.isMissing(oStartT)) {
thisOne.addTPair(startT, other, oStartT);
}
if (thisOne.isMissing(endT) || other.isMissing(oEndT)) {
other.addTPair(oEndT, thisOne, endT);
}
thisOne.addTCoincident(startT, endT, other, oStartT, oEndT);
}
}
}
const SkTArray<Segment>& segments() {
return fSegments;
}
void setWinding(int winding) {
SkASSERT(fWindingSum < 0);
fWindingSum = winding;
}
// OPTIMIZATION: feel pretty uneasy about this. It seems like once again
// we need to sort and walk edges in y, but that on the surface opens the
// same can of worms as before. But then, this is a rough sort based on
// segments' top, and not a true sort, so it could be ameniable to regular
// sorting instead of linear searching. Still feel like I'm missing something
Segment* topSegment(SkScalar& bestY) {
int segmentCount = fSegments.count();
SkASSERT(segmentCount > 0);
int best = -1;
Segment* bestSegment = NULL;
while (++best < segmentCount) {
Segment* testSegment = &fSegments[best];
#if 0 // FIXME: remove if not needed
if (testSegment->virtuallyDone()) {
continue;
}
#else
if (testSegment->done()) {
continue;
}
#endif
bestSegment = testSegment;
break;
}
if (!bestSegment) {
return NULL;
}
SkScalar bestTop = bestSegment->activeTop();
for (int test = best + 1; test < segmentCount; ++test) {
Segment* testSegment = &fSegments[test];
if (testSegment->done()) {
continue;
}
if (testSegment->bounds().fTop > bestTop) {
continue;
}
SkScalar testTop = testSegment->activeTop();
if (bestTop > testTop) {
bestTop = testTop;
bestSegment = testSegment;
}
}
bestY = bestTop;
return bestSegment;
}
int updateSegment(int index, const SkPoint* pts) {
Segment& segment = fSegments[index];
segment.updatePts(pts);
return segment.verb() + 1;
}
int winding() {
if (fWindingSum >= 0) {
return fWindingSum;
}
// check peers
int count = fCrosses.count();
for (int index = 0; index < count; ++index) {
const Contour* crosser = fCrosses[index];
if (0 <= crosser->fWindingSum) {
fWindingSum = crosser->fWindingSum;
break;
}
}
return fWindingSum;
}
#if DEBUG_TEST
SkTArray<Segment>& debugSegments() {
return fSegments;
}
#endif
#if DEBUG_DUMP
void dump() {
int i;
const char className[] = "Contour";
const int tab = 4;
SkDebugf("%s %p (contour=%d)\n", className, this, fID);
for (i = 0; i < fSegments.count(); ++i) {
SkDebugf("%*s.fSegments[%d]:\n", tab + sizeof(className),
className, i);
fSegments[i].dump();
}
SkDebugf("%*s.fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)\n",
tab + sizeof(className), className,
fBounds.fLeft, fBounds.fTop,
fBounds.fRight, fBounds.fBottom);
SkDebugf("%*s.fContainsIntercepts=%d\n", tab + sizeof(className),
className, fContainsIntercepts);
SkDebugf("%*s.fContainsCurves=%d\n", tab + sizeof(className),
className, fContainsCurves);
}
#endif
protected:
void setBounds() {
int count = fSegments.count();
if (count == 0) {
SkDebugf("%s empty contour\n", __FUNCTION__);
SkASSERT(0);
// FIXME: delete empty contour?
return;
}
fBounds = fSegments.front().bounds();
for (int index = 1; index < count; ++index) {
fBounds.add(fSegments[index].bounds());
}
}
private:
SkTArray<Segment> fSegments;
SkTDArray<Coincidence> fCoincidences;
SkTDArray<const Contour*> fCrosses;
Bounds fBounds;
bool fContainsIntercepts;
bool fContainsCurves;
int fWindingSum; // initial winding number outside
#if DEBUG_DUMP
int fID;
#endif
};
class EdgeBuilder {
public:
EdgeBuilder(const SkPath& path, SkTArray<Contour>& contours)
: fPath(path)
, fCurrentContour(NULL)
, fContours(contours)
{
#if DEBUG_DUMP
gContourID = 0;
gSegmentID = 0;
#endif
walk();
}
protected:
void complete() {
if (fCurrentContour && fCurrentContour->segments().count()) {
fCurrentContour->complete();
fCurrentContour = NULL;
}
}
void walk() {
// FIXME:remove once we can access path pts directly
SkPath::RawIter iter(fPath); // FIXME: access path directly when allowed
SkPoint pts[4];
SkPath::Verb verb;
do {
verb = iter.next(pts);
*fPathVerbs.append() = verb;
if (verb == SkPath::kMove_Verb) {
*fPathPts.append() = pts[0];
} else if (verb >= SkPath::kLine_Verb && verb <= SkPath::kCubic_Verb) {
fPathPts.append(verb, &pts[1]);
}
} while (verb != SkPath::kDone_Verb);
// FIXME: end of section to remove once path pts are accessed directly
SkPath::Verb reducedVerb;
uint8_t* verbPtr = fPathVerbs.begin();
const SkPoint* pointsPtr = fPathPts.begin();
const SkPoint* finalCurveStart = NULL;
const SkPoint* finalCurveEnd = NULL;
while ((verb = (SkPath::Verb) *verbPtr++) != SkPath::kDone_Verb) {
switch (verb) {
case SkPath::kMove_Verb:
complete();
if (!fCurrentContour) {
fCurrentContour = fContours.push_back_n(1);
finalCurveEnd = pointsPtr++;
*fExtra.append() = -1; // start new contour
}
continue;
case SkPath::kLine_Verb:
// skip degenerate points
if (pointsPtr[-1].fX != pointsPtr[0].fX
|| pointsPtr[-1].fY != pointsPtr[0].fY) {
fCurrentContour->addLine(&pointsPtr[-1]);
}
break;
case SkPath::kQuad_Verb:
reducedVerb = QuadReduceOrder(&pointsPtr[-1], fReducePts);
if (reducedVerb == 0) {
break; // skip degenerate points
}
if (reducedVerb == 1) {
*fExtra.append() =
fCurrentContour->addLine(fReducePts.end() - 2);
break;
}
fCurrentContour->addQuad(&pointsPtr[-1]);
break;
case SkPath::kCubic_Verb:
reducedVerb = CubicReduceOrder(&pointsPtr[-1], fReducePts);
if (reducedVerb == 0) {
break; // skip degenerate points
}
if (reducedVerb == 1) {
*fExtra.append() =
fCurrentContour->addLine(fReducePts.end() - 2);
break;
}
if (reducedVerb == 2) {
*fExtra.append() =
fCurrentContour->addQuad(fReducePts.end() - 3);
break;
}
fCurrentContour->addCubic(&pointsPtr[-1]);
break;
case SkPath::kClose_Verb:
SkASSERT(fCurrentContour);
if (finalCurveStart && finalCurveEnd
&& *finalCurveStart != *finalCurveEnd) {
*fReducePts.append() = *finalCurveStart;
*fReducePts.append() = *finalCurveEnd;
*fExtra.append() =
fCurrentContour->addLine(fReducePts.end() - 2);
}
complete();
continue;
default:
SkDEBUGFAIL("bad verb");
return;
}
finalCurveStart = &pointsPtr[verb - 1];
pointsPtr += verb;
SkASSERT(fCurrentContour);
}
complete();
if (fCurrentContour && !fCurrentContour->segments().count()) {
fContours.pop_back();
}
// correct pointers in contours since fReducePts may have moved as it grew
int cIndex = 0;
int extraCount = fExtra.count();
SkASSERT(extraCount == 0 || fExtra[0] == -1);
int eIndex = 0;
int rIndex = 0;
while (++eIndex < extraCount) {
int offset = fExtra[eIndex];
if (offset < 0) {
++cIndex;
continue;
}
fCurrentContour = &fContours[cIndex];
rIndex += fCurrentContour->updateSegment(offset - 1,
&fReducePts[rIndex]);
}
fExtra.reset(); // we're done with this
}
private:
const SkPath& fPath;
SkTDArray<SkPoint> fPathPts; // FIXME: point directly to path pts instead
SkTDArray<uint8_t> fPathVerbs; // FIXME: remove
Contour* fCurrentContour;
SkTArray<Contour>& fContours;
SkTDArray<SkPoint> fReducePts; // segments created on the fly
SkTDArray<int> fExtra; // -1 marks new contour, > 0 offsets into contour
};
class Work {
public:
enum SegmentType {
kHorizontalLine_Segment = -1,
kVerticalLine_Segment = 0,
kLine_Segment = SkPath::kLine_Verb,
kQuad_Segment = SkPath::kQuad_Verb,
kCubic_Segment = SkPath::kCubic_Verb,
};
void addCoincident(Work& other, const Intersections& ts, bool swap) {
fContour->addCoincident(fIndex, other.fContour, other.fIndex, ts, swap);
}
// FIXME: does it make sense to write otherIndex now if we're going to
// fix it up later?
void addOtherT(int index, double otherT, int otherIndex) {
fContour->addOtherT(fIndex, index, otherT, otherIndex);
}
// Avoid collapsing t values that are close to the same since
// we walk ts to describe consecutive intersections. Since a pair of ts can
// be nearly equal, any problems caused by this should be taken care
// of later.
// On the edge or out of range values are negative; add 2 to get end
int addT(double newT, const Work& other) {
return fContour->addT(fIndex, newT, other.fContour, other.fIndex);
}
bool advance() {
return ++fIndex < fLast;
}
SkScalar bottom() const {
return bounds().fBottom;
}
const Bounds& bounds() const {
return fContour->segments()[fIndex].bounds();
}
const SkPoint* cubic() const {
return fCubic;
}
void init(Contour* contour) {
fContour = contour;
fIndex = 0;
fLast = contour->segments().count();
}
bool isAdjacent(const Work& next) {
return fContour == next.fContour && fIndex + 1 == next.fIndex;
}
bool isFirstLast(const Work& next) {
return fContour == next.fContour && fIndex == 0
&& next.fIndex == fLast - 1;
}
SkScalar left() const {
return bounds().fLeft;
}
void promoteToCubic() {
fCubic[0] = pts()[0];
fCubic[2] = pts()[1];
fCubic[3] = pts()[2];
fCubic[1].fX = (fCubic[0].fX + fCubic[2].fX * 2) / 3;
fCubic[1].fY = (fCubic[0].fY + fCubic[2].fY * 2) / 3;
fCubic[2].fX = (fCubic[3].fX + fCubic[2].fX * 2) / 3;
fCubic[2].fY = (fCubic[3].fY + fCubic[2].fY * 2) / 3;
}
const SkPoint* pts() const {
return fContour->segments()[fIndex].pts();
}
SkScalar right() const {
return bounds().fRight;
}
ptrdiff_t segmentIndex() const {
return fIndex;
}
SegmentType segmentType() const {
const Segment& segment = fContour->segments()[fIndex];
SegmentType type = (SegmentType) segment.verb();
if (type != kLine_Segment) {
return type;
}
if (segment.isHorizontal()) {
return kHorizontalLine_Segment;
}
if (segment.isVertical()) {
return kVerticalLine_Segment;
}
return kLine_Segment;
}
bool startAfter(const Work& after) {
fIndex = after.fIndex;
return advance();
}
SkScalar top() const {
return bounds().fTop;
}
SkPath::Verb verb() const {
return fContour->segments()[fIndex].verb();
}
SkScalar x() const {
return bounds().fLeft;
}
bool xFlipped() const {
return x() != pts()[0].fX;
}
SkScalar y() const {
return bounds().fTop;
}
bool yFlipped() const {
return y() != pts()[0].fY;
}
protected:
Contour* fContour;
SkPoint fCubic[4];
int fIndex;
int fLast;
};
#if DEBUG_ADD_INTERSECTING_TS
static void debugShowLineIntersection(int pts, const Work& wt,
const Work& wn, const double wtTs[2], const double wnTs[2]) {
if (!pts) {
SkDebugf("%s no intersect (%1.9g,%1.9g %1.9g,%1.9g) (%1.9g,%1.9g %1.9g,%1.9g)\n",
__FUNCTION__, wt.pts()[0].fX, wt.pts()[0].fY,
wt.pts()[1].fX, wt.pts()[1].fY, wn.pts()[0].fX, wn.pts()[0].fY,
wn.pts()[1].fX, wn.pts()[1].fY);
return;
}
SkPoint wtOutPt, wnOutPt;
LineXYAtT(wt.pts(), wtTs[0], &wtOutPt);
LineXYAtT(wn.pts(), wnTs[0], &wnOutPt);
SkDebugf("%s wtTs[0]=%g (%g,%g, %g,%g) (%g,%g)",
__FUNCTION__,
wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY,
wt.pts()[1].fX, wt.pts()[1].fY, wtOutPt.fX, wtOutPt.fY);
if (pts == 2) {
SkDebugf(" wtTs[1]=%g", wtTs[1]);
}
SkDebugf(" wnTs[0]=%g (%g,%g, %g,%g) (%g,%g)",
wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY,
wn.pts()[1].fX, wn.pts()[1].fY, wnOutPt.fX, wnOutPt.fY);
if (pts == 2) {
SkDebugf(" wnTs[1]=%g", wnTs[1]);
}
SkDebugf("\n");
}
#else
static void debugShowLineIntersection(int , const Work& ,
const Work& , const double [2], const double [2]) {
}
#endif
static bool addIntersectTs(Contour* test, Contour* next) {
if (test != next) {
if (test->bounds().fBottom < next->bounds().fTop) {
return false;
}
if (!Bounds::Intersects(test->bounds(), next->bounds())) {
return true;
}
}
Work wt;
wt.init(test);
bool foundCommonContour = test == next;
do {
Work wn;
wn.init(next);
if (test == next && !wn.startAfter(wt)) {
continue;
}
do {
if (!Bounds::Intersects(wt.bounds(), wn.bounds())) {
continue;
}
int pts;
Intersections ts;
bool swap = false;
switch (wt.segmentType()) {
case Work::kHorizontalLine_Segment:
swap = true;
switch (wn.segmentType()) {
case Work::kHorizontalLine_Segment:
case Work::kVerticalLine_Segment:
case Work::kLine_Segment: {
pts = HLineIntersect(wn.pts(), wt.left(),
wt.right(), wt.y(), wt.xFlipped(), ts);
debugShowLineIntersection(pts, wt, wn,
ts.fT[1], ts.fT[0]);
break;
}
case Work::kQuad_Segment: {
pts = HQuadIntersect(wn.pts(), wt.left(),
wt.right(), wt.y(), wt.xFlipped(), ts);
break;
}
case Work::kCubic_Segment: {
pts = HCubicIntersect(wn.pts(), wt.left(),
wt.right(), wt.y(), wt.xFlipped(), ts);
break;
}
default:
SkASSERT(0);
}
break;
case Work::kVerticalLine_Segment:
swap = true;
switch (wn.segmentType()) {
case Work::kHorizontalLine_Segment:
case Work::kVerticalLine_Segment:
case Work::kLine_Segment: {
pts = VLineIntersect(wn.pts(), wt.top(),
wt.bottom(), wt.x(), wt.yFlipped(), ts);
debugShowLineIntersection(pts, wt, wn,
ts.fT[1], ts.fT[0]);
break;
}
case Work::kQuad_Segment: {
pts = VQuadIntersect(wn.pts(), wt.top(),
wt.bottom(), wt.x(), wt.yFlipped(), ts);
break;
}
case Work::kCubic_Segment: {
pts = VCubicIntersect(wn.pts(), wt.top(),
wt.bottom(), wt.x(), wt.yFlipped(), ts);
break;
}
default:
SkASSERT(0);
}
break;
case Work::kLine_Segment:
switch (wn.segmentType()) {
case Work::kHorizontalLine_Segment:
pts = HLineIntersect(wt.pts(), wn.left(),
wn.right(), wn.y(), wn.xFlipped(), ts);
debugShowLineIntersection(pts, wt, wn,
ts.fT[1], ts.fT[0]);
break;
case Work::kVerticalLine_Segment:
pts = VLineIntersect(wt.pts(), wn.top(),
wn.bottom(), wn.x(), wn.yFlipped(), ts);
debugShowLineIntersection(pts, wt, wn,
ts.fT[1], ts.fT[0]);
break;
case Work::kLine_Segment: {
pts = LineIntersect(wt.pts(), wn.pts(), ts);
debugShowLineIntersection(pts, wt, wn,
ts.fT[1], ts.fT[0]);
break;
}
case Work::kQuad_Segment: {
swap = true;
pts = QuadLineIntersect(wn.pts(), wt.pts(), ts);
break;
}
case Work::kCubic_Segment: {
swap = true;
pts = CubicLineIntersect(wn.pts(), wt.pts(), ts);
break;
}
default:
SkASSERT(0);
}
break;
case Work::kQuad_Segment:
switch (wn.segmentType()) {
case Work::kHorizontalLine_Segment:
pts = HQuadIntersect(wt.pts(), wn.left(),
wn.right(), wn.y(), wn.xFlipped(), ts);
break;
case Work::kVerticalLine_Segment:
pts = VQuadIntersect(wt.pts(), wn.top(),
wn.bottom(), wn.x(), wn.yFlipped(), ts);
break;
case Work::kLine_Segment: {
pts = QuadLineIntersect(wt.pts(), wn.pts(), ts);
break;
}
case Work::kQuad_Segment: {
pts = QuadIntersect(wt.pts(), wn.pts(), ts);
break;
}
case Work::kCubic_Segment: {
wt.promoteToCubic();
pts = CubicIntersect(wt.cubic(), wn.pts(), ts);
break;
}
default:
SkASSERT(0);
}
break;
case Work::kCubic_Segment:
switch (wn.segmentType()) {
case Work::kHorizontalLine_Segment:
pts = HCubicIntersect(wt.pts(), wn.left(),
wn.right(), wn.y(), wn.xFlipped(), ts);
break;
case Work::kVerticalLine_Segment:
pts = VCubicIntersect(wt.pts(), wn.top(),
wn.bottom(), wn.x(), wn.yFlipped(), ts);
break;
case Work::kLine_Segment: {
pts = CubicLineIntersect(wt.pts(), wn.pts(), ts);
break;
}
case Work::kQuad_Segment: {
wn.promoteToCubic();
pts = CubicIntersect(wt.pts(), wn.cubic(), ts);
break;
}
case Work::kCubic_Segment: {
pts = CubicIntersect(wt.pts(), wn.pts(), ts);
break;
}
default:
SkASSERT(0);
}
break;
default:
SkASSERT(0);
}
if (!foundCommonContour && pts > 0) {
test->addCross(next);
next->addCross(test);
foundCommonContour = true;
}
// in addition to recording T values, record matching segment
if (pts == 2 && wn.segmentType() <= Work::kLine_Segment
&& wt.segmentType() <= Work::kLine_Segment) {
wt.addCoincident(wn, ts, swap);
continue;
}
for (int pt = 0; pt < pts; ++pt) {
SkASSERT(ts.fT[0][pt] >= 0 && ts.fT[0][pt] <= 1);
SkASSERT(ts.fT[1][pt] >= 0 && ts.fT[1][pt] <= 1);
int testTAt = wt.addT(ts.fT[swap][pt], wn);
int nextTAt = wn.addT(ts.fT[!swap][pt], wt);
wt.addOtherT(testTAt, ts.fT[!swap][pt], nextTAt);
wn.addOtherT(nextTAt, ts.fT[swap][pt], testTAt);
}
} while (wn.advance());
} while (wt.advance());
return true;
}
// resolve any coincident pairs found while intersecting, and
// see if coincidence is formed by clipping non-concident segments
static void coincidenceCheck(SkTDArray<Contour*>& contourList, int winding) {
int contourCount = contourList.count();
for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
Contour* contour = contourList[cIndex];
contour->resolveCoincidence(winding);
}
for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
Contour* contour = contourList[cIndex];
contour->findTooCloseToCall(winding);
}
}
// project a ray from the top of the contour up and see if it hits anything
// note: when we compute line intersections, we keep track of whether
// two contours touch, so we need only look at contours not touching this one.
// OPTIMIZATION: sort contourList vertically to avoid linear walk
static int innerContourCheck(SkTDArray<Contour*>& contourList,
Contour* baseContour, const SkPoint& basePt) {
int contourCount = contourList.count();
int winding = 0;
SkScalar bestY = SK_ScalarMin;
for (int cTest = 0; cTest < contourCount; ++cTest) {
Contour* contour = contourList[cTest];
if (basePt.fY < contour->bounds().fTop) {
continue;
}
if (bestY > contour->bounds().fBottom) {
continue;
}
if (baseContour->crosses(contour)) {
continue;
}
int tIndex;
double tHit;
const Segment* test = contour->crossedSegment(basePt, bestY, tIndex,
tHit);
if (!test) {
continue;
}
// If the ray hit the end of a span, we need to construct the wheel of
// angles to find the span closest to the ray -- even if there are just
// two spokes on the wheel.
if (tHit == test->t(tIndex)) {
SkTDArray<Angle> angles;
int end = test->nextSpan(tIndex, 1);
if (end < 0) {
end = test->nextSpan(tIndex, -1);
}
test->addTwoAngles(tIndex, end, angles);
// test->buildAnglesInner(tIndex, angles);
test->buildAngles(tIndex, angles);
SkTDArray<Angle*> sorted;
sortAngles(angles, sorted);
const Angle* angle = sorted[0];
test = angle->segment();
SkScalar testDx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
if (testDx == 0) {
angle = *(sorted.end() - 1);
test = angle->segment();
SkASSERT((*SegmentDXAtT[test->verb()])(test->pts(), tHit) != 0);
}
tIndex = angle->start(); // lesser Y
winding = test->winding(SkMin32(tIndex, angle->end()));
#if DEBUG_WINDING
SkDebugf("%s 1 winding=%d\n", __FUNCTION__, winding);
#endif
} else {
winding = test->winding(tIndex);
#if DEBUG_WINDING
SkDebugf("%s 2 winding=%d\n", __FUNCTION__, winding);
#endif
}
// see if a + change in T results in a +/- change in X (compute x'(T))
SkScalar dx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
#if DEBUG_WINDING
SkDebugf("%s dx=%1.9g\n", __FUNCTION__, dx);
#endif
SkASSERT(dx != 0);
if (winding * dx > 0) { // if same signs, result is negative
winding += dx > 0 ? -1 : 1;
#if DEBUG_WINDING
SkDebugf("%s 3 winding=%d\n", __FUNCTION__, winding);
#endif
}
}
baseContour->setWinding(winding);
return winding;
}
// OPTIMIZATION: not crazy about linear search here to find top active y.
// seems like we should break down and do the sort, or maybe sort each
// contours' segments?
// Once the segment array is built, there's no reason I can think of not to
// sort it in Y. hmmm
// FIXME: return the contour found to pass to inner contour check
static Segment* findTopContour(SkTDArray<Contour*>& contourList,
Contour*& topContour) {
int contourCount = contourList.count();
int cIndex = 0;
Segment* topStart;
SkScalar bestY = SK_ScalarMax;
Contour* contour;
do {
contour = contourList[cIndex];
topStart = contour->topSegment(bestY);
} while (!topStart && ++cIndex < contourCount);
if (!topStart) {
return NULL;
}
topContour = contour;
while (++cIndex < contourCount) {
contour = contourList[cIndex];
if (bestY < contour->bounds().fTop) {
continue;
}
SkScalar testY = SK_ScalarMax;
Segment* test = contour->topSegment(testY);
if (!test || bestY <= testY) {
continue;
}
topContour = contour;
topStart = test;
bestY = testY;
}
return topStart;
}
// Each segment may have an inside or an outside. Segments contained within
// winding may have insides on either side, and form a contour that should be
// ignored. Segments that are coincident with opposing direction segments may
// have outsides on either side, and should also disappear.
// 'Normal' segments will have one inside and one outside. Subsequent connections
// when winding should follow the intersection direction. If more than one edge
// is an option, choose first edge that continues the inside.
// since we start with leftmost top edge, we'll traverse through a
// smaller angle counterclockwise to get to the next edge.
static void bridge(SkTDArray<Contour*>& contourList, SkPath& simple) {
// after findTopContour has already been called once, check if
// result of subsequent findTopContour has no winding set
bool firstContour = true;
do {
Contour* topContour;
Segment* topStart = findTopContour(contourList, topContour);
if (!topStart) {
break;
}
// Start at the top. Above the top is outside, below is inside.
// follow edges to intersection by changing the index by direction.
int index, endIndex;
Segment* current = topStart->findTop(index, endIndex);
int winding = 0;
if (!firstContour) {
int contourWinding = topContour->winding();
#if DEBUG_WINDING
SkDebugf("%s 1 winding=%d\n", __FUNCTION__, winding);
#endif
if (contourWinding == SK_MinS32) {
const SkPoint& topPoint = current->xyAtT(endIndex);
winding = innerContourCheck(contourList, topContour, topPoint);
#if DEBUG_WINDING
SkDebugf("%s 2 winding=%d\n", __FUNCTION__, winding);
#endif
}
}
const SkPoint* firstPt = NULL;
SkPoint lastPt;
bool firstTime = true;
int spanWinding = current->spanSign(index, endIndex);
if (firstContour) {
topContour->setWinding(spanWinding);
firstContour = false;
}
bool active = winding * spanWinding <= 0;
do {
SkASSERT(!current->done());
int nextStart, nextEnd;
Segment* next = current->findNext(winding + spanWinding, index,
endIndex, nextStart, nextEnd, firstTime);
if (!next) {
break;
}
if (!firstPt) {
firstPt = &current->addMoveTo(index, simple, active);
}
lastPt = current->addCurveTo(index, endIndex, simple, active);
current = next;
index = nextStart;
endIndex = nextEnd;
spanWinding = SkSign32(spanWinding) * next->windValue(
SkMin32(nextStart, nextEnd));
#if DEBUG_WINDING
SkDebugf("%s spanWinding=%d\n", __FUNCTION__, spanWinding);
#endif
firstTime = false;
} while (*firstPt != lastPt);
if (firstPt) {
#if DEBUG_PATH_CONSTRUCTION
SkDebugf("%s close\n", __FUNCTION__);
#endif
simple.close();
}
} while (true);
}
static void fixOtherTIndex(SkTDArray<Contour*>& contourList) {
int contourCount = contourList.count();
for (int cTest = 0; cTest < contourCount; ++cTest) {
Contour* contour = contourList[cTest];
contour->fixOtherTIndex();
}
}
static void makeContourList(SkTArray<Contour>& contours,
SkTDArray<Contour*>& list) {
int count = contours.count();
if (count == 0) {
return;
}
for (int index = 0; index < count; ++index) {
*list.append() = &contours[index];
}
QSort<Contour>(list.begin(), list.end() - 1);
}
void simplifyx(const SkPath& path, SkPath& simple) {
// returns 1 for evenodd, -1 for winding, regardless of inverse-ness
int winding = (path.getFillType() & 1) ? 1 : -1;
simple.reset();
simple.setFillType(SkPath::kEvenOdd_FillType);
// turn path into list of segments
SkTArray<Contour> contours;
// FIXME: add self-intersecting cubics' T values to segment
EdgeBuilder builder(path, contours);
SkTDArray<Contour*> contourList;
makeContourList(contours, contourList);
Contour** currentPtr = contourList.begin();
if (!currentPtr) {
return;
}
Contour** listEnd = contourList.end();
// find all intersections between segments
do {
Contour** nextPtr = currentPtr;
Contour* current = *currentPtr++;
Contour* next;
do {
next = *nextPtr++;
} while (addIntersectTs(current, next) && nextPtr != listEnd);
} while (currentPtr != listEnd);
// eat through coincident edges
coincidenceCheck(contourList, winding);
fixOtherTIndex(contourList);
// construct closed contours
bridge(contourList, simple);
}