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gerrit-public.fairphone.software / platform / external / skia / bcc8486ad421350ecd17c07c3ce76c016894abb3 / . / 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_DUMP 0
#else
//const bool gRunTestsInOneThread = true;
#define DEBUG_ADD_INTERSECTING_TS 1
#define DEBUG_BRIDGE 1
#define DEBUG_DUMP 1
#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
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 VLineIntersect(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 verticalIntersect(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 VQuadIntersect(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 verticalIntersect(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 VCubicIntersect(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 verticalIntersect(aCubic, left, right, y, flipped, intersections);
}
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 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
};
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);
}
}
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[0], *(double*) 0);
return startT < endT ? (float) startT : (float) endT;
}
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
};
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);
}
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;
}
// 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, bool coincident) {
SkASSERT(start != end);
fSegment = segment;
fStart = start;
fEnd = end;
fCoincident = coincident;
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, const Segment* segment,
int start, int end, bool coincident) {
fSegment = segment;
fStart = start;
fEnd = end;
fCoincident = coincident;
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
}
const Segment* segment() const {
return fSegment;
}
int sign() const {
int result = fStart - fEnd >> 31 | 1;
SkASSERT(result == fStart < fEnd ? -1 : 1);
return result;
}
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;
bool fCoincident;
};
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 vertical 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;
}
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 {
double fT;
Segment* fOther;
double fOtherT; // value at fOther[fOtherIndex].fT
int fOtherIndex; // can't be used during intersection
int fWinding; // accumulated from contours surrounding this one
// OPTIMIZATION: done needs only 2 bits (values are -1, 0, 1)
int fDone; // set when t to t+fDone is processed
// OPTIMIZATION: done needs only 2 bits (values are -1, 0, 1)
int fCoincident; // -1 start of coincidence, 0 no coincidence, 1 end
};
class Segment {
public:
Segment() {
#if DEBUG_DUMP
fID = ++gSegmentID;
#endif
}
void addAngle(SkTDArray<Angle>& angles, int start, int end,
bool coincident) 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, coincident);
}
void addCubic(const SkPoint pts[4]) {
init(pts, SkPath::kCubic_Verb);
fBounds.setCubicBounds(pts);
}
void addLine(const SkPoint pts[2]) {
init(pts, SkPath::kLine_Verb);
fBounds.set(pts, 2);
}
// 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);
}
int addT(double newT, Segment& other, int coincident) {
// FIXME: in the pathological case where there is a ton of intercepts,
// binary search?
int insertedAt = -1;
Span* span;
size_t tCount = fTs.count();
double delta;
for (size_t idx2 = 0; idx2 < tCount; ++idx2) {
// 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[idx2].fT) {
insertedAt = idx2;
span = fTs.insert(idx2);
goto finish;
}
}
insertedAt = tCount;
span = fTs.append();
finish:
span->fT = newT;
span->fOther = &other;
span->fWinding = 1;
span->fDone = 0;
span->fCoincident = coincident;
fCoincident |= coincident;
return insertedAt;
}
void addTwoAngles(int start, int end, const SkPoint& endLoc,
const Span* endSpan, bool startCo, SkTDArray<Angle>& angles) const {
// add edge leading into junction
addAngle(angles, end, start, startCo);
// add edge leading away from junction
bool coincident;
int step = start < end ? 1 : -1;
int tIndex = nextSpan(end, step, endLoc, endSpan, NULL, coincident);
if (tIndex >= 0) {
lastSpan(tIndex, step, endLoc, endSpan, coincident);
addAngle(angles, end, tIndex, coincident);
}
}
const Bounds& bounds() const {
return fBounds;
}
void buildAngles(int index, int last, int step, const SkPoint& loc,
SkTDArray<Angle>& angles) const {
SkASSERT(index - last != 0);
SkASSERT((index - last < 0) ^ (step < 0));
int end = last + step;
do {
Span* span = &fTs[index];
Segment* other = span->fOther;
if (other->fDone) {
continue;
}
// 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;
Span* otherSpan = &other->fTs[oIndex];
SkASSERT(otherSpan->fOther == this);
// if done == -1, prior span has already been processed
bool otherCo;
int localStep = step;
int next = other->nextSpan(oIndex, localStep, loc, otherSpan,
NULL, otherCo);
if (next < 0) {
localStep = -step;
next = other->nextSpan(oIndex, localStep, loc, otherSpan,
NULL, otherCo);
}
other->lastSpan(next, localStep, loc, otherSpan, otherCo);
// add candidate into and away from junction
other->addTwoAngles(next, oIndex, loc, span, otherCo, angles);
} while ((index += step) != end);
}
// 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;
}
bool done() const {
return fDone;
}
int findCoincidentEnd(int start) const {
int tCount = fTs.count();
SkASSERT(start < tCount);
const Span& span = fTs[start];
SkASSERT(span.fCoincident);
for (int index = start + 1; index < tCount; ++index) {
const Span& match = fTs[index];
if (match.fOther == span.fOther) {
SkASSERT(match.fCoincident);
return index;
}
}
SkASSERT(0); // should never get here
return -1;
}
// 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
// step is in/out -1 or 1
// spanIndex is returned
Segment* findNext(int start, int winding, int& step, int& spanIndex) const {
SkASSERT(step == 1 || step == -1);
int count = fTs.count();
SkASSERT(step > 0 ? start < count - 1 : start > 0);
Span* startSpan = &fTs[start];
// FIXME:
// since Ts can be stepped either way, done markers must be careful
// not to assume that segment was only ascending in T. This shouldn't
// be a problem unless pathologically a segment can be partially
// ascending and partially descending -- maybe quads/cubic can do this?
startSpan->fDone = step;
SkPoint startLoc; // OPTIMIZATION: store this in the t span?
xyAtT(startSpan->fT, &startLoc);
SkPoint endLoc;
bool startCo;
int end = nextSpan(start, step, startLoc, startSpan, &endLoc, startCo);
// if we hit the end looking for span end, is that always an error?
SkASSERT(step > 0 ? end + 1 < count : end - 1 >= 0);
// preflight for coincidence -- if present, it may change winding
// considerations and whether reversed edges can be followed
int last = lastSpan(end, step, startLoc, startSpan, startCo);
// Discard opposing direction candidates if no coincidence was found.
Span* endSpan = &fTs[end];
int candidateCount = abs(last - end);
Segment* other;
if (candidateCount == 1) {
SkASSERT(!startCo);
// move in winding direction until edge in correct direction
// balance wrong direction edges before finding correct one
// this requres that the intersection is angularly sorted
// for a single intersection, special case -- choose the opposite
// edge that steps the same
other = endSpan->fOther;
SkASSERT(!other->fDone);
spanIndex = endSpan->fOtherIndex;
SkASSERT(step < 0 ? spanIndex > 0
: spanIndex < other->fTs.count() - 1);
return other;
}
// more than one viable candidate -- measure angles to find best
SkTDArray<Angle> angles;
SkASSERT(end - start != 0);
SkASSERT((end - start < 0) ^ (step < 0));
addTwoAngles(start, end, endLoc, endSpan, startCo, angles);
buildAngles(end, last, step, endLoc, angles);
SkTDArray<Angle*> sorted;
sortAngles(angles, sorted);
// find the starting edge
int startIndex = -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() == start) {
startIndex = angleIndex;
break;
}
}
SkASSERT(startIndex >= 0);
winding += angle->sign();
int nextIndex = startIndex;
const Angle* nextAngle;
do {
if (++nextIndex == angleCount) {
nextIndex = 0;
}
SkASSERT(nextIndex != startIndex); // should never wrap around
nextAngle = sorted[nextIndex];
// OPTIMIZATION: Figure out all connections, given the initial
// winding info (e.g., accumulate winding in span for reuse)
winding -= nextAngle->sign();
} while (winding);
// FIXME: get rid of cast
return const_cast<Segment*>(nextAngle->segment());
// 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
}
void findTooCloseToCall(int winding) {
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();
} while (moCount >= 3 || ++matchIndex < count - 1); // require t=0, x, 1 at minimum
SkPoint matchPt;
// OPTIMIZATION: defer matchPt until qualifying toCount is found?
xyAtT(match->fT, &matchPt);
// 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];
Segment* tOther = test->fOther;
int toCount = tOther->fTs.count();
if (toCount < 3) { // require t=0, x, 1 at minimum
continue;
}
SkPoint testPt;
xyAtT(test->fT, &testPt);
if (matchPt != testPt) {
matchIndex = index;
moCount = toCount;
match = test;
mOther = tOther;
matchPt = testPt;
continue;
}
int moStart = -1; // FIXME: initialization is debugging only
for (int moIndex = 0; moIndex < moCount; ++moIndex) {
Span& moSpan = mOther->fTs[moIndex];
if (moSpan.fOther == this) {
if (moSpan.fOtherT == match->fT) {
moStart = moIndex;
}
continue;
}
if (moSpan.fOther != tOther) {
continue;
}
int toStart = -1;
int toIndex; // FIXME: initialization is debugging only
bool found = false;
for (toIndex = 0; toIndex < toCount; ++toIndex) {
Span& toSpan = tOther->fTs[toIndex];
if (toSpan.fOther == this) {
if (toSpan.fOtherT == test->fT) {
toStart = toIndex;
}
continue;
}
if (toSpan.fOther == mOther && toSpan.fOtherT == moSpan.fT) {
found = true;
break;
}
}
if (!found) {
continue;
}
SkASSERT(moStart >= 0);
SkASSERT(toStart >= 0);
// test to see if the segment between there and here is linear
if (!mOther->isLinear(moStart, moIndex)
|| !tOther->isLinear(toStart, toIndex)) {
continue;
}
mOther->fTs[moStart].fCoincident = -1;
tOther->fTs[toStart].fCoincident = -1;
mOther->fTs[moIndex].fCoincident = 1;
tOther->fTs[toIndex].fCoincident = 1;
}
nextStart:
;
}
}
// find the adjacent T that is leftmost, with a point != base
int findLefty(int tIndex, const SkPoint& base) const {
int bestTIndex = -1;
SkPoint test;
SkScalar bestX = FLT_MAX;
int testTIndex = tIndex;
while (--testTIndex >= 0) {
xyAtT(fTs[testTIndex].fT, &test);
if (test == base) {
continue;
}
bestX = test.fX;
bestTIndex = testTIndex;
break;
}
int count = fTs.count();
testTIndex = tIndex;
while (++testTIndex < count) {
xyAtT(fTs[testTIndex].fT, &test);
if (test == base) {
continue;
}
if (bestX > test.fX) {
bestTIndex = testTIndex;
}
break;
}
SkASSERT(bestTIndex != -1);
return bestTIndex;
}
// 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
const Segment* findTop(int& tIndex, int& direction) const {
// iterate through T intersections and return topmost
// topmost tangent from y-min to first pt is closer to horizontal
int firstT = 0;
int lastT = 0;
SkScalar topY = fPts[0].fY;
int count = fTs.count();
int index;
for (index = 1; index < count; ++index) {
const Span& span = fTs[index];
double t = span.fT;
SkScalar yIntercept = t == 1 ? fPts[fVerb].fY : yAtT(t);
if (topY > yIntercept) {
topY = yIntercept;
firstT = lastT = index;
} else if (topY == yIntercept) {
lastT = index;
}
}
// if there's only a pair of segments, go with the endpoint chosen above
if (firstT == lastT) {
tIndex = firstT;
return this;
}
// sort the edges to find the leftmost
SkPoint startLoc; // OPTIMIZATION: store this in the t span?
const Span* startSpan = &fTs[firstT];
xyAtT(startSpan->fT, &startLoc);
SkPoint endLoc;
bool nextCo;
int end = nextSpan(firstT, 1, startLoc, startSpan, &endLoc, nextCo);
if (end == -1) {
end = nextSpan(firstT, -1, startLoc, startSpan, &endLoc, nextCo);
}
// 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, endLoc, &fTs[firstT], nextCo, angles);
buildAngles(firstT, lastT, 1, startLoc, angles);
SkTDArray<Angle*> sorted;
sortAngles(angles, sorted);
const Segment* leftSegment = sorted[0]->segment();
tIndex = sorted[0]->end();
direction = sorted[0]->start() - tIndex;
SkASSERT(direction);
direction = direction < 0 ? -1 : 1;
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;
}
}
}
}
void init(const SkPoint pts[], SkPath::Verb verb) {
fPts = pts;
fVerb = verb;
fDone = false;
fCoincident = 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);
}
}
bool isHorizontal() const {
return fBounds.fTop == fBounds.fBottom;
}
bool isVertical() const {
return fBounds.fLeft == fBounds.fRight;
}
int lastSpan(int end, int step, const SkPoint& startLoc,
const Span* startSpan, bool& coincident) const {
int last = end;
int count = fTs.count();
SkPoint lastLoc;
do {
end = last;
if (fTs[end].fCoincident == -step) {
coincident = true;
}
if (step > 0 ? ++last >= count : --last < 0) {
return end;
}
const Span& lastSpan = fTs[last];
if (lastSpan.fDone == -step) {
return end;
}
if (lastSpan.fT == startSpan->fT) {
continue;
}
xyAtT(lastSpan.fT, &lastLoc);
} while (startLoc == lastLoc);
return end;
}
SkScalar leftMost(int start, int end) const {
return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
}
int nextSpan(int from, int step, const SkPoint& fromLoc,
const Span* fromSpan, SkPoint* toLoc, bool& coincident) const {
coincident = false;
if (fDone) {
return -1;
}
int count = fTs.count();
int to = from;
while (step > 0 ? ++to < count : --to >= 0) {
Span* span = &fTs[to];
if (span->fCoincident == step) {
coincident = true;
}
if (fromSpan->fT == span->fT) {
continue;
}
SkPoint loc;
xyAtT(span->fT, &loc);
if (fromLoc == loc) {
continue;
}
if (span->fDone == -step) {
return -1;
}
if (toLoc) {
*toLoc = loc;
}
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: remove this function if it's never called
double t(int tIndex) const {
return fTs[tIndex].fT;
}
void updatePts(const SkPoint pts[]) {
fPts = pts;
}
SkPath::Verb verb() const {
return fVerb;
}
SkScalar xAtT(double t) const {
SkASSERT(t >= 0 && t <= 1);
return (*SegmentXAtT[fVerb])(fPts, t);
}
void xyAtT(double t, SkPoint* pt) const {
SkASSERT(t >= 0 && t <= 1);
(*SegmentXYAtT[fVerb])(fPts, t, pt);
}
SkScalar yAtT(double t) const {
SkASSERT(t >= 0 && t <= 1);
return (*SegmentYAtT[fVerb])(fPts, t);
}
#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 winding=%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].fWinding);
}
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)
// FIXME: coincident only needs two bits (-1, 0, 1)
int fCoincident; // non-zero if some coincident span inside
bool fDone;
#if DEBUG_DUMP
int fID;
#endif
};
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 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();
}
int addQuad(const SkPoint pts[3]) {
fSegments.push_back().addQuad(pts);
fContainsCurves = true;
return fSegments.count();
}
const Bounds& bounds() const {
return fBounds;
}
void complete() {
setBounds();
fContainsIntercepts = false;
}
void containsIntercepts() {
fContainsIntercepts = true;
}
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;
}
// 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() {
int segmentCount = fSegments.count();
SkASSERT(segmentCount > 0);
int best = -1;
Segment* bestSegment = NULL;
while (++best < segmentCount) {
Segment* testSegment = &fSegments[best];
if (testSegment->done()) {
continue;
}
bestSegment = testSegment;
break;
}
if (!bestSegment) {
return NULL;
}
SkScalar bestTop = bestSegment->bounds().fTop;
for (int test = best + 1; test < segmentCount; ++test) {
Segment* testSegment = &fSegments[test];
if (testSegment->done()) {
continue;
}
SkScalar testTop = testSegment->bounds().fTop;
if (bestTop > testTop) {
bestTop = testTop;
bestSegment = testSegment;
}
}
return bestSegment;
}
#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.growToInclude(fSegments[index].bounds());
}
}
public:
SkTArray<Segment> fSegments; // not worth accessor functions?
private:
Bounds fBounds;
bool fContainsIntercepts;
bool fContainsCurves;
#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->fSegments.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->fSegments.count()) {
fContours.pop_back();
}
// correct pointers in contours since fReducePts may have moved as it grew
int cIndex = 0;
fCurrentContour = &fContours[0];
int extraCount = fExtra.count();
SkASSERT(fExtra[0] == -1);
int eIndex = 0;
int rIndex = 0;
while (++eIndex < extraCount) {
int offset = fExtra[eIndex];
if (offset < 0) {
fCurrentContour = &fContours[++cIndex];
continue;
}
Segment& segment = fCurrentContour->fSegments[offset - 1];
segment.updatePts(&fReducePts[rIndex]);
rIndex += segment.verb() + 1;
}
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,
};
// 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->fSegments[fIndex].addOtherT(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, int coincident) {
fContour->containsIntercepts();
return fContour->fSegments[fIndex].addT(newT,
other.fContour->fSegments[other.fIndex], coincident);
}
bool advance() {
return ++fIndex < fLast;
}
SkScalar bottom() const {
return bounds().fBottom;
}
const Bounds& bounds() const {
return fContour->fSegments[fIndex].bounds();
}
const SkPoint* cubic() const {
return fCubic;
}
void init(Contour* contour) {
fContour = contour;
fIndex = 0;
fLast = contour->fSegments.count();
}
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->fSegments[fIndex].pts();
}
SkScalar right() const {
return bounds().fRight;
}
ptrdiff_t segmentIndex() const {
return fIndex;
}
SegmentType segmentType() const {
const Segment& segment = fContour->fSegments[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->fSegments[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].fX;
}
protected:
Contour* fContour;
SkPoint fCubic[4];
int fIndex;
int fLast;
};
static void debugShowLineIntersection(int pts, const Work& wt,
const Work& wn, const double wtTs[2], const double wnTs[2]) {
#if DEBUG_ADD_INTERSECTING_TS
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)\n",
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");
}
#endif
}
static bool addIntersectTs(Contour* test, Contour* next, int winding) {
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);
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);
}
// in addition to recording T values, record matching segment
int coincident = pts == 2 && wn.segmentType() <= Work::kLine_Segment
&& wt.segmentType() <= Work::kLine_Segment ? -1 :0;
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, coincident);
int nextTAt = wn.addT(ts.fT[!swap][pt], wt, coincident);
wt.addOtherT(testTAt, ts.fT[!swap][pt], nextTAt);
wn.addOtherT(nextTAt, ts.fT[swap][pt], testTAt);
coincident = -coincident;
}
} while (wn.advance());
} while (wt.advance());
return true;
}
// see if coincidence is formed by clipping non-concident segments
static void coincidenceCheck(SkTDArray<Contour*>& contourList, int winding) {
int contourCount = contourList.count();
for (size_t cIndex = 0; cIndex < contourCount; ++cIndex) {
Contour* contour = contourList[cIndex];
contour->findTooCloseToCall(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
static Segment* findTopContour(SkTDArray<Contour*>& contourList,
int contourCount) {
int cIndex = 0;
Segment* topStart;
do {
Contour* topContour = contourList[cIndex];
topStart = topContour->topSegment();
} while (!topStart && ++cIndex < contourCount);
if (!topStart) {
return NULL;
}
SkScalar top = topStart->bounds().fTop;
for (int cTest = cIndex + 1; cTest < contourCount; ++cTest) {
Contour* contour = contourList[cTest];
if (top < contour->bounds().fTop) {
continue;
}
Segment* test = contour->topSegment();
if (top > test->bounds().fTop) {
cIndex = cTest;
topStart = test;
top = test->bounds().fTop;
}
}
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) {
int contourCount = contourList.count();
int winding = 0; // there are no contours outside this one
do {
Segment* topStart = findTopContour(contourList, contourCount);
if (!topStart) {
break;
}
// Start at the top. Above the top is outside, below is inside.
// follow edges to intersection by changing the tIndex by direction.
int tIndex, step;
const Segment* topSegment = topStart->findTop(tIndex, step);
const Segment* next = topSegment;
do {
int spanIndex;
next = next->findNext(tIndex, winding, step, spanIndex);
} while (next != topSegment);
// at intersection, stay on outside, but mark remaining edges as inside
// or, only mark first pair as inside?
// how is this going to work for contained (but not intersecting)
// segments?
// start here ;
// find span
// mark neighbors winding coverage
// output span
// mark span as processed
} 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, Contour& sentinel,
SkTDArray<Contour*>& list) {
int count = contours.count();
if (count == 0) {
return;
}
for (int index = 0; index < count; ++index) {
*list.append() = &contours[index];
}
*list.append() = &sentinel;
QSort<Contour>(list.begin(), list.end() - 1);
}
void simplifyx(const SkPath& path, bool asFill, 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;
Contour sentinel;
sentinel.reset();
makeContourList(contours, sentinel, contourList);
Contour** currentPtr = contourList.begin();
if (!currentPtr) {
return;
}
// find all intersections between segments
do {
Contour** nextPtr = currentPtr;
Contour* current = *currentPtr++;
Contour* next;
do {
next = *nextPtr++;
} while (next != &sentinel && addIntersectTs(current, next, winding));
} while (*currentPtr != &sentinel);
fixOtherTIndex(contourList);
// eat through coincident edges
coincidenceCheck(contourList, winding);
// construct closed contours
bridge(contourList);
}