work in progress
git-svn-id: http://skia.googlecode.com/svn/trunk@3443 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/experimental/Intersection/DataTypes.cpp b/experimental/Intersection/DataTypes.cpp
index 07e7548..a68cb9a 100644
--- a/experimental/Intersection/DataTypes.cpp
+++ b/experimental/Intersection/DataTypes.cpp
@@ -1,5 +1,19 @@
#include "DataTypes.h"
+#include <sys/types.h>
+#include <stdlib.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void *memcpy(void *, const void *, size_t);
+
+#ifdef __cplusplus
+}
+#endif
+
+
const double PointEpsilon = 0.000001;
const double SquaredEpsilon = PointEpsilon * PointEpsilon;
@@ -111,3 +125,58 @@
y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
}
}
+
+
+// from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
+union Float_t
+{
+ Float_t(float num = 0.0f) : f(num) {}
+ // Portable extraction of components.
+ bool Negative() const { return (i >> 31) != 0; }
+ int32_t RawMantissa() const { return i & ((1 << 23) - 1); }
+ int32_t RawExponent() const { return (i >> 23) & 0xFF; }
+
+ int32_t i;
+ float f;
+#ifdef _DEBUG
+ struct
+ { // Bitfields for exploration. Do not use in production code.
+ uint32_t mantissa : 23;
+ uint32_t exponent : 8;
+ uint32_t sign : 1;
+ } parts;
+#endif
+};
+
+bool AlmostEqualUlps(float A, float B, int maxUlpsDiff)
+{
+ Float_t uA(A);
+ Float_t uB(B);
+
+ // Different signs means they do not match.
+ if (uA.Negative() != uB.Negative())
+ {
+ // Check for equality to make sure +0==-0
+ return A == B;
+ }
+
+ // Find the difference in ULPs.
+ int ulpsDiff = abs(uA.i - uB.i);
+ return ulpsDiff <= maxUlpsDiff;
+}
+
+int UlpsDiff(float A, float B)
+{
+ Float_t uA(A);
+ Float_t uB(B);
+
+ return abs(uA.i - uB.i);
+}
+
+int FloatAsInt(float A)
+{
+ Float_t uA(A);
+ return uA.i;
+}
+
+
diff --git a/experimental/Intersection/DataTypes.h b/experimental/Intersection/DataTypes.h
index 94373cd..8b97cec 100644
--- a/experimental/Intersection/DataTypes.h
+++ b/experimental/Intersection/DataTypes.h
@@ -1,6 +1,16 @@
#ifndef __DataTypes_h__
#define __DataTypes_h__
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+extern double fabs( double );
+
+#ifdef __cplusplus
+}
+#endif
+
extern const double PointEpsilon;
extern const double SquaredEpsilon;
@@ -123,4 +133,8 @@
void xy_at_t(const _Line& , double t, double& x, double& y);
void xy_at_t(const Quadratic& , double t, double& x, double& y);
+bool AlmostEqualUlps(float A, float B, int maxUlpsDiff);
+int UlpsDiff(float A, float B);
+int FloatAsInt(float A);
+
#endif // __DataTypes_h__
diff --git a/experimental/Intersection/EdgeWalker.cpp b/experimental/Intersection/EdgeWalker.cpp
index 771e639..e33fd94 100644
--- a/experimental/Intersection/EdgeWalker.cpp
+++ b/experimental/Intersection/EdgeWalker.cpp
@@ -14,9 +14,43 @@
#include "SkTDArray.h"
#include "TSearch.h"
+#if 0 // set to 1 for no debugging whatsoever
static bool gShowDebugf = false; // FIXME: remove once debugging is complete
-static bool gShowPath = false;
-static bool gDebugLessThan = false;
+
+#define DEBUG_DUMP 0
+#define DEBUG_ADD 0
+#define DEBUG_ADD_INTERSECTING_TS 0
+#define DEBUG_ADD_BOTTOM_TS 0
+#define COMPARE_DOUBLE 0
+#define ASSERT_ON_ULPS 0
+#define DEBUG_ABOVE_BELOW 0
+#define DEBUG_ACTIVE_LESS_THAN 0
+#define DEBUG_SORT_HORIZONTAL 0
+#define DEBUG_OUT 0
+#define DEBUG_OUT_LESS_THAN 0
+#define DEBUG_ADJUST_COINCIDENT 0
+#else
+static bool gShowDebugf = true; // FIXME: remove once debugging is complete
+
+#define DEBUG_DUMP 01
+#define DEBUG_ADD 01
+#define DEBUG_ADD_INTERSECTING_TS 0
+#define DEBUG_ADD_BOTTOM_TS 0
+#define COMPARE_DOUBLE 0
+#define ASSERT_ON_ULPS 0
+#define DEBUG_ABOVE_BELOW 01
+#define DEBUG_ACTIVE_LESS_THAN 0
+#define DEBUG_SORT_HORIZONTAL 01
+#define DEBUG_OUT 01
+#define DEBUG_OUT_LESS_THAN 0
+#define DEBUG_ADJUST_COINCIDENT 1
+#endif
+
+// FIXME: not wild about this -- min delta should be based on size of curve, not t
+// #define MIN_T_DELTA 0.000001
+// not wild about this either -- for SkScalars backed by floats, would like to
+// represent deltas in terms of number of significant matching bits
+#define MIN_PT_DELTA 0.000001
static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
double aRange[2], double bRange[2]) {
@@ -25,9 +59,10 @@
return intersect(aLine, bLine, aRange, bRange);
}
-static int LineIntersect(const SkPoint a[2], SkScalar y, double aRange[2]) {
+static int LineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
+ SkScalar y, double aRange[2]) {
_Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
- return horizontalIntersect(aLine, y, aRange);
+ return horizontalLineIntersect(aLine, left, right, y, aRange);
}
static void LineXYAtT(const SkPoint a[2], double t, SkPoint* out) {
@@ -38,6 +73,22 @@
out->fY = SkDoubleToScalar(y);
}
+#if COMPARE_DOUBLE
+static void LineXYAtT(const SkPoint a[2], double t, _Point* out) {
+ _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+ xy_at_t(aLine, t, out->x, out->y);
+}
+#endif
+
+#if 0 // unused for now
+static SkScalar LineXAtT(const SkPoint a[2], double t) {
+ _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);
+}
+#endif
+
static SkScalar LineYAtT(const SkPoint a[2], double t) {
_Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
double y;
@@ -56,6 +107,13 @@
sub[1].fY = SkDoubleToScalar(dst[1].y);
}
+#if COMPARE_DOUBLE
+static void LineSubDivide(const SkPoint a[2], double startT, double endT,
+ _Line& dst) {
+ _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+ sub_divide(aLine, startT, endT, dst);
+}
+#endif
// functions
void contourBounds(const SkPath& path, SkTDArray<SkRect>& boundsArray);
@@ -125,6 +183,8 @@
return dx1 * dy2 == dx2 * dy1;
}
+// OPTIMIZATION: this should point to a list of input data rather than duplicating
+// the line data here. This would reduce the need to assemble the results.
struct OutEdge {
bool operator<(const OutEdge& rh) const {
const SkPoint& first = fPts[0];
@@ -135,7 +195,9 @@
}
SkPoint fPts[4];
+ int fID; // id of edge generating data
uint8_t fVerb; // FIXME: not read from everywhere
+ bool fCloseCall; // edge is trimmable if not originally coincident
};
class OutEdgeBuilder {
@@ -144,11 +206,40 @@
: fFill(fill) {
}
- void addLine(const SkPoint line[2]) {
+ void addLine(const SkPoint line[2], int id, bool closeCall) {
OutEdge& newEdge = fEdges.push_back();
newEdge.fPts[0] = line[0];
newEdge.fPts[1] = line[1];
newEdge.fVerb = SkPath::kLine_Verb;
+ newEdge.fID = id;
+ newEdge.fCloseCall = closeCall;
+ }
+
+ bool trimLine(SkScalar y, int id) {
+ size_t count = fEdges.count();
+ while (count-- != 0) {
+ OutEdge& edge = fEdges[count];
+ if (edge.fID != id) {
+ continue;
+ }
+ if (edge.fCloseCall) {
+ return false;
+ }
+ SkASSERT(edge.fPts[0].fY <= y);
+ if (edge.fPts[1].fY <= y) {
+ continue;
+ }
+ edge.fPts[1].fX = edge.fPts[0].fX + (y - edge.fPts[0].fY)
+ * (edge.fPts[1].fX - edge.fPts[0].fX)
+ / (edge.fPts[1].fY - edge.fPts[0].fY);
+ edge.fPts[1].fY = y;
+ if (gShowDebugf) {
+ SkDebugf("%s edge=%d %1.9g,%1.9g\n", __FUNCTION__, id,
+ edge.fPts[1].fX, y);
+ }
+ return true;
+ }
+ return false;
}
void assemble(SkPath& simple) {
@@ -238,6 +329,10 @@
if (edgeIndex == closeEdgeIndex || edgeIndex == 0) {
if (lastLine[1] != firstPt) {
simple.lineTo(lastLine[1].fX, lastLine[1].fY);
+ if (gShowDebugf) {
+ SkDebugf("%s lineTo last (%g, %g)\n", __FUNCTION__,
+ lastLine[1].fX, lastLine[1].fY);
+ }
}
simple.lineTo(firstPt.fX, firstPt.fY);
simple.close();
@@ -267,19 +362,19 @@
int twoIndex = two < 0 ? 0 : twoEdge.fVerb;
const SkPoint& startPt2 = twoEdge.fPts[twoIndex];
if (startPt1.fY != startPt2.fY) {
- if (gDebugLessThan) {
- SkDebugf("%s %d<%d (%g,%g) %s startPt1.fY < startPt2.fY\n", __FUNCTION__,
- one, two, startPt1.fY, startPt2.fY,
- startPt1.fY < startPt2.fY ? "true" : "false");
- }
+ #if DEBUG_OUT_LESS_THAN
+ SkDebugf("%s %d<%d (%g,%g) %s startPt1.fY < startPt2.fY\n", __FUNCTION__,
+ one, two, startPt1.fY, startPt2.fY,
+ startPt1.fY < startPt2.fY ? "true" : "false");
+ #endif
return startPt1.fY < startPt2.fY;
}
if (startPt1.fX != startPt2.fX) {
- if (gDebugLessThan) {
- SkDebugf("%s %d<%d (%g,%g) %s startPt1.fX < startPt2.fX\n", __FUNCTION__,
- one, two, startPt1.fX, startPt2.fX,
- startPt1.fX < startPt2.fX ? "true" : "false");
- }
+ #if DEBUG_OUT_LESS_THAN
+ SkDebugf("%s %d<%d (%g,%g) %s startPt1.fX < startPt2.fX\n", __FUNCTION__,
+ one, two, startPt1.fX, startPt2.fX,
+ startPt1.fX < startPt2.fX ? "true" : "false");
+ #endif
return startPt1.fX < startPt2.fX;
}
const SkPoint& endPt1 = oneEdge.fPts[oneIndex ^ oneEdge.fVerb];
@@ -288,25 +383,25 @@
SkScalar dy2 = startPt2.fY - endPt2.fY;
SkScalar dy1y2 = dy1 * dy2;
if (dy1y2 < 0) { // different signs
- if (gDebugLessThan) {
+ #if DEBUG_OUT_LESS_THAN
SkDebugf("%s %d<%d %s dy1 > 0\n", __FUNCTION__, one, two,
dy1 > 0 ? "true" : "false");
- }
+ #endif
return dy1 > 0; // one < two if one goes up and two goes down
}
if (dy1y2 == 0) {
- if (gDebugLessThan) {
- SkDebugf("%s %d<%d %s endPt1.fX < endPt2.fX\n", __FUNCTION__,
- one, two, endPt1.fX < endPt2.fX ? "true" : "false");
- }
+ #if DEBUG_OUT_LESS_THAN
+ SkDebugf("%s %d<%d %s endPt1.fX < endPt2.fX\n", __FUNCTION__,
+ one, two, endPt1.fX < endPt2.fX ? "true" : "false");
+ #endif
return endPt1.fX < endPt2.fX;
}
SkScalar dx1y2 = (startPt1.fX - endPt1.fX) * dy2;
SkScalar dx2y1 = (startPt2.fX - endPt2.fX) * dy1;
- if (gDebugLessThan) {
- SkDebugf("%s %d<%d %s dy2 < 0 ^ dx1y2 < dx2y1\n", __FUNCTION__,
- one, two, dy2 < 0 ^ dx1y2 < dx2y1 ? "true" : "false");
- }
+ #if DEBUG_OUT_LESS_THAN
+ SkDebugf("%s %d<%d %s dy2 < 0 ^ dx1y2 < dx2y1\n", __FUNCTION__,
+ one, two, dy2 < 0 ^ dx1y2 < dx2y1 ? "true" : "false");
+ #endif
return dy2 > 0 ^ dx1y2 < dx2y1;
}
@@ -349,8 +444,19 @@
right.fPts[rightIndex < 0 ? 0 : right.fVerb];
pairUp = leftMatch == rightMatch;
} else {
+ #if DEBUG_OUT
+ if (left.fPts[leftIndex < 0 ? 0 : left.fVerb].fY
+ != right.fPts[rightIndex < 0 ? 0 : right.fVerb].fY) {
+ *fMismatches.append() = leftIndex;
+ if (rightPtr == lastPtr) {
+ *fMismatches.append() = rightIndex;
+ }
+ pairUp = false;
+ }
+ #else
SkASSERT(left.fPts[leftIndex < 0 ? 0 : left.fVerb].fY
== right.fPts[rightIndex < 0 ? 0 : right.fVerb].fY);
+ #endif
}
if (pairUp) {
if (leftIndex < 0) {
@@ -367,6 +473,19 @@
}
leftPtr = rightPtr;
}
+#if DEBUG_OUT
+ int* mismatch = fMismatches.begin();
+ while (mismatch != fMismatches.end()) {
+ int leftIndex = *mismatch++;
+ int leftOutIndex = abs(leftIndex) - 1;
+ const OutEdge& left = fEdges[leftOutIndex];
+ const SkPoint& leftPt = left.fPts[leftIndex < 0 ? 0 : left.fVerb];
+ SkDebugf("%s left=%d %s (%1.9g,%1.9g)\n",
+ __FUNCTION__, left.fID, leftIndex < 0 ? "top" : "bot",
+ leftPt.fX, leftPt.fY);
+ }
+ SkASSERT(fMismatches.count() == 0);
+#endif
}
protected:
@@ -374,6 +493,9 @@
SkTDArray<int> fTops;
SkTDArray<int> fBottoms;
bool fFill;
+#if DEBUG_OUT
+ SkTDArray<int> fMismatches;
+#endif
};
// Bounds, unlike Rect, does not consider a vertical line to be empty.
@@ -397,11 +519,51 @@
: fTopIntercepts(0)
, fBottomIntercepts(0) {
}
+
+#if DEBUG_DUMP
+ // FIXME: pass current verb as parameter
+ void dump(const SkPoint* pts) {
+ const char className[] = "Intercepts";
+ const int tab = 8;
+ for (int i = 0; i < fTs.count(); ++i) {
+ SkPoint out;
+ LineXYAtT(pts, fTs[i], &out);
+ SkDebugf("%*s.fTs[%d]=%g (%g,%g)\n", tab + sizeof(className),
+ className, i, fTs[i], out.fX, out.fY);
+ }
+ SkDebugf("%*s.fTopIntercepts=%d\n", tab + sizeof(className),
+ className, fTopIntercepts);
+ SkDebugf("%*s.fBottomIntercepts=%d\n", tab + sizeof(className),
+ className, fBottomIntercepts);
+ }
+#endif
+
SkTDArray<double> fTs;
int fTopIntercepts;
int fBottomIntercepts;
};
+struct HorizontalEdge {
+ bool operator<(const HorizontalEdge& rh) const {
+ return fY == rh.fY ? fLeft == rh.fLeft ? fRight < rh.fRight
+ : fLeft < rh.fLeft : fY < rh.fY;
+ }
+
+#if DEBUG_DUMP
+ void dump() {
+ const char className[] = "HorizontalEdge";
+ const int tab = 4;
+ SkDebugf("%*s.fLeft=%g\n", tab + sizeof(className), className, fLeft);
+ SkDebugf("%*s.fRight=%g\n", tab + sizeof(className), className, fRight);
+ SkDebugf("%*s.fY=%g\n", tab + sizeof(className), className, fY);
+ }
+#endif
+
+ SkScalar fLeft;
+ SkScalar fRight;
+ SkScalar fY;
+};
+
struct InEdge {
bool operator<(const InEdge& rh) const {
return fBounds.fTop == rh.fBounds.fTop
@@ -409,9 +571,14 @@
: fBounds.fTop < rh.fBounds.fTop;
}
- void add(double* ts, size_t count, ptrdiff_t verbIndex) {
+ // 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.
+ int add(double* ts, size_t count, ptrdiff_t verbIndex) {
// FIXME: in the pathological case where there is a ton of intercepts, binary search?
bool foundIntercept = false;
+ int insertedAt = -1;
Intercepts& intercepts = fIntercepts[verbIndex];
for (size_t index = 0; index < count; ++index) {
double t = ts[index];
@@ -425,21 +592,27 @@
}
foundIntercept = true;
size_t tCount = intercepts.fTs.count();
+ double delta;
for (size_t idx2 = 0; idx2 < tCount; ++idx2) {
if (t <= intercepts.fTs[idx2]) {
- double delta = intercepts.fTs[idx2] - t;
+ // FIXME: ? if (t < intercepts.fTs[idx2]) // failed
+ delta = intercepts.fTs[idx2] - t;
if (delta > 0) {
+ insertedAt = idx2;
*intercepts.fTs.insert(idx2) = t;
}
- fContainsIntercepts = true;
- return;
+ goto nextPt;
}
}
- if (tCount == 0 || t > intercepts.fTs[tCount - 1]) {
+ if (tCount == 0 || (delta = t - intercepts.fTs[tCount - 1]) > 0) {
+ insertedAt = tCount;
*intercepts.fTs.append() = t;
}
+ nextPt:
+ ;
}
fContainsIntercepts |= foundIntercept;
+ return insertedAt;
}
bool cached(const InEdge* edge) {
@@ -458,7 +631,7 @@
return false;
}
- void complete(signed char winding) {
+ void complete(signed char winding, int id) {
SkPoint* ptPtr = fPts.begin();
SkPoint* ptLast = fPts.end();
if (ptPtr == ptLast) {
@@ -486,8 +659,46 @@
}
}
fContainsIntercepts = false;
+ fID = id;
}
+#if DEBUG_DUMP
+ void dump() {
+ int i;
+ const char className[] = "InEdge";
+ const int tab = 4;
+ SkDebugf("InEdge %p (edge=%d)\n", this, fID);
+ for (i = 0; i < fCached.count(); ++i) {
+ SkDebugf("%*s.fCached[%d]=0x%08x\n", tab + sizeof(className),
+ className, i, fCached[i]);
+ }
+ uint8_t* verbs = fVerbs.begin();
+ SkPoint* pts = fPts.begin();
+ for (i = 0; i < fIntercepts.count(); ++i) {
+ SkDebugf("%*s.fIntercepts[%d]:\n", tab + sizeof(className),
+ className, i);
+ // FIXME: take current verb into consideration
+ fIntercepts[i].dump(pts);
+ pts += *verbs++;
+ }
+ for (i = 0; i < fPts.count(); ++i) {
+ SkDebugf("%*s.fPts[%d]=(%g,%g)\n", tab + sizeof(className),
+ className, i, fPts[i].fX, fPts[i].fY);
+ }
+ for (i = 0; i < fVerbs.count(); ++i) {
+ SkDebugf("%*s.fVerbs[%d]=%d\n", tab + sizeof(className),
+ className, i, fVerbs[i]);
+ }
+ SkDebugf("%*s.fBounds=(%g. %g, %g, %g)\n", tab + sizeof(className),
+ className, fBounds.fLeft, fBounds.fTop,
+ fBounds.fRight, fBounds.fBottom);
+ SkDebugf("%*s.fWinding=%d\n", tab + sizeof(className), className,
+ fWinding);
+ SkDebugf("%*s.fContainsIntercepts=%d\n", tab + sizeof(className),
+ className, fContainsIntercepts);
+ }
+#endif
+
// temporary data : move this to a separate struct?
SkTDArray<const InEdge*> fCached; // list of edges already intercepted
SkTArray<Intercepts> fIntercepts; // one per verb
@@ -496,6 +707,7 @@
SkTDArray<SkPoint> fPts;
SkTDArray<uint8_t> fVerbs;
Bounds fBounds;
+ int fID;
signed char fWinding;
bool fContainsIntercepts;
};
@@ -503,10 +715,13 @@
class InEdgeBuilder {
public:
-InEdgeBuilder(const SkPath& path, bool ignoreHorizontal, SkTArray<InEdge>& edges)
+InEdgeBuilder(const SkPath& path, bool ignoreHorizontal, SkTArray<InEdge>& edges,
+ SkTDArray<HorizontalEdge>& horizontalEdges)
: fPath(path)
, fCurrentEdge(NULL)
, fEdges(edges)
+ , fID(0)
+ , fHorizontalEdges(horizontalEdges)
, fIgnoreHorizontal(ignoreHorizontal)
{
walk();
@@ -523,7 +738,7 @@
bool complete() {
if (fCurrentEdge && fCurrentEdge->fVerbs.count()) {
- fCurrentEdge->complete(fWinding);
+ fCurrentEdge->complete(fWinding, ++fID);
fCurrentEdge = NULL;
return true;
}
@@ -532,8 +747,7 @@
int direction(int count) {
fPtCount = count;
- fIgnorableHorizontal = fIgnoreHorizontal && isHorizontal();
- if (fIgnorableHorizontal) {
+ if (fIgnoreHorizontal && isHorizontal()) {
return 0;
}
int last = count - 1;
@@ -562,40 +776,22 @@
void walk() {
SkPath::Iter iter(fPath, true);
- int winding;
+ int winding = 0;
while ((fVerb = iter.next(fPts)) != SkPath::kDone_Verb) {
switch (fVerb) {
case SkPath::kMove_Verb:
- if (gShowPath) {
- SkDebugf("path.moveTo(%g, %g);\n", fPts[0].fX, fPts[0].fY);
- }
startEdge();
continue;
case SkPath::kLine_Verb:
- if (gShowPath) {
- SkDebugf("path.lineTo(%g, %g);\n", fPts[1].fX, fPts[1].fY);
- }
winding = direction(2);
break;
case SkPath::kQuad_Verb:
- if (gShowPath) {
- SkDebugf("path.quadTo(%g, %g, %g, %g);\n",
- fPts[1].fX, fPts[1].fY, fPts[2].fX, fPts[2].fY);
- }
winding = direction(3);
break;
case SkPath::kCubic_Verb:
- if (gShowPath) {
- SkDebugf("path.cubicTo(%g, %g, %g, %g);\n",
- fPts[1].fX, fPts[1].fY, fPts[2].fX, fPts[2].fY,
- fPts[3].fX, fPts[3].fY);
- }
winding = direction(4);
break;
case SkPath::kClose_Verb:
- if (gShowPath) {
- SkDebugf("path.close();\n");
- }
SkASSERT(fCurrentEdge);
complete();
continue;
@@ -603,7 +799,15 @@
SkDEBUGFAIL("bad verb");
return;
}
- if (fIgnorableHorizontal) {
+ if (winding == 0) {
+ HorizontalEdge* horizontalEdge = fHorizontalEdges.append();
+ // FIXME: for degenerate quads and cubics, compute x extremes
+ horizontalEdge->fLeft = fPts[0].fX;
+ horizontalEdge->fRight = fPts[fVerb].fX;
+ horizontalEdge->fY = fPts[0].fY;
+ if (horizontalEdge->fLeft > horizontalEdge->fRight) {
+ SkTSwap<SkScalar>(horizontalEdge->fLeft, horizontalEdge->fRight);
+ }
if (complete()) {
startEdge();
}
@@ -625,21 +829,19 @@
fEdges.pop_back();
}
}
- if (gShowPath) {
- SkDebugf("\n");
- }
}
private:
const SkPath& fPath;
InEdge* fCurrentEdge;
SkTArray<InEdge>& fEdges;
+ SkTDArray<HorizontalEdge>& fHorizontalEdges;
SkPoint fPts[4];
SkPath::Verb fVerb;
int fPtCount;
int fPtOffset;
+ int fID;
int8_t fWinding;
- bool fIgnorableHorizontal;
bool fIgnoreHorizontal;
};
@@ -689,7 +891,8 @@
// OPTIMIZATION: Brian suggests that global sorting should be unnecessary, since
// as active edges are introduced, only local sorting should be required
-struct ActiveEdge {
+class ActiveEdge {
+public:
// OPTIMIZATION: fold return statements into one
bool operator<(const ActiveEdge& rh) const {
if (rh.fAbove.fY - fAbove.fY > fBelow.fY - rh.fAbove.fY
@@ -700,43 +903,109 @@
const SkPoint& check = rh.fBelow.fY <= fBelow.fY
&& fBelow != rh.fBelow ? rh.fBelow :
rh.fAbove;
- if (gDebugLessThan) {
- SkDebugf("%s < %c %cthis (%d){%1.2g,%1.2g %1.2g,%1.2g}"
- " < rh (%d){%1.2g,%1.2g %1.2g,%1.2g}\n", __FUNCTION__,
- rh.fBelow.fY <= fBelow.fY && fBelow != rh.fBelow ? 'B' : 'A',
- (check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX)
- < (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX)
- ? ' ' : '!',
- fIndex, fAbove.fX, fAbove.fY, fBelow.fX, fBelow.fY,
- rh.fIndex, rh.fAbove.fX, rh.fAbove.fY,
- rh.fBelow.fX, rh.fBelow.fY);
- }
+ #if COMPARE_DOUBLE
+ SkASSERT(((check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX)
+ < (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX))
+ == ((check.fY - fDAbove.y) * (fDBelow.x - fDAbove.x)
+ < (fDBelow.y - fDAbove.y) * (check.fX - fDAbove.x)));
+ #endif
+ #if DEBUG_ACTIVE_LESS_THAN
+ SkDebugf("%s 1 %c %cthis (edge=%d) {%g,%g %g,%g}"
+ " < rh (edge=%d) {%g,%g %g,%g} upls=(%d)\n", __FUNCTION__,
+ rh.fBelow.fY <= fBelow.fY && fBelow != rh.fBelow ? 'B' : 'A',
+ (check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX)
+ < (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX) ? ' '
+ : '!', ID(), fAbove.fX, fAbove.fY, fBelow.fX, fBelow.fY,
+ rh.ID(), rh.fAbove.fX, rh.fAbove.fY, rh.fBelow.fX, rh.fBelow.fY,
+ UlpsDiff((check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX),
+ (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX)));
+ #endif
+ #if ASSERT_ON_ULPS
+ int ulps = UlpsDiff((check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX),
+ (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX));
+ SkASSERT((unsigned) ulps == 0x80000000 || ulps == 0 || ulps > 32);
+ #endif
return (check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX)
< (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX);
}
// FIXME: need to compute distance, not check for points equal
const SkPoint& check = fBelow.fY <= rh.fBelow.fY
&& fBelow != rh.fBelow ? fBelow : fAbove;
- if (gDebugLessThan) {
- SkDebugf("%s > %c %cthis (%d){%1.2g,%1.2g %1.2g,%1.2g}"
- " < rh (%d){%1.2g,%1.2g %1.2g,%1.2g}\n", __FUNCTION__,
- fBelow.fY <= rh.fBelow.fY & fBelow != rh.fBelow ? 'B' : 'A',
- (rh.fBelow.fY - rh.fAbove.fY) * (check.fX - rh.fAbove.fX)
- < (check.fY - rh.fAbove.fY) * (rh.fBelow.fX - rh.fAbove.fX)
- ? ' ' : '!',
- fIndex, fAbove.fX, fAbove.fY, fBelow.fX, fBelow.fY,
- rh.fIndex, rh.fAbove.fX, rh.fAbove.fY,
- rh.fBelow.fX, rh.fBelow.fY);
- }
+ #if COMPARE_DOUBLE
+ SkASSERT(((rh.fBelow.fY - rh.fAbove.fY) * (check.fX - rh.fAbove.fX)
+ < (check.fY - rh.fAbove.fY) * (rh.fBelow.fX - rh.fAbove.fX))
+ == ((rh.fDBelow.y - rh.fDAbove.y) * (check.fX - rh.fDAbove.x)
+ < (check.fY - rh.fDAbove.y) * (rh.fDBelow.x - rh.fDAbove.x)));
+ #endif
+ #if DEBUG_ACTIVE_LESS_THAN
+ SkDebugf("%s 2 %c %cthis (edge=%d) {%g,%g %g,%g}"
+ " < rh (edge=%d) {%g,%g %g,%g} upls=(%d)\n", __FUNCTION__,
+ fBelow.fY <= rh.fBelow.fY & fBelow != rh.fBelow ? 'B' : 'A',
+ (rh.fBelow.fY - rh.fAbove.fY) * (check.fX - rh.fAbove.fX)
+ < (check.fY - rh.fAbove.fY) * (rh.fBelow.fX - rh.fAbove.fX)
+ ? ' ' : '!', ID(), fAbove.fX, fAbove.fY, fBelow.fX, fBelow.fY,
+ rh.ID(), rh.fAbove.fX, rh.fAbove.fY, rh.fBelow.fX, rh.fBelow.fY,
+ UlpsDiff((rh.fBelow.fY - rh.fAbove.fY) * (check.fX - rh.fAbove.fX),
+ (check.fY - rh.fAbove.fY) * (rh.fBelow.fX - rh.fAbove.fX)));
+ #endif
+ #if ASSERT_ON_ULPS
+ int ulps = UlpsDiff((rh.fBelow.fY - rh.fAbove.fY) * (check.fX - rh.fAbove.fX),
+ (check.fY - rh.fAbove.fY) * (rh.fBelow.fX - rh.fAbove.fX));
+ SkASSERT((unsigned) ulps == 0x80000000 || ulps == 0 || ulps > 32);
+ #endif
return (rh.fBelow.fY - rh.fAbove.fY) * (check.fX - rh.fAbove.fX)
< (check.fY - rh.fAbove.fY) * (rh.fBelow.fX - rh.fAbove.fX);
}
+
+ // If a pair of edges are nearly coincident for some span, add a T in the
+ // edge so it can be shortened to match the other edge. Note that another
+ // approach is to trim the edge after it is added to the OutBuilder list --
+ // FIXME: since this has no effect if the edge is already done (i.e.,
+ // fYBottom >= y) maybe this can only be done by calling trimLine later.
+ void addTatYBelow(SkScalar y) {
+ if (fBelow.fY <= y || fYBottom >= y) {
+ return;
+ }
+ addTatYInner(y);
+ fFixBelow = true;
+ }
+
+ void addTatYAbove(SkScalar y) {
+ if (fBelow.fY <= y) {
+ return;
+ }
+ addTatYInner(y);
+ }
+
+ void addTatYInner(SkScalar y) {
+ double ts[2];
+ SkScalar left = fWorkEdge.fPts[0].fX;
+ SkScalar right = fWorkEdge.fPts[1].fX;
+ if (left > right) {
+ SkTSwap(left, right);
+ }
+ int pts = LineIntersect(fWorkEdge.fPts, left, right, y, ts);
+ SkASSERT(pts == 1);
+ // An ActiveEdge or WorkEdge has no need to modify the T values computed
+ // in the InEdge, except in the following case. If a pair of edges are
+ // nearly coincident, this may not be detected when the edges are
+ // intersected. Later, when sorted, and this near-coincidence is found,
+ // an additional t value must be added, requiring the cast below.
+ InEdge* writable = const_cast<InEdge*>(fWorkEdge.fEdge);
+ int insertedAt = writable->add(ts, pts, fWorkEdge.verbIndex());
+ if (insertedAt >= 0) {
+ if (insertedAt + 1 < fTIndex) {
+ SkASSERT(insertedAt + 2 == fTIndex);
+ --fTIndex;
+ }
+ }
+ }
bool advanceT() {
SkASSERT(fTIndex <= fTs->count());
return ++fTIndex <= fTs->count();
}
-
+
bool advance() {
// FIXME: flip sense of next
bool result = fWorkEdge.advance();
@@ -766,6 +1035,23 @@
LineXYAtT(fWorkEdge.fPts, tAbove, &fAbove);
double tBelow = t(fTIndex - ~add);
LineXYAtT(fWorkEdge.fPts, tBelow, &fBelow);
+ SkASSERT(tAbove != tBelow);
+// maybe the following is the right sort of thing to do, but it's fragile and
+// it breaks testSimplifySkinnyTriangle4
+#if 0
+ if (fAbove == fBelow && !add) {
+ tBelow = t(fTIndex - ~add + 1);
+ LineXYAtT(fWorkEdge.fPts, tBelow, &fBelow);
+ }
+#endif
+ #if COMPARE_DOUBLE
+ LineXYAtT(fWorkEdge.fPts, tAbove, &fDAbove);
+ LineXYAtT(fWorkEdge.fPts, tBelow, &fDBelow);
+ #endif
+ #if DEBUG_ABOVE_BELOW
+ fTAbove = tAbove;
+ fTBelow = tBelow;
+ #endif
break;
}
default:
@@ -774,10 +1060,17 @@
}
}
- bool done(SkScalar y) {
+ bool done(SkScalar y) const {
return fDone || fYBottom > y;
}
+ void fixBelow() {
+ if (fFixBelow) {
+ LineXYAtT(fWorkEdge.fPts, nextT(), &fBelow);
+ fFixBelow = false;
+ }
+ }
+
void init(const InEdge* edge) {
fWorkEdge.init(edge);
initT();
@@ -802,7 +1095,9 @@
// t values, since the same t values could exist intersecting non-coincident
// edges.
bool isCoincidentWith(const ActiveEdge* edge, SkScalar y) const {
- if (fAbove != edge->fAbove || fBelow != edge->fBelow) {
+
+ if (!fAbove.equalsWithinTolerance(edge->fAbove, MIN_PT_DELTA)
+ || !fBelow.equalsWithinTolerance(edge->fBelow, MIN_PT_DELTA)) {
return false;
}
uint8_t verb = fDone ? fWorkEdge.lastVerb() : fWorkEdge.verb();
@@ -822,6 +1117,19 @@
return false;
}
+ // The shortest close call edge should be moved into a position where
+ // it contributes if the winding is transitioning to or from zero.
+ bool swapClose(const ActiveEdge* next, int prev, int wind, int mask) const {
+ if ((prev & mask) == 0 || (wind & mask) == 0) {
+ return next->fBelow.fY < fBelow.fY;
+ }
+ int nextWinding = wind + next->fWorkEdge.winding();
+ if ((nextWinding & mask) == 0) {
+ return fBelow.fY < next->fBelow.fY;
+ }
+ return false;
+ }
+
bool swapCoincident(const ActiveEdge* edge, SkScalar bottom) const {
if (fBelow.fY >= bottom || fDone || edge->fDone) {
return false;
@@ -841,8 +1149,32 @@
}
return false;
}
+
+ bool tooCloseToCall(const ActiveEdge* edge) const {
+ int ulps;
+ // FIXME: don't compare points for equality
+ // OPTIMIZATION: refactor to make one call to UlpsDiff
+ if (edge->fAbove.fY - fAbove.fY > fBelow.fY - edge->fAbove.fY
+ && fBelow.fY < edge->fBelow.fY
+ || fAbove.fY - edge->fAbove.fY < edge->fBelow.fY - fAbove.fY
+ && edge->fBelow.fY < fBelow.fY) {
+ const SkPoint& check = edge->fBelow.fY <= fBelow.fY
+ && fBelow != edge->fBelow ? edge->fBelow :
+ edge->fAbove;
+ ulps = UlpsDiff((check.fY - fAbove.fY) * (fBelow.fX - fAbove.fX),
+ (fBelow.fY - fAbove.fY) * (check.fX - fAbove.fX));
+ } else {
+ const SkPoint& check = fBelow.fY <= edge->fBelow.fY
+ && fBelow != edge->fBelow ? fBelow : fAbove;
+ ulps = UlpsDiff((edge->fBelow.fY - edge->fAbove.fY)
+ * (check.fX - edge->fAbove.fX),
+ (check.fY - edge->fAbove.fY)
+ * (edge->fBelow.fX - edge->fAbove.fX));
+ }
+ return ulps >= 0 && ulps <= 32;
+ }
- double nextT() {
+ double nextT() const {
SkASSERT(fTIndex <= fTs->count());
return t(fTIndex + 1);
}
@@ -867,15 +1199,31 @@
return (*fTs)[tIndex - 1];
}
+ // FIXME: debugging only
+ int ID() {
+ return fWorkEdge.fEdge->fID;
+ }
+
+public:
WorkEdge fWorkEdge;
const SkTDArray<double>* fTs;
SkPoint fAbove;
SkPoint fBelow;
+#if COMPARE_DOUBLE
+ _Point fDAbove;
+ _Point fDBelow;
+#endif
+#if DEBUG_ABOVE_BELOW
+ double fTAbove;
+ double fTBelow;
+#endif
SkScalar fYBottom;
+ int fCoincident;
int fTIndex;
- bool fSkip;
+ bool fSkip; // OPTIMIZATION: use bitfields?
+ bool fCloseCall;
bool fDone;
- int fIndex; // REMOVE: debugging only
+ bool fFixBelow;
};
static void addToActive(SkTDArray<ActiveEdge>& activeEdges, const InEdge* edge) {
@@ -892,32 +1240,49 @@
// Find any intersections in the range of active edges. A pair of edges, on
// either side of another edge, may change the winding contribution for part of
// the edge.
-// OPTIMIZATION: Another approach would be to keep horizontal edges just for
+// Keep horizontal edges just for
// the purpose of computing when edges change their winding contribution, since
// this is essentially computing the horizontal intersection.
-static void addBottomT(InEdge** currentPtr, InEdge** lastPtr, SkScalar bottom) {
- InEdge** testPtr = currentPtr;
- InEdge* test = *testPtr;
- while (testPtr != lastPtr) {
- if (test->fBounds.fBottom > bottom) {
- WorkEdge wt;
- wt.init(test);
+static void addBottomT(InEdge** currentPtr, InEdge** lastPtr,
+ HorizontalEdge** horizontal) {
+ InEdge** testPtr = currentPtr - 1;
+ HorizontalEdge* horzEdge = *horizontal;
+ SkScalar left = horzEdge->fLeft;
+ SkScalar bottom = horzEdge->fY;
+ while (++testPtr != lastPtr) {
+ InEdge* test = *testPtr;
+ if (test->fBounds.fBottom <= bottom || test->fBounds.fRight <= left) {
+ continue;
+ }
+ WorkEdge wt;
+ wt.init(test);
+ do {
+ HorizontalEdge** sorted = horizontal;
+ horzEdge = *sorted;
do {
- // OPTIMIZATION: if bottom intersection does not change
- // the winding on either side of the split, don't intersect
if (wt.verb() == SkPath::kLine_Verb) {
double wtTs[2];
- int pts = LineIntersect(wt.fPts, bottom, wtTs);
+ int pts = LineIntersect(wt.fPts, horzEdge->fLeft,
+ horzEdge->fRight, horzEdge->fY, wtTs);
if (pts) {
+#if DEBUG_ADD_BOTTOM_TS
+ SkDebugf("%s y=%g wtTs[0]=%g (%g,%g, %g,%g)\n", __FUNCTION__,
+ horzEdge->fY, wtTs[0], wt.fPts[0].fX, wt.fPts[0].fY,
+ wt.fPts[1].fX, wt.fPts[1].fY);
+ if (pts == 2) {
+ SkDebugf("%s wtTs[1]=%g\n", __FUNCTION__, wtTs[1]);
+ }
+#endif
test->add(wtTs, pts, wt.verbIndex());
}
} else {
// FIXME: add all curve types
SkASSERT(0);
}
- } while (wt.advance());
- }
- test = *++testPtr;
+ horzEdge = *++sorted;
+ } while (horzEdge->fY == bottom
+ && horzEdge->fLeft <= test->fBounds.fRight);
+ } while (wt.advance());
}
}
@@ -943,6 +1308,27 @@
double wtTs[2], wnTs[2];
int pts = LineIntersect(wt.fPts, wn.fPts, wtTs, wnTs);
if (pts) {
+#if DEBUG_ADD_INTERSECTING_TS
+ SkPoint wtOutPt, wnOutPt;
+ LineXYAtT(wt.fPts, wtTs[0], &wtOutPt);
+ LineXYAtT(wn.fPts, wnTs[0], &wnOutPt);
+ SkDebugf("%s wtTs[0]=%g (%g,%g, %g,%g) (%g,%g) (%d,%d)\n",
+ __FUNCTION__,
+ wtTs[0], wt.fPts[0].fX, wt.fPts[0].fY,
+ wt.fPts[1].fX, wt.fPts[1].fY, wtOutPt.fX, wtOutPt.fY,
+ test->fID, next->fID);
+ if (pts == 2) {
+ SkDebugf("%s wtTs[1]=%g\n", __FUNCTION__, wtTs[1]);
+ }
+ SkDebugf("%s wnTs[0]=%g (%g,%g, %g,%g) (%g,%g) (%d,%d)\n",
+ __FUNCTION__,
+ wnTs[0], wn.fPts[0].fX, wn.fPts[0].fY,
+ wn.fPts[1].fX, wn.fPts[1].fY, wnOutPt.fX, wnOutPt.fY,
+ test->fID, next->fID);
+ if (pts == 2) {
+ SkDebugf("%s wnTs[1]=%g\n", __FUNCTION__, wnTs[1]);
+ }
+#endif
test->add(wtTs, pts, wt.verbIndex());
next->add(wnTs, pts, wn.verbIndex());
}
@@ -955,20 +1341,22 @@
}
}
-static InEdge** advanceEdges(SkTDArray<ActiveEdge>& activeEdges,
+static InEdge** advanceEdges(SkTDArray<ActiveEdge>* activeEdges,
InEdge** currentPtr, InEdge** lastPtr, SkScalar y) {
InEdge** testPtr = currentPtr - 1;
while (++testPtr != lastPtr) {
if ((*testPtr)->fBounds.fBottom > y) {
continue;
}
- InEdge* test = *testPtr;
- ActiveEdge* activePtr = activeEdges.begin() - 1;
- ActiveEdge* lastActive = activeEdges.end();
- while (++activePtr != lastActive) {
- if (activePtr->fWorkEdge.fEdge == test) {
- activeEdges.remove(activePtr - activeEdges.begin());
- break;
+ if (activeEdges) {
+ InEdge* test = *testPtr;
+ ActiveEdge* activePtr = activeEdges->begin() - 1;
+ ActiveEdge* lastActive = activeEdges->end();
+ while (++activePtr != lastActive) {
+ if (activePtr->fWorkEdge.fEdge == test) {
+ activeEdges->remove(activePtr - activeEdges->begin());
+ break;
+ }
}
}
if (testPtr == currentPtr) {
@@ -978,9 +1366,17 @@
return currentPtr;
}
+// OPTIMIZE: inline?
+static HorizontalEdge** advanceHorizontal(HorizontalEdge** edge, SkScalar y) {
+ while ((*edge)->fY < y) {
+ ++edge;
+ }
+ return edge;
+}
+
// compute bottom taking into account any intersected edges
-static void computeInterceptBottom(SkTDArray<ActiveEdge>& activeEdges,
- SkScalar y, SkScalar& bottom) {
+static SkScalar computeInterceptBottom(SkTDArray<ActiveEdge>& activeEdges,
+ SkScalar y, SkScalar bottom) {
ActiveEdge* activePtr = activeEdges.begin() - 1;
ActiveEdge* lastActive = activeEdges.end();
while (++activePtr != lastActive) {
@@ -1019,10 +1415,11 @@
}
} while (wt.advance());
}
+ return bottom;
}
static SkScalar findBottom(InEdge** currentPtr,
- InEdge** edgeListEnd, SkTDArray<ActiveEdge>& activeEdges, SkScalar y,
+ InEdge** edgeListEnd, SkTDArray<ActiveEdge>* activeEdges, SkScalar y,
bool asFill, InEdge**& testPtr) {
InEdge* current = *currentPtr;
SkScalar bottom = current->fBounds.fBottom;
@@ -1046,7 +1443,9 @@
if (bottom > testBottom) {
bottom = testBottom;
}
- addToActive(activeEdges, test);
+ if (activeEdges) {
+ addToActive(*activeEdges, test);
+ }
}
test = *++testPtr;
}
@@ -1067,12 +1466,26 @@
QSort<InEdge>(edgeList.begin(), edgeList.end() - 1);
}
+static void makeHorizontalList(SkTDArray<HorizontalEdge>& edges,
+ HorizontalEdge& edgeSentinel, SkTDArray<HorizontalEdge*>& edgeList) {
+ size_t edgeCount = edges.count();
+ if (edgeCount == 0) {
+ return;
+ }
+ for (size_t index = 0; index < edgeCount; ++index) {
+ *edgeList.append() = &edges[index];
+ }
+ edgeSentinel.fLeft = edgeSentinel.fRight = edgeSentinel.fY = SK_ScalarMax;
+ *edgeList.append() = &edgeSentinel;
+ QSort<HorizontalEdge>(edgeList.begin(), edgeList.end() - 1);
+}
static void skipCoincidence(int lastWinding, int winding, int windingMask,
ActiveEdge* activePtr, ActiveEdge* firstCoincident) {
if (((lastWinding & windingMask) == 0) ^ (winding & windingMask) != 0) {
return;
}
+ // FIXME: ? shouldn't this be if (lastWinding & windingMask) ?
if (lastWinding) {
activePtr->fSkip = false;
} else {
@@ -1081,66 +1494,162 @@
}
static void sortHorizontal(SkTDArray<ActiveEdge>& activeEdges,
- SkTDArray<ActiveEdge*>& edgeList, int windingMask, SkScalar y,
- SkScalar bottom) {
+ SkTDArray<ActiveEdge*>& edgeList, SkScalar y) {
+ const int tab = 3; // FIXME: debugging only
size_t edgeCount = activeEdges.count();
if (edgeCount == 0) {
return;
}
+#if DEBUG_SORT_HORIZONTAL
+ SkDebugf("%s y=%1.9g\n", __FUNCTION__, y);
+#endif
size_t index;
for (index = 0; index < edgeCount; ++index) {
ActiveEdge& activeEdge = activeEdges[index];
- activeEdge.calcLeft(y);
- activeEdge.fSkip = false;
- activeEdge.fIndex = index; // REMOVE: debugging only
+ do {
+ activeEdge.calcLeft(y);
+ // skip segments that don't span y
+ if (activeEdge.fAbove != activeEdge.fBelow) {
+ break;
+ }
+ if (activeEdge.fDone) {
+#if DEBUG_SORT_HORIZONTAL
+ SkDebugf("%*s edge=%d done\n", tab, "", activeEdge.ID());
+#endif
+ goto nextEdge;
+ }
+#if DEBUG_SORT_HORIZONTAL
+ SkDebugf("%*s edge=%d above==below\n", tab, "", activeEdge.ID());
+#endif
+ } while (activeEdge.advanceT() || activeEdge.advance());
+#if DEBUG_SORT_HORIZONTAL
+ SkDebugf("%*s edge=%d above=(%1.9g,%1.9g) (%1.9g) below=(%1.9g,%1.9g)"
+ " (%1.9g)\n", tab, "", activeEdge.ID(),
+ activeEdge.fAbove.fX, activeEdge.fAbove.fY, activeEdge.fTAbove,
+ activeEdge.fBelow.fX, activeEdge.fBelow.fY, activeEdge.fTBelow);
+#endif
+ activeEdge.fSkip = activeEdge.fCloseCall = activeEdge.fFixBelow = false;
*edgeList.append() = &activeEdge;
+nextEdge:
+ ;
}
QSort<ActiveEdge>(edgeList.begin(), edgeList.end() - 1);
- // remove coincident edges
- // OPTIMIZE: remove edges? This is tricky because the current logic expects
- // the winding count to be maintained while skipping coincident edges. In
- // addition to removing the coincident edges, the remaining edges would need
- // to have a different winding value, possibly different per intercept span.
- int lastWinding = 0;
- bool lastSkipped = false;
+}
+
+// remove coincident edges
+// OPTIMIZE: remove edges? This is tricky because the current logic expects
+// the winding count to be maintained while skipping coincident edges. In
+// addition to removing the coincident edges, the remaining edges would need
+// to have a different winding value, possibly different per intercept span.
+static SkScalar adjustCoincident(SkTDArray<ActiveEdge*>& edgeList,
+ int windingMask, SkScalar y, SkScalar bottom, OutEdgeBuilder& outBuilder)
+{
+#if DEBUG_ADJUST_COINCIDENT
+ SkDebugf("%s y=%1.9g bottom=%1.9g\n", __FUNCTION__, y, bottom);
+#endif
+ size_t edgeCount = edgeList.count();
+ if (edgeCount == 0) {
+ return bottom;
+ }
ActiveEdge* activePtr = edgeList[0];
- ActiveEdge* firstCoincident = NULL;
- int winding = 0;
+ size_t index;
+ bool foundCoincident = false;
+ int firstIndex = 0;
for (index = 1; index < edgeCount; ++index) {
+ ActiveEdge* nextPtr = edgeList[index];
+ bool closeCall = false;
+ activePtr->fCoincident = firstIndex;
+ if (activePtr->isCoincidentWith(nextPtr, y)
+ || (closeCall = activePtr->tooCloseToCall(nextPtr))) {
+ activePtr->fSkip = nextPtr->fSkip = foundCoincident = true;
+ activePtr->fCloseCall = nextPtr->fCloseCall = closeCall;
+ } else {
+ firstIndex = index;
+ }
+ activePtr = nextPtr;
+ }
+ activePtr->fCoincident = firstIndex;
+ if (!foundCoincident) {
+ return bottom;
+ }
+ int winding = 0;
+ activePtr = edgeList[0];
+ for (index = 1; index < edgeCount; ++index) {
+ int priorWinding = winding;
winding += activePtr->fWorkEdge.winding();
ActiveEdge* nextPtr = edgeList[index];
- if (activePtr->isCoincidentWith(nextPtr, y)) {
+ if (activePtr->fCoincident == nextPtr->fCoincident) {
// the coincident edges may not have been sorted above -- advance
// the edges and resort if needed
// OPTIMIZE: if sorting is done incrementally as new edges are added
// and not all at once as is done here, fold this test into the
// current less than test.
- if (activePtr->swapCoincident(nextPtr, bottom)) {
+ if (activePtr->fCloseCall ? activePtr->swapClose(nextPtr,
+ priorWinding, winding, windingMask)
+ : activePtr->swapCoincident(nextPtr, bottom)) {
winding -= activePtr->fWorkEdge.winding();
SkTSwap<ActiveEdge*>(edgeList[index - 1], edgeList[index]);
SkTSwap<ActiveEdge*>(activePtr, nextPtr);
winding += activePtr->fWorkEdge.winding();
}
- if (!firstCoincident) {
- firstCoincident = activePtr;
- }
- activePtr->fSkip = nextPtr->fSkip = lastSkipped = true;
- } else if (lastSkipped) {
- skipCoincidence(lastWinding, winding, windingMask, activePtr,
- firstCoincident);
- lastSkipped = false;
- firstCoincident = NULL;
- }
- if (!lastSkipped) {
- lastWinding = winding;
}
activePtr = nextPtr;
}
- if (lastSkipped) {
+ int firstCoincidentWinding = 0;
+ ActiveEdge* firstCoincident = NULL;
+ winding = 0;
+ activePtr = edgeList[0];
+ for (index = 1; index < edgeCount; ++index) {
+ int priorWinding = winding;
winding += activePtr->fWorkEdge.winding();
- skipCoincidence(lastWinding, winding, windingMask, activePtr,
+ ActiveEdge* nextPtr = edgeList[index];
+ if (activePtr->fCoincident == nextPtr->fCoincident) {
+ if (!firstCoincident) {
+ firstCoincident = activePtr;
+ firstCoincidentWinding = priorWinding;
+ }
+ if (activePtr->fCloseCall) {
+ // If one of the edges has already been added to out as a non
+ // coincident edge, trim it back to the top of this span
+ if (outBuilder.trimLine(y, activePtr->ID())) {
+ activePtr->addTatYAbove(y);
+ activePtr->fYBottom = y;
+ }
+ if (outBuilder.trimLine(y, nextPtr->ID())) {
+ nextPtr->addTatYAbove(y);
+ nextPtr->fYBottom = y;
+ }
+ // add missing t values so edges can be the same length
+ SkScalar testY = activePtr->fBelow.fY;
+ nextPtr->addTatYBelow(testY);
+ if (bottom > testY && testY > y) {
+ bottom = testY;
+ }
+ testY = nextPtr->fBelow.fY;
+ activePtr->addTatYBelow(testY);
+ if (bottom > testY && testY > y) {
+ bottom = testY;
+ }
+ }
+ } else if (firstCoincident) {
+ skipCoincidence(firstCoincidentWinding, winding, windingMask,
+ activePtr, firstCoincident);
+ firstCoincident = NULL;
+ }
+ activePtr = nextPtr;
+ }
+ if (firstCoincident) {
+ winding += activePtr->fWorkEdge.winding();
+ skipCoincidence(firstCoincidentWinding, winding, windingMask, activePtr,
firstCoincident);
}
+ // fix up the bottom for close call edges. OPTIMIZATION: maybe this could
+ // be in the loop above, but moved here since loop above reads fBelow and
+ // it felt unsafe to write it in that loop
+ for (index = 0; index < edgeCount; ++index) {
+ (edgeList[index])->fixBelow();
+ }
+ return bottom;
}
// stitch edge and t range that satisfies operation
@@ -1149,24 +1658,52 @@
int winding = 0;
ActiveEdge** activeHandle = edgeList.begin() - 1;
ActiveEdge** lastActive = edgeList.end();
+ const int tab = 7; // FIXME: debugging only
if (gShowDebugf) {
- SkDebugf("%s y=%g bottom=%g\n", __FUNCTION__, y, bottom);
+ SkDebugf("%s y=%1.9g bottom=%1.9g\n", __FUNCTION__, y, bottom);
}
while (++activeHandle != lastActive) {
ActiveEdge* activePtr = *activeHandle;
const WorkEdge& wt = activePtr->fWorkEdge;
int lastWinding = winding;
winding += wt.winding();
+ if (gShowDebugf) {
+ SkDebugf("%*s edge=%d lastWinding=%d winding=%d skip=%d close=%d"
+#if DEBUG_ABOVE_BELOW
+ " above=%1.9g below=%1.9g"
+#endif
+ "\n",
+ tab-4, "", activePtr->ID(), lastWinding,
+ winding, activePtr->fSkip, activePtr->fCloseCall
+#if DEBUG_ABOVE_BELOW
+ , activePtr->fTAbove, activePtr->fTBelow
+#endif
+ );
+ }
if (activePtr->done(y)) {
+ if (activePtr->fCloseCall) {
+ // if the top has already advanced, trim the last edge add
+ // FIXME: not so simple
+ outBuilder.trimLine(y, activePtr->ID());
+ activePtr->fYBottom = y;
+ }
// FIXME: if this is successful, rewrite done to take bottom as well
if (activePtr->fDone) {
+ if (gShowDebugf) {
+ SkDebugf("%*s activePtr->fDone\n", tab, "");
+ }
continue;
}
if (activePtr->fYBottom >= bottom) {
+ if (gShowDebugf) {
+ SkDebugf("%*s activePtr->fYBottom=%1.9g >= bottom\n", tab, "",
+ activePtr->fYBottom);
+ }
continue;
}
if (0) {
- SkDebugf("%s bot %g,%g\n", __FUNCTION__, activePtr->fYBottom, bottom);
+ SkDebugf("%s bot %1.9g,%1.9g\n", __FUNCTION__, activePtr->fYBottom,
+ bottom);
}
}
int opener = (lastWinding & windingMask) == 0;
@@ -1175,6 +1712,11 @@
bool inWinding = opener | closer;
SkPoint clippedPts[2];
const SkPoint* clipped = NULL;
+ #if COMPARE_DOUBLE
+ _Line dPoints;
+ _Line clippedDPts;
+ const _Point* dClipped = NULL;
+ #endif
uint8_t verb = wt.verb();
bool moreToDo, aboveBottom;
do {
@@ -1192,31 +1734,93 @@
// clipped[1].fY
LineSubDivide(points, currentT, nextT, clippedPts);
clipped = clippedPts;
+ #if COMPARE_DOUBLE
+ LineSubDivide(points, currentT, nextT, clippedDPts);
+ dClipped = clippedDPts;
+ #endif
} else {
clipped = points;
+ #if COMPARE_DOUBLE
+ dPoints[0].x = SkScalarToDouble(points[0].fX);
+ dPoints[0].y = SkScalarToDouble(points[1].fY);
+ dPoints[1].x = SkScalarToDouble(points[0].fX);
+ dPoints[1].y = SkScalarToDouble(points[1].fY);
+ dClipped = dPoints;
+ #endif
}
if (inWinding && !activePtr->fSkip) {
if (gShowDebugf) {
- SkDebugf("%s line %g,%g %g,%g\n", __FUNCTION__,
+ SkDebugf("%*s line %1.9g,%1.9g %1.9g,%1.9g edge=%d"
+ " v=%d t=(%1.9g,%1.9g)\n", tab, "",
clipped[0].fX, clipped[0].fY,
- clipped[1].fX, clipped[1].fY);
+ clipped[1].fX, clipped[1].fY,
+ activePtr->ID(),
+ activePtr->fWorkEdge.fVerb
+ - activePtr->fWorkEdge.fEdge->fVerbs.begin(),
+ currentT, nextT);
}
- outBuilder.addLine(clipped);
+ outBuilder.addLine(clipped, activePtr->fWorkEdge.fEdge->fID,
+ activePtr->fCloseCall);
+ } else {
+ if (gShowDebugf) {
+ SkDebugf("%*s skip %1.9g,%1.9g %1.9g,%1.9g"
+ " edge=%d v=%d t=(%1.9g,%1.9g)\n", tab, "",
+ clipped[0].fX, clipped[0].fY,
+ clipped[1].fX, clipped[1].fY,
+ activePtr->ID(),
+ activePtr->fWorkEdge.fVerb
+ - activePtr->fWorkEdge.fEdge->fVerbs.begin(),
+ currentT, nextT);
+ }
}
+ // by advancing fAbove/fBelow, the next call to sortHorizontal
+ // will use these values if they're still valid instead of
+ // recomputing
+ #if COMPARE_DOUBLE
+ SkASSERT((clipped[1].fY > activePtr->fBelow.fY
+ && bottom >= activePtr->fBelow.fY)
+ == (dClipped[1].y > activePtr->fDBelow.y
+ && bottom >= activePtr->fDBelow.y));
+ #endif
if (clipped[1].fY > activePtr->fBelow.fY
&& bottom >= activePtr->fBelow.fY ) {
activePtr->fAbove = activePtr->fBelow;
activePtr->fBelow = clipped[1];
+ #if COMPARE_DOUBLE
+ activePtr->fDAbove = activePtr->fDBelow;
+ activePtr->fDBelow = dClipped[1];
+ #endif
+ #if DEBUG_ABOVE_BELOW
+ activePtr->fTAbove = activePtr->fTBelow;
+ activePtr->fTBelow = nextT;
+ #endif
}
- activePtr->fSkip = false;
} else {
// FIXME: add all curve types
SkASSERT(0);
}
currentT = nextT;
moreToDo = activePtr->advanceT();
- activePtr->fYBottom = clipped[verb].fY;
- aboveBottom = activePtr->fYBottom < bottom;
+ activePtr->fYBottom = clipped[verb].fY; // was activePtr->fCloseCall ? bottom :
+
+ // clearing the fSkip/fCloseCall bit here means that trailing edges
+ // fall out of sync, if one edge is long and another is a series of short pieces
+ // if fSkip/fCloseCall is set, need to recompute coincidence/too-close-to-call
+ // after advancing
+ // another approach would be to restrict bottom to smaller part of close call
+ // maybe this is already happening with coincidence when intersection is computed,
+ // and needs to be added to the close call computation as well
+ // this is hard to do because that the bottom is important is not known when
+ // the lines are intersected; only when the computation for edge sorting is done
+ // does the need for new bottoms become apparent.
+ // maybe this is good incentive to scrap the current sort and do an insertion
+ // sort that can take this into consideration when the x value is computed
+
+ // FIXME: initialized in sortHorizontal, cleared here as well so
+ // that next edge is not skipped -- but should skipped edges ever
+ // continue? (probably not)
+ aboveBottom = clipped[verb].fY < bottom && !activePtr->fCloseCall; // TEST: added close call
+ activePtr->fSkip = activePtr->fCloseCall = false;
} while (moreToDo & aboveBottom);
} while ((moreToDo || activePtr->advance()) & aboveBottom);
}
@@ -1233,32 +1837,69 @@
// twice that have y extrema's on top) and detect crossings -- look for raw
// bounds that cross over, then tight bounds that cross
SkTArray<InEdge> edges;
- InEdgeBuilder builder(path, asFill, edges);
+ SkTDArray<HorizontalEdge> horizontalEdges;
+ InEdgeBuilder builder(path, asFill, edges, horizontalEdges);
SkTDArray<InEdge*> edgeList;
InEdge edgeSentinel;
makeEdgeList(edges, edgeSentinel, edgeList);
+ SkTDArray<HorizontalEdge*> horizontalList;
+ HorizontalEdge horizontalSentinel;
+ makeHorizontalList(horizontalEdges, horizontalSentinel, horizontalList);
InEdge** currentPtr = edgeList.begin();
if (!currentPtr) {
return;
}
- // walk the sorted edges from top to bottom, computing accumulated winding
- SkTDArray<ActiveEdge> activeEdges;
- OutEdgeBuilder outBuilder(asFill);
+ // find all intersections between edges
+// beyond looking for horizontal intercepts, we need to know if any active edges
+// intersect edges below 'bottom', but above the active edge segment.
+// maybe it makes more sense to compute all intercepts before doing anything
+// else, since the intercept list is long-lived, at least in the current design.
SkScalar y = (*currentPtr)->fBounds.fTop;
+ HorizontalEdge** currentHorizontal = horizontalList.begin();
do {
InEdge** lastPtr = currentPtr; // find the edge below the bottom of the first set
SkScalar bottom = findBottom(currentPtr, edgeList.end(),
- activeEdges, y, asFill, lastPtr);
+ NULL, y, asFill, lastPtr);
if (lastPtr > currentPtr) {
- addBottomT(currentPtr, lastPtr, bottom);
+ if (currentHorizontal) {
+ if ((*currentHorizontal)->fY < SK_ScalarMax) {
+ addBottomT(currentPtr, lastPtr, currentHorizontal);
+ }
+ currentHorizontal = advanceHorizontal(currentHorizontal, bottom);
+ }
addIntersectingTs(currentPtr, lastPtr);
- computeInterceptBottom(activeEdges, y, bottom);
+ }
+ y = bottom;
+ currentPtr = advanceEdges(NULL, currentPtr, lastPtr, y);
+ } while (*currentPtr != &edgeSentinel);
+
+#if DEBUG_DUMP
+ InEdge** debugPtr = edgeList.begin();
+ do {
+ (*debugPtr++)->dump();
+ } while (*debugPtr != &edgeSentinel);
+#endif
+
+ // walk the sorted edges from top to bottom, computing accumulated winding
+ SkTDArray<ActiveEdge> activeEdges;
+ OutEdgeBuilder outBuilder(asFill);
+ currentPtr = edgeList.begin();
+ y = (*currentPtr)->fBounds.fTop;
+ do {
+ InEdge** lastPtr = currentPtr; // find the edge below the bottom of the first set
+ SkScalar bottom = findBottom(currentPtr, edgeList.end(),
+ &activeEdges, y, asFill, lastPtr);
+ if (lastPtr > currentPtr) {
+ bottom = computeInterceptBottom(activeEdges, y, bottom);
SkTDArray<ActiveEdge*> activeEdgeList;
- sortHorizontal(activeEdges, activeEdgeList, windingMask, y, bottom);
+ sortHorizontal(activeEdges, activeEdgeList, y);
+ bottom = adjustCoincident(activeEdgeList, windingMask, y, bottom,
+ outBuilder);
stitchEdge(activeEdgeList, y, bottom, windingMask, outBuilder);
}
y = bottom;
- currentPtr = advanceEdges(activeEdges, currentPtr, lastPtr, y);
+ // OPTIMIZATION: as edges expire, InEdge allocations could be released
+ currentPtr = advanceEdges(&activeEdges, currentPtr, lastPtr, y);
} while (*currentPtr != &edgeSentinel);
// assemble output path from string of pts, verbs
outBuilder.bridge();
diff --git a/experimental/Intersection/EdgeWalkerPolygons_Mismatches.cpp b/experimental/Intersection/EdgeWalkerPolygons_Mismatches.cpp
new file mode 100644
index 0000000..0054cfb
--- /dev/null
+++ b/experimental/Intersection/EdgeWalkerPolygons_Mismatches.cpp
@@ -0,0 +1,1614 @@
+#include "EdgeWalker_Test.h"
+#include "Intersection_Tests.h"
+
+// edges that didn't match
+struct misMatch {
+ SkPath::FillType fType;
+ int a, b, c, d, e, f, g, h;
+} misMatches[] = {
+/*
+___________________________________|___________________________________
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx__|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx__
+__xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx___|__xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx___
+__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____|__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____
+___xxxxxxxxxx__xxxxxxxxxxxxxx______|___xxxxxxxxxx__xxxxxxxxxxxxxx______
+___xxxxxxx______xxxxxxxxxxx________|___xxxxxxx______xxxxxxxxxxx________
+____xxx__________xxxxxxxxx_________|____xxx__________xxxxxxxxx_________
+____x_____________xxxxxxx__________|____x_____________xxxxxxx__________
+__xx_______________xxxx____________|__xxx______________xxxx____________
+___xx_______________xx_____________|___xx_______________xx_____________
+____________________x______________|____________________x______________
+______x____________xxx_____________|______x____________xxx_____________
+______xxx_________xxxxx____________|______xxx_________xxxxx____________
+_______xxxx_____xxxxxxxx___________|_______xxxx_____xxxxxxxx___________
+_______xxxxxx__xxxxxxxxx___________|_______xxxxxx__xxxxxxxxxx__________
+________xxxxx__xxxxxxxxxx__________|________xxxxx__xxxxxxxxxx__________
+________xxxx_____xxxxxxxxx_________|________xxxx_____xxxxxxxxx_________
+_________xxx_______xxxxxxxx________|_________xxx_______xxxxxxxx________
+_________xxx_________xxxxxxx_______|_________xxx_________xxxxxxx_______
+__________xx____________xxxxx______|__________xx____________xxxxx______
+__________xx______________xxxx_____|__________xx______________xxxx_____
+___________x________________xxx____|___________x________________xxx____
+___________x__________________xx___|___________x__________________xx___
+___________x____________________x__|___________x____________________x__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 0, 3, 9, 13, 1, 2, 4, 15 },
+/*
+___________________________________|___________________________________
+_xxxxxxxxxxx_________xxxxxxxxxxxx__|_xxxxxxxxxxx_________xxxxxxxxxxxx__
+__xxxxxxxxxxx______xxxxxxxxxxxxx___|__xxxxxxxxxxx______xxxxxxxxxxxxx___
+__xxxxxxxxxxxx__xxxxxxxxxxxxxx_____|__xxxxxxxxxxxx__xxxxxxxxxxxxxx_____
+___xxxxxxxxxx__xxxxxxxxxxxxxx______|___xxxxxxxxxx__xxxxxxxxxxxxxx______
+___xxxxxxx______xxxxxxxxxxx________|___xxxxxxx______xxxxxxxxxxx________
+____xxx__________xxxxxxxxx_________|____xxx__________xxxxxxxxx_________
+____x_____________xxxxxxx__________|____x_____________xxxxxxx__________
+__xx_______________xxxx____________|__xxx______________xxxx____________
+___xx_______________xx_____________|___xx_______________xx_____________
+____________________x______________|____________________x______________
+______x____________xxx_____________|______x____________xxx_____________
+______xxx_________xxxxx____________|______xxx_________xxxxx____________
+_______xxxx_____xxxxxxxx___________|_______xxxx_____xxxxxxxx___________
+_______xxxxxx__xxxxxxxxx___________|_______xxxxxx__xxxxxxxxxx__________
+________xxxxx__xxxxxxxxxx__________|________xxxxx__xxxxxxxxxx__________
+________xxxx_____xxxxxxxxx_________|________xxxx_____xxxxxxxxx_________
+_________xxx_______xxxxxxxx________|_________xxx_______xxxxxxxx________
+_________xxx_________xxxxxxx_______|_________xxx_________xxxxxxx_______
+__________xx____________xxxxx______|__________xx____________xxxxx______
+__________xx______________xxxx_____|__________xx______________xxxx_____
+___________x________________xxx____|___________x________________xxx____
+___________x__________________xx___|___________x__________________xx___
+___________x____________________x__|___________x____________________x__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 0, 3, 9, 13, 1, 2, 4, 15 },
+/*
+___________________________________|___________________________________
+_x__________xxxxxxxxx______________|_x__________xxxxxxxxx______________
+__xxx________xxxxxx________________|__xxx________xxxxxx________________
+__xxxxxx______xx___________________|__xxxxxx______xx___________________
+___xxxxxxxx__xx____________________|___xxxxxxxx__xx____________________
+___xxxxxxx____xx___________________|___xxxxxxx____xx___________________
+____xxx_________x__________________|____xxx_________x__________________
+____x_____________x________________|____x_____________x________________
+__xx_______________xxx_____________|__xxx______________xxx_____________
+___xx_______________xx_____________|___xx_______________xx_____________
+____________________x______________|____________________x______________
+______x____________xxx_____________|______x____________xxx_____________
+______xxx_________xxxxx____________|______xxx_________xxxxx____________
+_______xxxx_____xxxxxxxx___________|_______xxxx_____xxxxxxxx___________
+_______xxxxxx__xxxxxxxxx___________|_______xxxxxx__xxxxxxxxxx__________
+________xxxxx__xxxxxxxxxx__________|________xxxxx__xxxxxxxxxx__________
+________xxxx_____xxxxxxxxx_________|________xxxx_____xxxxxxxxx_________
+_________xxx_______xxxxxxxx________|_________xxx_______xxxxxxxx________
+_________xxx_________xxxxxxx_______|_________xxx_________xxxxxxx_______
+__________xx____________xxxxx______|__________xx____________xxxxx______
+__________xx______________xxxx_____|__________xx______________xxxx_____
+___________x________________xxx____|___________x________________xxx____
+___________x__________________xx___|___________x__________________xx___
+___________x____________________x__|___________x____________________x__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 0, 6, 9, 13, 1, 2, 4, 15 },
+/*
+___________________________________|___________________________________
+_x__________xxxxxxxxx______________|_x__________xxxxxxxxx______________
+__xxx________xxxxxx________________|__xxx________xxxxxx________________
+__xxxxxx______xx___________________|__xxxxxx______xx___________________
+___xxxxxxxx__xx____________________|___xxxxxxxx__xx____________________
+___xxxxxxx____xx___________________|___xxxxxxx____xx___________________
+____xxx_________x__________________|____xxx_________x__________________
+____x_____________x________________|____x_____________x________________
+__xx_______________xxx_____________|__xxx______________xxx_____________
+___xx_______________xx_____________|___xx_______________xx_____________
+____________________x______________|____________________x______________
+______x____________xxx_____________|______x____________xxx_____________
+______xxx_________xxxxx____________|______xxx_________xxxxx____________
+_______xxxx_____xxxxxxxx___________|_______xxxx_____xxxxxxxx___________
+_______xxxxxx__xxxxxxxxx___________|_______xxxxxx__xxxxxxxxxx__________
+________xxxxx__xxxxxxxxxx__________|________xxxxx__xxxxxxxxxx__________
+________xxxx_____xxxxxxxxx_________|________xxxx_____xxxxxxxxx_________
+_________xxx_______xxxxxxxx________|_________xxx_______xxxxxxxx________
+_________xxx_________xxxxxxx_______|_________xxx_________xxxxxxx_______
+__________xx____________xxxxx______|__________xx____________xxxxx______
+__________xx______________xxxx_____|__________xx______________xxxx_____
+___________x________________xxx____|___________x________________xxx____
+___________x__________________xx___|___________x__________________xx___
+___________x____________________x__|___________x____________________x__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 0, 6, 9, 13, 1, 2, 4, 15 },
+/*
+___________________________________|___________________________________
+_xx__________________x_____________|_xx__________________x_____________
+__xxxxx____________xx______________|__xxxxx____________xx______________
+__xxxxxxxxxx____xxxx_______________|__xxxxxxxxxx____xxxx_______________
+___xxxxxxxxxx___xxx________________|___xxxxxxxxxx___xxx________________
+___xxxxxxx_________x_______________|___xxxxxxx_________x_______________
+____xxx___________xxxxxx___________|____xxx___________xxxxxx___________
+____x____________xxxxxxxxxxx_______|____x____________xxxxxxxxxxx_______
+__xx____________xxxxxxxxxxxxxxxxx__|__xxx___________xxxxxxxxxxxxxxxxx__
+__xxx__________xxxxxxxxxxxxxxxx____|__xxx__________xxxxxxxxxxxxxxxx____
+___xx_________xxxxxxxxxxxx_________|___xx_________xxxxxxxxxxxx_________
+_____x_______xxxxxxxxx_____________|_____x_______xxxxxxxxx_____________
+____________xxxxxx_________________|____________xxxxxx_________________
+_______x___xxx_____________________|_______x___xxx_____________________
+_______xx__________________________|_______xx__________________________
+_____xxx_x_________________________|_____xxx_x_________________________
+_xxxxxxxxxxx_______________________|_xxxxxxxxxxx_______________________
+__xxxxx__xx________________________|__xxxxx__xx________________________
+____xx_____________________________|____xx_____________________________
+________xx_________________________|________xx_________________________
+_____x_xxx_________________________|_____x_xxx_________________________
+____x___xxx________________________|____x___xxx________________________
+___x_____xx________________________|___x_____xx________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 0, 7, 8, 13, 2, 4, 9, 12 },
+/*
+___________________________________|___________________________________
+_xx__________________x_____________|_xx__________________x_____________
+__xxxxx____________xx______________|__xxxxx____________xx______________
+__xxxxxxxxxx____xxxx_______________|__xxxxxxxxxx____xxxx_______________
+___xxxxxxxxxx___xxx________________|___xxxxxxxxxx___xxx________________
+___xxxxxxx_________x_______________|___xxxxxxx_________x_______________
+____xxx___________xxxxxx___________|____xxx___________xxxxxx___________
+____x____________xxxxxxxxxxx_______|____x____________xxxxxxxxxxx_______
+__xx____________xxxxxxxxxxxxxxxxx__|__xxx___________xxxxxxxxxxxxxxxxx__
+__xxx__________xxxxxxxxxxxxxxxx____|__xxx__________xxxxxxxxxxxxxxxx____
+___xx_________xxxxxxxxxxxx_________|___xx_________xxxxxxxxxxxx_________
+_____x_______xxxxxxxxx_____________|_____x_______xxxxxxxxx_____________
+____________xxxxxx_________________|____________xxxxxx_________________
+_______x___xxx_____________________|_______x___xxx_____________________
+_______xx__________________________|_______xx__________________________
+_____xxx_x_________________________|_____xxx_x_________________________
+_xxxxxxxxxxx_______________________|_xxxxxxxxxxx_______________________
+__xxxxx__xx________________________|__xxxxx__xx________________________
+____xx_____________________________|____xx_____________________________
+________xx_________________________|________xx_________________________
+_____x_xxx_________________________|_____x_xxx_________________________
+____x___xxx________________________|____x___xxx________________________
+___x_____xx________________________|___x_____xx________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 0, 7, 8, 13, 2, 4, 9, 12 },
+/*
+___________________________________|___________________________________
+_x_________x_______________________|_x_________x_______________________
+__x_______xxx______________________|__x_______xxx______________________
+___x____xxxxxx_____________________|___x____xxxxxx_____________________
+____xx_xxxxxxxx____________________|____xx_xxxxxxxx____________________
+_____x_xxxxxxxxx___________________|_____x_xxxxxxxxx___________________
+____xx___xxxxxxxx__________________|____xx___xxxxxxxx__________________
+___xxxx___xxxxxxxx_________________|___xxxx___xxxxxxxx_________________
+_xxxxxxx___xxxxxxxx________________|_xxxxxxx____xxxxxxx________________
+__xxxxxxx____xxxxxxx_______________|__xxxxxxx____xxxxxxx_______________
+___xxxxxxx____xxxxxxx______________|___xxxxxxx____xxxxxxx______________
+_____xxxxxx_____xxxxxx_____________|_____xxxxxx_____xxxxxx_____________
+______xxxxxx_____xxxxxx____________|______xxxxxx_____xxxxxx____________
+________xxxxx______xxxxx___________|________xxxxx______xxxxx___________
+_________xxxxx______xxxx___________|_________xxxxx______xxxx___________
+__________xxxxx______xxxx__________|__________xxxxx______xxxx__________
+____________xxx________xxx_________|____________xxx________xxx_________
+_______________x___________xxxxx___|_______________x___________xxxxx___
+____________________________xxx____|____________________________xxx____
+__________________xx_______________|__________________xx_________x_____
+___________________xxxx_____xx_____|___________________xxxx_____xx_____
+____________________xxxxxx_xxxx____|____________________xxxxxx_xxxx____
+_____________________xxxx____xxx___|_____________________xxxx____xxx___
+______________________xx_______xx__|______________________xx_______xx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 0, 10, 11, 14, 1, 4, 9, 15 },
+/*
+___________________________________|___________________________________
+_x_________x_______________________|_x_________x_______________________
+__x_______xxx______________________|__x_______xxx______________________
+___x____xxxxxx_____________________|___x____xxxxxx_____________________
+____xx_xxxxxxxx____________________|____xx_xxxxxxxx____________________
+_____x_xxxxxxxxx___________________|_____x_xxxxxxxxx___________________
+____xx___xxxxxxxx__________________|____xx___xxxxxxxx__________________
+___xxxx___xxxxxxxx_________________|___xxxx___xxxxxxxx_________________
+_xxxxxxx___xxxxxxxx________________|_xxxxxxx____xxxxxxx________________
+__xxxxxxx____xxxxxxx_______________|__xxxxxxx____xxxxxxx_______________
+___xxxxxxx____xxxxxxx______________|___xxxxxxx____xxxxxxx______________
+_____xxxxxx_____xxxxxx_____________|_____xxxxxx_____xxxxxx_____________
+______xxxxxx_____xxxxxx____________|______xxxxxx_____xxxxxx____________
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+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 0, 10, 11, 14, 1, 4, 9, 15 },
+/*
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+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 1, 7, 12, 1, 3, 4, 15 },
+/*
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+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 2, 4, 15, 0, 3, 9, 13 },
+/*
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+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 2, 4, 15, 0, 3, 9, 13 },
+/*
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+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 2, 4, 15, 0, 6, 9, 13 },
+/*
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+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 2, 4, 15, 0, 6, 9, 13 },
+/*
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+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 2, 7, 12, 1, 3, 4, 15 },
+/*
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+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 4, 15, 1, 1, 7, 12 },
+/*
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+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 4, 15, 1, 2, 7, 12 },
+/*
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+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 4, 15, 1, 3, 7, 12 },
+/*
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+___________________________________|___________________________________
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+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 4, 15, 1, 7, 7, 12 },
+/*
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+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 4, 15, 1, 7, 12, 12 },
+/*
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+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 7, 12, 1, 3, 4, 15 },
+/*
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+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 3, 12, 15, 2, 6, 8, 15 },
+/*
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+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 4, 9, 15, 0, 10, 11, 14 },
+/*
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+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 4, 9, 15, 0, 10, 11, 14 },
+/*
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+_______xxxxxxxx_________xxxxx______|_______xxxxxxxx__________xxxx______
+____xxxxxxxxx____________xxxxx_____|____xxxxxxxxx____________xxxxx_____
+_xxxxxxxxxxx______________xxxx_____|_xxxxxxxxxxx______________xxxx_____
+_____xxxxxx________________xxx_____|_____xxxxxx________________xxx_____
+____________________________xxx____|____________________________xxx____
+________xxxxx________________xx____|________xxxxx________________xx____
+______xxxxxxxxxxxx____________xx___|______xxxxxxxxxxxx____________xx___
+_____xxxxxxxxxxxxxxxxx_________x___|_____xxxxxxxxxxxxxxxxx_________x___
+____xxxxxxxxxxxxxxxxxxxxxx______x__|____xxxxxxxxxxxxxxxxxxxxxx______x__
+__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____|__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 6, 8, 15, 2, 3, 12, 15 },
+/*
+___________________________________|___________________________________
+____________x________x_____________|____________x________x_____________
+_____________x_____xx______________|_____________x_____xx______________
+______________x_xxxx_______________|______________x_xxxx_______________
+_____________xx__xx________________|_____________xx__xx________________
+__________xxxxxx__x________________|__________xxxxxx__x________________
+_______xxxxxxxxxx_xx_______________|_______xxxxxxxxxx_xx_______________
+_____xxxxxxxxxxxx_xxx______________|_____xxxxxxxxxxxx_xxx______________
+__xxxxxxxxxxxxxx___xxx_____________|__xxxxxxxxxxxxxx___xxx_____________
+____xxxxxxxxxxx_____xx_____________|____xxxxxxxxxxx_____xx_____________
+________xxxxxx______x______________|________xxxxxx______x______________
+____________x______xxx_____________|____________x______xxx_____________
+____________xxxxx_xxxxx____________|____________xxxxx_xxxxx____________
+___________xxxxx_____xxx___________|___________xxxxx_____xxx___________
+__________xxxxx_________x__________|__________xxxxx____________________
+_________xxxx____________xxxx______|_________xxxx____________xxxx______
+________xxxx______________xxxxxxxx_|________xxxx______________xxxxxxxx_
+_______xxxxxxxx____________xxx_____|_______xxxxxxxx____________xxx_____
+______xxxxxxxxxxx________xxx_______|______xxxxxxxxxxx________xxx_______
+_____xxxxxxxxxxxxxxx_xxxxxxxx______|_____xxxxxxxxxxxxxxx_xxxxxxxx______
+_____xxxxxxxxxxxx______xxxxxxx_____|_____xxxxxxxxxxxx______xxxxxxx_____
+____xxxxxxxxx_____________xxxxx____|____xxxxxxxxx_____________xxxxx____
+___xxxxxx____________________xxx___|___xxxxxx____________________xxx___
+__xx___________________________xx__|__xx___________________________xx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 6, 9, 15, 2, 4, 11, 12 },
+/*
+___________________________________|___________________________________
+____________x________x_____________|____________x________x_____________
+_____________x_____xx______________|_____________x_____xx______________
+______________x_xxxx_______________|______________x_xxxx_______________
+_____________xx__xx________________|_____________xx__xx________________
+__________xxxxxx__x________________|__________xxxxxx__x________________
+_______xxxxxxxxxx_xx_______________|_______xxxxxxxxxx_xx_______________
+_____xxxxxxxxxxxx_xxx______________|_____xxxxxxxxxxxx_xxx______________
+__xxxxxxxxxxxxxx___xxx_____________|__xxxxxxxxxxxxxx___xxx_____________
+____xxxxxxxxxxx_____xx_____________|____xxxxxxxxxxx_____xx_____________
+________xxxxxx______x______________|________xxxxxx______x______________
+____________x______xxx_____________|____________x______xxx_____________
+____________xxxxx_xxxxx____________|____________xxxxx_xxxxx____________
+___________xxxxx_____xxx___________|___________xxxxx_____xxx___________
+__________xxxxx_________x__________|__________xxxxx____________________
+_________xxxx____________xxxx______|_________xxxx____________xxxx______
+________xxxx______________xxxxxxxx_|________xxxx______________xxxxxxxx_
+_______xxxxxxxx____________xxx_____|_______xxxxxxxx____________xxx_____
+______xxxxxxxxxxx________xxx_______|______xxxxxxxxxxx________xxx_______
+_____xxxxxxxxxxxxxxx_xxxxxxxx______|_____xxxxxxxxxxxxxxx_xxxxxxxx______
+_____xxxxxxxxxxxx______xxxxxxx_____|_____xxxxxxxxxxxx______xxxxxxx_____
+____xxxxxxxxx_____________xxxxx____|____xxxxxxxxx_____________xxxxx____
+___xxxxxx____________________xxx___|___xxxxxx____________________xxx___
+__xx___________________________xx__|__xx___________________________xx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 6, 9, 15, 2, 4, 11, 12 },
+/*
+___________________________________|___________________________________
+_____________xxxxxxxxxxxxxxxxxxx___|_____________xxxxxxxxxxxxxxxxxxx___
+___________xx___xxxxxxxxxxx________|___________xx___xxxxxxxxxxx________
+___________xxx_____xxxx____________|___________xxx_____xxxx____________
+__________xxxxx____xxx_____________|__________xxxxx____xxx_____________
+__________xxxxx_xxxxxxxx___________|__________xxxxx_xxxxxxxxx__________
+_________xx______xxxxxxxxxx________|_________x_______xxxxxxxxxx________
+______xxx_________xxxxxxxxxxxx_____|______xxx_________xxxxxxxxxxxx_____
+__xxxxxx___________xxxxxxxxxxxxxx__|__xxxxxx___________xxxxxxxxxxxxxx__
+___xxxxx____________xxxxxxxxxxxx___|___xxxxx____________xxxxxxxxxxxx___
+_____xx______________xxxxxxxxx_____|_____xx______________xxxxxxxxx_____
+______________________xxxxxx_______|______________________xxxxxx_______
+_______xx______________xxx_________|_______xx______________xxx_________
+______xxxxx________________________|______xxxxx________________________
+______xxxxxxx_________xx___________|______xxxxxxx_________xxx__________
+_____xxxxxxxxxx____xxxxxx__________|_____xxxxxxxxxx____xxxxxx__________
+_____xxxxxxxxxxxxxxxxxxxxx_________|_____xxxxxxxxxxxxxxxxxxxxx_________
+____xxxxxxxxxxx____xxxxxxxx________|____xxxxxxxxxxx____xxxxxxxx________
+____xxxxxxxxx________xxxxxxx_______|____xxxxxxxxx________xxxxxxx_______
+___xxxxxxxx_____________xxxxx______|___xxxxxxxx_____________xxxxx______
+___xxxxxx_________________xxxx_____|___xxxxxx_________________xxxx_____
+__xxxxx_____________________xxx____|__xxxxx_____________________xxx____
+__xxx_________________________xx___|__xxx_________________________xx___
+_xx_____________________________x__|_xx_____________________________x__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 7, 12, 1, 3, 4, 15 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 3, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x___________________x__|____________x___________________x__
+_____________xxx___________xxxxxx__|_____________xxx___________xxxxxx__
+______________xxxxx____xxxxxxxxx___|______________xxxxx____xxxxxxxxx___
+_______________xxxx___xxxxxxxxxx___|_______________xxxx___xxxxxxxxxx___
+_______________x________xxxxxxxx___|_______________x_________xxxxxxx___
+___________xxxxxx__________xxxx____|___________xxxxxx__________xxxx____
+______xxxxxxxxxxxx____________x____|______xxxxxxxxxxxx____________x____
+__xxxxxxxxxxxxxxxxx___________xxx__|__xxxxxxxxxxxxxxxxx___________xxx__
+____xxxxxxxxxxxxxxxx__________x____|____xxxxxxxxxxxxxxxx__________x____
+________xxxxxxxxxxxxx_____xxx______|________xxxxxxxxxxxxx_____xxx______
+____________xxxxxxxxxxxxxxxxx______|_____________xxxxxxxxxxxxxxxx______
+_________________xxxxxxxxxxx_______|_________________xxxxxxxxxxx_______
+______________xxxxxxxxxxxxxx_______|______________xxxxxxxxxxxxxx_______
+__________xxxxxxxxxxxxxx_xx________|__________xxxxxxxxxxxxxxxxx________
+_____xxxxxxxxxxxxxxxxxxxx__xx______|_____xxxxxxxxxxxxxxxxxxxx__xx______
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 7, 8, 15, 3, 4, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x___________________x__|____________x___________________x__
+_____________xxx___________xxxxxx__|_____________xxx___________xxxxxx__
+______________xxxxx____xxxxxxxxx___|______________xxxxx____xxxxxxxxx___
+_______________xxxx___xxxxxxxxxx___|_______________xxxx___xxxxxxxxxx___
+_______________x________xxxxxxxx___|_______________x_________xxxxxxx___
+___________xxxxxx__________xxxx____|___________xxxxxx__________xxxx____
+______xxxxxxxxxxxx____________x____|______xxxxxxxxxxxx____________x____
+__xxxxxxxxxxxxxxxxx___________xxx__|__xxxxxxxxxxxxxxxxx___________xxx__
+____xxxxxxxxxxxxxxxx__________x____|____xxxxxxxxxxxxxxxx__________x____
+________xxxxxxxxxxxxx_____xxx______|________xxxxxxxxxxxxx_____xxx______
+____________xxxxxxxxxxxxxxxxx______|_____________xxxxxxxxxxxxxxxx______
+_________________x_____xxxxx_______|_________________x_____xxxxx_______
+______________xxxxxxx___xxxx_______|______________xxxxxxx___xxxx_______
+__________xxxxxxxxxxxxxx_xx________|__________xxxxxxxxxxxxxxxxx________
+_____xxxxxxxxxxxxxxxxxxxx__xx______|_____xxxxxxxxxxxxxxxxxxxx__xx______
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 4, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx________________x__|_____________xxx________________x__
+______________xxxxx___________xx___|______________xxxxx___________xx___
+_______________xxxxxxx_______xxx___|_______________xxxxxxx_______xxx___
+________________xxxxxxxx___xxxxx___|________________xxxxxxxxx__xxxxx___
+_________________xxxxxxxxx_xxxx____|_________________xxxxxxxxx_xxxx____
+__________________xxxxxxx_____x____|__________________xxxxxxx_____x____
+___________________xxxx_______xxx__|___________________xxxx_______xxx__
+____________________xxxx______x____|____________________xxxx______x____
+_____________________xxxx_xxx______|_____________________xxxx_xxx______
+___________________________xx______|___________________________xx______
+__________________xxxxx____________|__________________xxxxx____________
+______________xxxxxxxxxx____x______|______________xxxxxxxxxx____x______
+__________xxxxxxxxxxxxxx___xxxx____|__________xxxxxxxxxxxxxx___xxxx____
+_____xxxxxxxxxxxxxxxxxxxx__xxxxx___|_____xxxxxxxxxxxxxxxxxxxx__xxxxx___
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 7, 8, 15, 3, 6, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx________________x__|_____________xxx________________x__
+______________xxxxx___________xx___|______________xxxxx___________xx___
+_______________xxxxxxx_______xxx___|_______________xxxxxxx_______xxx___
+________________xxxxxxxx___xxxxx___|________________xxxxxxxxx__xxxxx___
+_________________xxxxxxxxx_xxxx____|_________________xxxxxxxxx_xxxx____
+__________________xxxxxxx_____x____|__________________xxxxxxx_____x____
+___________________xxxx_______xxx__|___________________xxxx_______xxx__
+____________________xxxx______x____|____________________xxxx______x____
+_____________________xxxx_xxx______|_____________________xxxx_xxx______
+___________________________xx______|___________________________xx______
+__________________xxxxx____________|__________________xxxxx____________
+______________xxxxxxxxxx____x______|______________xxxxxxxxxx____x______
+__________xxxxxxxxxxxxxx___xxxx____|__________xxxxxxxxxxxxxx___xxxx____
+_____xxxxxxxxxxxxxxxxxxxx__xxxxx___|_____xxxxxxxxxxxxxxxxxxxx__xxxxx___
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 6, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 7, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx___________________|_____________xxx___________________
+______________xxxxx________________|______________xxxxx________________
+_______________xxxxxxx_________x___|_______________xxxxxxx_________x___
+________________xxxxxxxx______xx___|________________xxxxxxxxx_____xx___
+_________________xxxxxxxxxx___x____|_________________xxxxxxxxxx___x____
+__________________xxxxxxxxxxx_x____|__________________xxxxxxxxxxx_x____
+___________________xxxxxxxxx__xxx__|___________________xxxxxxxxx__xxx__
+____________________xxxxxxxx__x____|____________________xxxxxxxx__x____
+_____________________xxxxx_xx______|_____________________xxxxx_xx______
+__________________________xxx______|__________________________xxx______
+__________________xxxxx___xx_______|__________________xxxxx___xx_______
+______________xxxxxxxxxx_xxx_______|______________xxxxxxxxxx_xxx_______
+__________xxxxxxxxxxxxxxxxx________|__________xxxxxxxxxxxxxxxxx________
+_____xxxxxxxxxxxxxxxxxxxxxx________|_____xxxxxxxxxxxxxxxxxxxxxx________
+_xxxxxxxxxxxxxxxxxxxxxxxxx_________|_xxxxxxxxxxxxxxxxxxxxxxxxx_________
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 1, 7, 8, 15, 3, 10, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx___________________|_____________xxx___________________
+______________xxxxx________________|______________xxxxx________________
+_______________xxxxxxx_________x___|_______________xxxxxxx_________x___
+________________xxxxxxxx______xx___|________________xxxxxxxxx_____xx___
+_________________xxxxxxxxxx___x____|_________________xxxxxxxxxx___x____
+__________________xxxxxxxxxxx_x____|__________________xxxxxxxxxxx_x____
+___________________xxxxxxxxx__xxx__|___________________xxxxxxxxx__xxx__
+____________________xxxxxxxx__x____|____________________xxxxxxxx__x____
+_____________________xxxxx_xx______|_____________________xxxxx_xx______
+__________________________xxx______|__________________________xxx______
+__________________xxxxx___xx_______|__________________xxxxx___xx_______
+______________xxxxxxxxxx_xxx_______|______________xxxxxxxxxx_xxx_______
+__________xxxxxxxxxxxxxxxxx________|__________xxxxxxxxxxxxxx_xx________
+_____xxxxxxxxxxxxxxxxxx__xx________|_____xxxxxxxxxxxxxxxxxx__xx________
+_xxxxxxxxxxxxxxxxxxxxxx____________|_xxxxxxxxxxxxxxxxxxxxxx____________
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 10, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 11, 11, 14 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 8, 15, 3, 11, 14, 14 },
+/*
+___________________________________|___________________________________
+_____________xxxxxxxxxxxxxxxxxxx___|_____________xxxxxxxxxxxxxxxxxxx___
+___________xx___xxxxxxxxxxx________|___________xx___xxxxxxxxxxx________
+___________xxx_____xxxx____________|___________xxx_____xxxx____________
+__________xxxxx____xxx_____________|__________xxxxx____xxx_____________
+__________xxxxx_xxxxxxxx___________|__________xxxxx_xxxxxxxxx__________
+_________xx______xxxxxxxxxx________|_________x_______xxxxxxxxxx________
+______xxx_________xxxxxxxxxxxx_____|______xxx_________xxxxxxxxxxxx_____
+__xxxxxx___________xxxxxxxxxxxxxx__|__xxxxxx___________xxxxxxxxxxxxxx__
+___xxxxx____________xxxxxxxxxxxx___|___xxxxx____________xxxxxxxxxxxx___
+_____xx______________xxxxxxxxx_____|_____xx______________xxxxxxxxx_____
+______________________xxxxxx_______|______________________xxxxxx_______
+_______xx______________xxx_________|_______xx______________xxx_________
+______xxxxx________________________|______xxxxx________________________
+______xxxxxxx_________xx___________|______xxxxxxx_________xxx__________
+_____xxxxxxxxxx____xxxxxx__________|_____xxxxxxxxxx____xxxxxx__________
+_____xxxxxxxxxxxxxxxxxxxxx_________|_____xxxxxxxxxxxxxxxxxxxxx_________
+____xxxxxxxxxxx____xxxxxxxx________|____xxxxxxxxxxx____xxxxxxxx________
+____xxxxxxxxx________xxxxxxx_______|____xxxxxxxxx________xxxxxxx_______
+___xxxxxxxx_____________xxxxx______|___xxxxxxxx_____________xxxxx______
+___xxxxxx_________________xxxx_____|___xxxxxx_________________xxxx_____
+__xxxxx_____________________xxx____|__xxxxx_____________________xxx____
+__xxx_________________________xx___|__xxx_________________________xx___
+_xx_____________________________x__|_xx_____________________________x__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 1, 7, 12, 12, 1, 3, 4, 15 },
+/*
+___________________________________|___________________________________
+____________x__________xxxxxxxxxx__|____________x__________xxxxxxxxxx__
+_____________x_________xxxxxxxxx___|_____________x_________xxxxxxxxx___
+______________x_________xxxxxx_____|______________x_________xxxxxx_____
+_______________xx_______xxxxx______|_______________xx_______xxxxx______
+________________xx_______xx________|________________xx_______xx________
+_________________xxx_____x_________|_________________xxx_____x_________
+__________________xxx____x_________|__________________xxx____x_________
+___________________xxx_xxx_________|___________________xxx_xxx_________
+____________________x_xxxxx________|____________________x_xxxxx________
+__________________xx_xxxxxx________|__________________xx_xxxxxx________
+_______________xxxx___xxxxxx_______|_______________xxxx___xxxxxx_______
+____________xxxxxx_____xxxxx_______|____________xxxxxx_____xxxxx_______
+_________xxxxxxx________xxxxx______|_________xxxxxxx________xxxxx______
+_______xxxxxxxx_________xxxxx______|_______xxxxxxxx__________xxxx______
+____xxxxxxxxx____________xxxxx_____|____xxxxxxxxx____________xxxxx_____
+_xxxxxxxxxxx______________xxxx_____|_xxxxxxxxxxx______________xxxx_____
+_____xxxxxx________________xxx_____|_____xxxxxx________________xxx_____
+____________________________xxx____|____________________________xxx____
+________xxxxx________________xx____|________xxxxx________________xx____
+______xxxxxxxxxxxx____________xx___|______xxxxxxxxxxxx____________xx___
+_____xxxxxxxxxxxxxxxxx_________x___|_____xxxxxxxxxxxxxxxxx_________x___
+____xxxxxxxxxxxxxxxxxxxxxx______x__|____xxxxxxxxxxxxxxxxxxxxxx______x__
+__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____|__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 2, 3, 12, 15, 1, 6, 8, 15 },
+/*
+___________________________________|___________________________________
+_xx__________________x_____________|_xx__________________x_____________
+__xxxxx____________xx______________|__xxxxx____________xx______________
+__xxxxxxxxxx____xxxx_______________|__xxxxxxxxxx____xxxx_______________
+___xxxxxxxxxx___xxx________________|___xxxxxxxxxx___xxx________________
+___xxxxxxx_________x_______________|___xxxxxxx_________x_______________
+____xxx___________xxxxxx___________|____xxx___________xxxxxx___________
+____x____________xxxxxxxxxxx_______|____x____________xxxxxxxxxxx_______
+__xx____________xxxxxxxxxxxxxxxxx__|__xxx___________xxxxxxxxxxxxxxxxx__
+__xxx__________xxxxxxxxxxxxxxxx____|__xxx__________xxxxxxxxxxxxxxxx____
+___xx_________xxxxxxxxxxxx_________|___xx_________xxxxxxxxxxxx_________
+_____x_______xxxxxxxxx_____________|_____x_______xxxxxxxxx_____________
+____________xxxxxx_________________|____________xxxxxx_________________
+_______x___xxx_____________________|_______x___xxx_____________________
+_______xx__________________________|_______xx__________________________
+_____xxx_x_________________________|_____xxx_x_________________________
+_xxxxxxxxxxx_______________________|_xxxxxxxxxxx_______________________
+__xxxxx__xx________________________|__xxxxx__xx________________________
+____xx_____________________________|____xx_____________________________
+________xx_________________________|________xx_________________________
+_____x_xxx_________________________|_____x_xxx_________________________
+____x___xxx________________________|____x___xxx________________________
+___x_____xx________________________|___x_____xx________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 2, 4, 9, 12, 0, 7, 8, 13 },
+/*
+___________________________________|___________________________________
+_xx__________________x_____________|_xx__________________x_____________
+__xxxxx____________xx______________|__xxxxx____________xx______________
+__xxxxxxxxxx____xxxx_______________|__xxxxxxxxxx____xxxx_______________
+___xxxxxxxxxx___xxx________________|___xxxxxxxxxx___xxx________________
+___xxxxxxx_________x_______________|___xxxxxxx_________x_______________
+____xxx___________xxxxxx___________|____xxx___________xxxxxx___________
+____x____________xxxxxxxxxxx_______|____x____________xxxxxxxxxxx_______
+__xx____________xxxxxxxxxxxxxxxxx__|__xxx___________xxxxxxxxxxxxxxxxx__
+__xxx__________xxxxxxxxxxxxxxxx____|__xxx__________xxxxxxxxxxxxxxxx____
+___xx_________xxxxxxxxxxxx_________|___xx_________xxxxxxxxxxxx_________
+_____x_______xxxxxxxxx_____________|_____x_______xxxxxxxxx_____________
+____________xxxxxx_________________|____________xxxxxx_________________
+_______x___xxx_____________________|_______x___xxx_____________________
+_______xx__________________________|_______xx__________________________
+_____xxx_x_________________________|_____xxx_x_________________________
+_xxxxxxxxxxx_______________________|_xxxxxxxxxxx_______________________
+__xxxxx__xx________________________|__xxxxx__xx________________________
+____xx_____________________________|____xx_____________________________
+________xx_________________________|________xx_________________________
+_____x_xxx_________________________|_____x_xxx_________________________
+____x___xxx________________________|____x___xxx________________________
+___x_____xx________________________|___x_____xx________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 2, 4, 9, 12, 0, 7, 8, 13 },
+/*
+___________________________________|___________________________________
+____________x________x_____________|____________x________x_____________
+_____________x_____xx______________|_____________x_____xx______________
+______________x_xxxx_______________|______________x_xxxx_______________
+_____________xx__xx________________|_____________xx__xx________________
+__________xxxxxx__x________________|__________xxxxxx__x________________
+_______xxxxxxxxxx_xx_______________|_______xxxxxxxxxx_xx_______________
+_____xxxxxxxxxxxx_xxx______________|_____xxxxxxxxxxxx_xxx______________
+__xxxxxxxxxxxxxx___xxx_____________|__xxxxxxxxxxxxxx___xxx_____________
+____xxxxxxxxxxx_____xx_____________|____xxxxxxxxxxx_____xx_____________
+________xxxxxx______x______________|________xxxxxx______x______________
+____________x______xxx_____________|____________x______xxx_____________
+____________xxxxx_xxxxx____________|____________xxxxx_xxxxx____________
+___________xxxxx_____xxx___________|___________xxxxx_____xxx___________
+__________xxxxx_________x__________|__________xxxxx____________________
+_________xxxx____________xxxx______|_________xxxx____________xxxx______
+________xxxx______________xxxxxxxx_|________xxxx______________xxxxxxxx_
+_______xxxxxxxx____________xxx_____|_______xxxxxxxx____________xxx_____
+______xxxxxxxxxxx________xxx_______|______xxxxxxxxxxx________xxx_______
+_____xxxxxxxxxxxxxxx_xxxxxxxx______|_____xxxxxxxxxxxxxxx_xxxxxxxx______
+_____xxxxxxxxxxxx______xxxxxxx_____|_____xxxxxxxxxxxx______xxxxxxx_____
+____xxxxxxxxx_____________xxxxx____|____xxxxxxxxx_____________xxxxx____
+___xxxxxx____________________xxx___|___xxxxxx____________________xxx___
+__xx___________________________xx__|__xx___________________________xx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 2, 4, 11, 12, 1, 6, 9, 15 },
+/*
+___________________________________|___________________________________
+____________x________x_____________|____________x________x_____________
+_____________x_____xx______________|_____________x_____xx______________
+______________x_xxxx_______________|______________x_xxxx_______________
+_____________xx__xx________________|_____________xx__xx________________
+__________xxxxxx__x________________|__________xxxxxx__x________________
+_______xxxxxxxxxx_xx_______________|_______xxxxxxxxxx_xx_______________
+_____xxxxxxxxxxxx_xxx______________|_____xxxxxxxxxxxx_xxx______________
+__xxxxxxxxxxxxxx___xxx_____________|__xxxxxxxxxxxxxx___xxx_____________
+____xxxxxxxxxxx_____xx_____________|____xxxxxxxxxxx_____xx_____________
+________xxxxxx______x______________|________xxxxxx______x______________
+____________x______xxx_____________|____________x______xxx_____________
+____________xxxxx_xxxxx____________|____________xxxxx_xxxxx____________
+___________xxxxx_____xxx___________|___________xxxxx_____xxx___________
+__________xxxxx_________x__________|__________xxxxx____________________
+_________xxxx____________xxxx______|_________xxxx____________xxxx______
+________xxxx______________xxxxxxxx_|________xxxx______________xxxxxxxx_
+_______xxxxxxxx____________xxx_____|_______xxxxxxxx____________xxx_____
+______xxxxxxxxxxx________xxx_______|______xxxxxxxxxxx________xxx_______
+_____xxxxxxxxxxxxxxx_xxxxxxxx______|_____xxxxxxxxxxxxxxx_xxxxxxxx______
+_____xxxxxxxxxxxx______xxxxxxx_____|_____xxxxxxxxxxxx______xxxxxxx_____
+____xxxxxxxxx_____________xxxxx____|____xxxxxxxxx_____________xxxxx____
+___xxxxxx____________________xxx___|___xxxxxx____________________xxx___
+__xx___________________________xx__|__xx___________________________xx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 2, 4, 11, 12, 1, 6, 9, 15 },
+/*
+___________________________________|___________________________________
+____________xxxxxxxxxxxxxxxxxxxxx__|____________xxxxxxxxxxxxxxxxxxxxx__
+_____________xxxxxxxxxxxxxxxxxxx___|_____________xxxxxxxxxxxxxxxxxxx___
+______________xxxxxxxxx_xxxxxx_____|______________xxxxxxxxx_xxxxxx_____
+_______________xxxxxxxx_xxxxx______|_______________xxxxxxxx_xxxxx______
+________________xxxxxxx__xx________|________________xxxxxxx__xx________
+_________________xxxxxx__x_________|_________________xxxxxx__x_________
+__________________xxxxx__x_________|__________________xxxxx__x_________
+___________________xxxxxxx_________|___________________xxxxxxx_________
+____________________x_xxxxx________|____________________x_xxxxx________
+__________________xx_xxxxxx________|__________________xx_xxxxxx________
+_______________xxxx___xxxxxx_______|_______________xxxx___xxxxxx_______
+____________xxxxxx_____xxxxx_______|____________xxxxxx_____xxxxx_______
+_________xxxxxxx________xxxxx______|_________xxxxxxx________xxxxx______
+_______xxxxxxxx_________xxxxx______|_______xxxxxxxx__________xxxx______
+____xxxxxxxxx____________xxxxx_____|____xxxxxxxxx____________xxxxx_____
+_xxxxxxxxxxx______________xxxx_____|_xxxxxxxxxxx______________xxxx_____
+_____xxxxxx________________xxx_____|_____xxxxxx________________xxx_____
+____________________________xxx____|____________________________xxx____
+________xxxxx________________xx____|________xxxxx________________xx____
+______xxxxxxxxxxxx____________xx___|______xxxxxxxxxxxx____________xx___
+_____xxxxxxxxxxxxxxxxx_________x___|_____xxxxxxxxxxxxxxxxx_________x___
+____xxxxxxxxxxxxxxxxxxxxxx______x__|____xxxxxxxxxxxxxxxxxxxxxx______x__
+__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____|__xxxxxxxxxxxxxxxxxxxxxxxxxxxx_____
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 2, 6, 8, 15, 1, 3, 12, 15 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 3, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x___________________x__|____________x___________________x__
+_____________xxx___________xxxxxx__|_____________xxx___________xxxxxx__
+______________xxxxx____xxxxxxxxx___|______________xxxxx____xxxxxxxxx___
+_______________xxxx___xxxxxxxxxx___|_______________xxxx___xxxxxxxxxx___
+_______________x________xxxxxxxx___|_______________x_________xxxxxxx___
+___________xxxxxx__________xxxx____|___________xxxxxx__________xxxx____
+______xxxxxxxxxxxx____________x____|______xxxxxxxxxxxx____________x____
+__xxxxxxxxxxxxxxxxx___________xxx__|__xxxxxxxxxxxxxxxxx___________xxx__
+____xxxxxxxxxxxxxxxx__________x____|____xxxxxxxxxxxxxxxx__________x____
+________xxxxxxxxxxxxx_____xxx______|________xxxxxxxxxxxxx_____xxx______
+____________xxxxxxxxxxxxxxxxx______|_____________xxxxxxxxxxxxxxxx______
+_________________xxxxxxxxxxx_______|_________________xxxxxxxxxxx_______
+______________xxxxxxxxxxxxxx_______|______________xxxxxxxxxxxxxx_______
+__________xxxxxxxxxxxxxx_xx________|__________xxxxxxxxxxxxxxxxx________
+_____xxxxxxxxxxxxxxxxxxxx__xx______|_____xxxxxxxxxxxxxxxxxxxx__xx______
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 3, 4, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x___________________x__|____________x___________________x__
+_____________xxx___________xxxxxx__|_____________xxx___________xxxxxx__
+______________xxxxx____xxxxxxxxx___|______________xxxxx____xxxxxxxxx___
+_______________xxxx___xxxxxxxxxx___|_______________xxxx___xxxxxxxxxx___
+_______________x________xxxxxxxx___|_______________x_________xxxxxxx___
+___________xxxxxx__________xxxx____|___________xxxxxx__________xxxx____
+______xxxxxxxxxxxx____________x____|______xxxxxxxxxxxx____________x____
+__xxxxxxxxxxxxxxxxx___________xxx__|__xxxxxxxxxxxxxxxxx___________xxx__
+____xxxxxxxxxxxxxxxx__________x____|____xxxxxxxxxxxxxxxx__________x____
+________xxxxxxxxxxxxx_____xxx______|________xxxxxxxxxxxxx_____xxx______
+____________xxxxxxxxxxxxxxxxx______|_____________xxxxxxxxxxxxxxxx______
+_________________x_____xxxxx_______|_________________x_____xxxxx_______
+______________xxxxxxx___xxxx_______|______________xxxxxxx___xxxx_______
+__________xxxxxxxxxxxxxx_xx________|__________xxxxxxxxxxxxxxxxx________
+_____xxxxxxxxxxxxxxxxxxxx__xx______|_____xxxxxxxxxxxxxxxxxxxx__xx______
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 4, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx________________x__|_____________xxx________________x__
+______________xxxxx___________xx___|______________xxxxx___________xx___
+_______________xxxxxxx_______xxx___|_______________xxxxxxx_______xxx___
+________________xxxxxxxx___xxxxx___|________________xxxxxxxxx__xxxxx___
+_________________xxxxxxxxx_xxxx____|_________________xxxxxxxxx_xxxx____
+__________________xxxxxxx_____x____|__________________xxxxxxx_____x____
+___________________xxxx_______xxx__|___________________xxxx_______xxx__
+____________________xxxx______x____|____________________xxxx______x____
+_____________________xxxx_xxx______|_____________________xxxx_xxx______
+___________________________xx______|___________________________xx______
+__________________xxxxx____________|__________________xxxxx____________
+______________xxxxxxxxxx____x______|______________xxxxxxxxxx____x______
+__________xxxxxxxxxxxxxx___xxxx____|__________xxxxxxxxxxxxxx___xxxx____
+_____xxxxxxxxxxxxxxxxxxxx__xxxxx___|_____xxxxxxxxxxxxxxxxxxxx__xxxxx___
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 3, 6, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx________________x__|_____________xxx________________x__
+______________xxxxx___________xx___|______________xxxxx___________xx___
+_______________xxxxxxx_______xxx___|_______________xxxxxxx_______xxx___
+________________xxxxxxxx___xxxxx___|________________xxxxxxxxx__xxxxx___
+_________________xxxxxxxxx_xxxx____|_________________xxxxxxxxx_xxxx____
+__________________xxxxxxx_____x____|__________________xxxxxxx_____x____
+___________________xxxx_______xxx__|___________________xxxx_______xxx__
+____________________xxxx______x____|____________________xxxx______x____
+_____________________xxxx_xxx______|_____________________xxxx_xxx______
+___________________________xx______|___________________________xx______
+__________________xxxxx____________|__________________xxxxx____________
+______________xxxxxxxxxx____x______|______________xxxxxxxxxx____x______
+__________xxxxxxxxxxxxxx___xxxx____|__________xxxxxxxxxxxxxx___xxxx____
+_____xxxxxxxxxxxxxxxxxxxx__xxxxx___|_____xxxxxxxxxxxxxxxxxxxx__xxxxx___
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 6, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 7, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx___________________|_____________xxx___________________
+______________xxxxx________________|______________xxxxx________________
+_______________xxxxxxx_________x___|_______________xxxxxxx_________x___
+________________xxxxxxxx______xx___|________________xxxxxxxxx_____xx___
+_________________xxxxxxxxxx___x____|_________________xxxxxxxxxx___x____
+__________________xxxxxxxxxxx_x____|__________________xxxxxxxxxxx_x____
+___________________xxxxxxxxx__xxx__|___________________xxxxxxxxx__xxx__
+____________________xxxxxxxx__x____|____________________xxxxxxxx__x____
+_____________________xxxxx_xx______|_____________________xxxxx_xx______
+__________________________xxx______|__________________________xxx______
+__________________xxxxx___xx_______|__________________xxxxx___xx_______
+______________xxxxxxxxxx_xxx_______|______________xxxxxxxxxx_xxx_______
+__________xxxxxxxxxxxxxxxxx________|__________xxxxxxxxxxxxxxxxx________
+_____xxxxxxxxxxxxxxxxxxxxxx________|_____xxxxxxxxxxxxxxxxxxxxxx________
+_xxxxxxxxxxxxxxxxxxxxxxxxx_________|_xxxxxxxxxxxxxxxxxxxxxxxxx_________
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kWinding_FillType, 3, 10, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x______________________|____________x______________________
+_____________xxx___________________|_____________xxx___________________
+______________xxxxx________________|______________xxxxx________________
+_______________xxxxxxx_________x___|_______________xxxxxxx_________x___
+________________xxxxxxxx______xx___|________________xxxxxxxxx_____xx___
+_________________xxxxxxxxxx___x____|_________________xxxxxxxxxx___x____
+__________________xxxxxxxxxxx_x____|__________________xxxxxxxxxxx_x____
+___________________xxxxxxxxx__xxx__|___________________xxxxxxxxx__xxx__
+____________________xxxxxxxx__x____|____________________xxxxxxxx__x____
+_____________________xxxxx_xx______|_____________________xxxxx_xx______
+__________________________xxx______|__________________________xxx______
+__________________xxxxx___xx_______|__________________xxxxx___xx_______
+______________xxxxxxxxxx_xxx_______|______________xxxxxxxxxx_xxx_______
+__________xxxxxxxxxxxxxxxxx________|__________xxxxxxxxxxxxxx_xx________
+_____xxxxxxxxxxxxxxxxxx__xx________|_____xxxxxxxxxxxxxxxxxx__xx________
+_xxxxxxxxxxxxxxxxxxxxxx____________|_xxxxxxxxxxxxxxxxxxxxxx____________
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 10, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 11, 11, 14, 1, 7, 8, 15 },
+/*
+___________________________________|___________________________________
+____________x____________________x_|____________x____________________x_
+_____________xxx_________________x_|_____________xxx_________________x_
+______________xxxxx_____________xx_|______________xxxxx_____________xx_
+_______________xxxxxxx__________xx_|_______________xxxxxxx__________xx_
+________________xxxxxxxx________xx_|________________xxxxxxxx________xx_
+_________________xxxxxxxxxx____xxx_|_________________xxxxxxxxxx____xxx_
+__________________xxxxxxxxxxxx_xxx_|__________________xxxxxxxxxxxx_xxx_
+___________________xxxxxxxxxxx___x_|___________________xxxxxxxxxxx___x_
+____________________xxxxxxxxxx_xxx_|____________________xxxxxxxxxx_xxx_
+_____________________xxxxx___xxxxx_|_____________________xxxxx___xxxxx_
+_____________________________xxxxx_|_____________________________xxxxx_
+__________________xxxxx_____xxxxxx_|__________________xxxxx_____xxxxxx_
+______________xxxxxxxxxx____xxxxxx_|______________xxxxxxxxxx____xxxxxx_
+__________xxxxxxxxxxxxxx___xxxxxxx_|__________xxxxxxxxxxxxxx___xxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_|_____xxxxxxxxxxxxxxxxxxxx__xxxxxxx_
+_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_|_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx_
+_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___|_____xxxxxxxxxxxxxxxxxxxxx_xxxxx___
+_________xxxxxxxxxxxxxxxx___xxx____|_________xxxxxxxxxxxxxxxx___xxx____
+_____________xxxxxxxxxxxx__________|_____________xxxxxxxxxxxx____x_____
+__________________xxxxxxx___xx_____|__________________xxxxxxx___xx_____
+______________________xx___xxxx____|______________________xx___xxxx____
+________________________x_xxxxxx___|________________________x_xxxxxx___
+_______________________x______xxx__|_______________________x______xxx__
+___________________________________|___________________________________
+___________________________________|___________________________________
+*/
+{ SkPath::kEvenOdd_FillType, 3, 11, 14, 14, 1, 7, 8, 15 },
+};
+
+size_t misMatchCount = sizeof(misMatches) / sizeof(misMatches[0]);
+
+void TestMismatches();
+
+void TestMismatches() {
+ for (size_t index = 0; index < misMatchCount; ++index) {
+ const misMatch& miss = misMatches[index];
+ int ax = miss.a & 0x03;
+ int ay = miss.a >> 2;
+ int bx = miss.b & 0x03;
+ int by = miss.b >> 2;
+ int cx = miss.c & 0x03;
+ int cy = miss.c >> 2;
+ int dx = miss.d & 0x03;
+ int dy = miss.d >> 2;
+ int ex = miss.e & 0x03;
+ int ey = miss.e >> 2;
+ int fx = miss.f & 0x03;
+ int fy = miss.f >> 2;
+ int gx = miss.g & 0x03;
+ int gy = miss.g >> 2;
+ int hx = miss.h & 0x03;
+ int hy = miss.h >> 2;
+ SkPath path, out;
+ path.setFillType(miss.fType);
+ path.moveTo(ax, ay);
+ path.lineTo(bx, by);
+ path.lineTo(cx, cy);
+ path.lineTo(dx, dy);
+ path.close();
+ path.moveTo(ex, ey);
+ path.lineTo(fx, fy);
+ path.lineTo(gx, gy);
+ path.lineTo(hx, hy);
+ path.close();
+ testSimplify(path, true, out);
+ }
+}
diff --git a/experimental/Intersection/EdgeWalkerPolygons_Mismatches.h b/experimental/Intersection/EdgeWalkerPolygons_Mismatches.h
new file mode 100644
index 0000000..d038172
--- /dev/null
+++ b/experimental/Intersection/EdgeWalkerPolygons_Mismatches.h
@@ -0,0 +1,9 @@
+/*
+ * EdgeWalkerPolygons_Mismatches.h
+ * edge
+ *
+ * Created by Cary Clark on 3/6/12.
+ * Copyright 2012 __MyCompanyName__. All rights reserved.
+ *
+ */
+
diff --git a/experimental/Intersection/EdgeWalkerPolygons_Test.cpp b/experimental/Intersection/EdgeWalkerPolygons_Test.cpp
index 07ce6c8..9a740e9 100644
--- a/experimental/Intersection/EdgeWalkerPolygons_Test.cpp
+++ b/experimental/Intersection/EdgeWalkerPolygons_Test.cpp
@@ -12,8 +12,8 @@
path.lineTo(10,30); // /_|
path.lineTo(20,30);
path.close();
- simplify(path, true, out); // expect |\/|
- comparePaths(path, out); // |__|
+ testSimplify(path, true, out); // expect |\/|
+ // |__|
}
static void testSimplifyTriangle3() {
@@ -26,8 +26,7 @@
path.lineTo(1, 0);
path.lineTo(3, 1);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle4() {
@@ -40,8 +39,7 @@
path.lineTo(1, 0);
path.lineTo(2, 1);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle5() {
@@ -54,8 +52,7 @@
path.lineTo(1, 1);
path.lineTo(2, 1);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle6() {
@@ -70,8 +67,7 @@
path.lineTo(3, 1);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle7() {
@@ -86,8 +82,7 @@
path.lineTo(0, 2);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle8() {
@@ -102,8 +97,7 @@
path.lineTo(1, 3);
path.lineTo(0, 1);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle9() {
@@ -118,8 +112,7 @@
path.lineTo(2, 1);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle10() {
@@ -134,8 +127,7 @@
path.lineTo(0, 1);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle11() {
@@ -150,8 +142,7 @@
path.lineTo(2, 2);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle12() {
@@ -166,8 +157,7 @@
path.lineTo(1, 1);
path.lineTo(2, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle13() {
@@ -182,8 +172,7 @@
path.lineTo(1, 1);
path.lineTo(3, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle14() {
@@ -198,8 +187,7 @@
path.lineTo(0, 1);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle15() {
@@ -213,8 +201,7 @@
path.lineTo(0, 1);
path.lineTo(2, 2);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle16() {
@@ -227,8 +214,7 @@
path.lineTo(0, 1);
path.lineTo(1, 3);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle17() {
@@ -241,8 +227,7 @@
path.lineTo(1, 3);
path.lineTo(0, 1);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle18() {
@@ -255,8 +240,7 @@
path.lineTo(0, 1);
path.lineTo(0, 3);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle19() {
@@ -270,8 +254,7 @@
path.lineTo(1, 1);
path.lineTo(2, 1);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle20() {
@@ -284,8 +267,7 @@
path.lineTo(3, 2);
path.lineTo(0, 3);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyTriangle21() {
@@ -298,8 +280,7 @@
path.lineTo(2, 1);
path.lineTo(0, 3);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyDegenerateTriangle1() {
@@ -312,8 +293,7 @@
path.lineTo(0, 0);
path.lineTo(0, 0);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyDegenerateTriangle2() {
@@ -326,8 +306,7 @@
path.lineTo(2, 2);
path.lineTo(3, 3);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
static void testSimplifyWindingParallelogram() {
@@ -343,9 +322,9 @@
path.lineTo(20,30); // /_/
path.lineTo(30,10);
path.close();
- simplify(path, true, out); // expect _
- comparePaths(path, out); // / \ .
-} // /___\ .
+ testSimplify(path, true, out); // expect _
+ // / \ .
+} // /___\ .
static void testSimplifyXorParallelogram() {
SkPath path, out;
@@ -360,9 +339,8 @@
path.lineTo(20,30); // /_/
path.lineTo(30,10);
path.close();
- simplify(path, true, out); // expect _
- comparePaths(path, out); // \ /
-} //
+ testSimplify(path, true, out); // expect _
+} // \ /
static void testSimplifyTriangle2() {
SkPath path, out;
@@ -374,10 +352,9 @@
path.moveTo(10,10); // triangle _
path.lineTo(20,10); // \ |
path.lineTo(20,30); // \|
- path.close(); // _
- simplify(path, true, out); // expect | |
- comparePaths(path, out); // |_|
-}
+ path.close(); // _
+ testSimplify(path, true, out); // expect | |
+} // |_|
static void testSimplifyNondegenerate4x4Triangles() {
char pathStr[1024];
@@ -433,11 +410,9 @@
str += sprintf(str, " path.lineTo(%d, %d);\n", fx, fy);
str += sprintf(str, " path.close();");
}
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
path.setFillType(SkPath::kEvenOdd_FillType);
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
}
}
@@ -494,11 +469,9 @@
str += sprintf(str, " path.lineTo(%d, %d);\n", fx, fy);
str += sprintf(str, " path.close();");
}
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
path.setFillType(SkPath::kEvenOdd_FillType);
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
}
}
@@ -527,7 +500,165 @@
}
}
+static void testSimplifySkinnyTriangle1() {
+ for (int x = 1; x < 255; ++x) {
+ SkPath path, out;
+ path.moveTo((x * 101) % 10, 0);
+ path.lineTo((x * 91) % 10, 1000);
+ path.lineTo((x * 71) % 10, 2000);
+ path.lineTo((x * 51) % 10, 3000);
+ path.close();
+ path.moveTo((x * 101) % 20, 0);
+ path.lineTo((x * 91) % 20, 1000);
+ path.lineTo((x * 71) % 20, 2000);
+ path.lineTo((x * 51) % 20, 3000);
+ path.close();
+ path.moveTo((x * 101) % 30, 0);
+ path.lineTo((x * 91) % 30, 1000);
+ path.lineTo((x * 71) % 30, 2000);
+ path.lineTo((x * 51) % 30, 3000);
+ path.close();
+ testSimplify(path, true, out);
+ }
+}
+
+static void testSimplifySkinnyTriangle2() {
+ SkPath path, out;
+#if 01
+path.moveTo(591.091064, 627.534851);
+path.lineTo(541.088135, 560.707642);
+path.lineTo(491.085175, 493.880310);
+path.lineTo(441.082214, 427.053101);
+//path.lineTo(591.091064, 627.534851);
+path.close();
+#endif
+path.moveTo(317.093445, 592.013306);
+path.lineTo(366.316162, 542.986572);
+path.lineTo(416.051514, 486.978577);
+path.lineTo(465.786865, 430.970581);
+//path.lineTo(317.093445, 592.013306);
+path.close();
+#if 0
+path.moveTo(289.392517, 517.138489);
+path.lineTo(249.886078, 508.598022);
+path.lineTo(217.110916, 450.916443);
+path.lineTo(196.621033, 394.917633);
+//path.lineTo(289.392517, 517.138489);
+path.close();
+#endif
+ testSimplify(path, true, out);
+}
+
+static void testSimplifySkinnyTriangle3() {
+ SkPath path, out;
+ path.moveTo(591, 627.534851);
+ path.lineTo(541, 560.707642);
+ path.lineTo(491, 493.880310);
+ path.lineTo(441, 427.053101);
+ path.close();
+ path.moveTo(317, 592.013306);
+ path.lineTo(366, 542.986572);
+ path.lineTo(416, 486.978577);
+ path.lineTo(465, 430.970581);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifySkinnyTriangle4() {
+ SkPath path, out;
+path.moveTo(572.655212, 614.959961);
+path.lineTo(524.618896, 549.339600);
+path.lineTo(476.582581, 483.719269);
+path.lineTo(428.546265, 418.098938);
+path.lineTo(572.655212, 614.959961);
+path.close();
+path.moveTo(312.166382, 583.723083);
+path.lineTo(361.047791, 529.824219);
+path.lineTo(409.929230, 475.925354);
+path.lineTo(458.810669, 422.026520);
+path.lineTo(312.166382, 583.723083);
+path.close();
+path.moveTo(278.742737, 508.065643);
+path.lineTo(241.475800, 493.465118);
+path.lineTo(210.344177, 437.315125);
+path.lineTo(197.019455, 383.794556);
+path.lineTo(278.742737, 508.065643);
+path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifySkinnyTriangle5() {
+ SkPath path, out;
+path.moveTo(554.690613, 602.286072);
+path.lineTo(508.590057, 537.906250);
+path.lineTo(462.489441, 473.526520);
+path.lineTo(416.388855, 409.146729);
+path.lineTo(554.690613, 602.286072);
+path.close();
+path.moveTo(307.216949, 575.189270);
+path.lineTo(355.826965, 516.804688);
+path.lineTo(403.815918, 464.990753);
+path.lineTo(451.804871, 413.176819);
+path.lineTo(307.216949, 575.189270);
+path.close();
+path.moveTo(271.998901, 521.301025);
+path.lineTo(234.619705, 499.687683);
+path.lineTo(203.059692, 441.332336);
+path.lineTo(195.994370, 386.856506);
+path.lineTo(271.998901, 521.301025);
+path.close();
+ testSimplify(path, true, out);
+}
+
+
+static void testSimplifyTriangle22() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(1, 0);
+ path.lineTo(0, 2);
+ path.close();
+ path.moveTo(1, 0);
+ path.lineTo(0, 2);
+ path.lineTo(0, 1);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyTriangle23() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(0, 0);
+ path.close();
+ path.moveTo(0, 0);
+ path.lineTo(0, 1);
+ path.lineTo(1, 2);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyTriangle24() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(0, 1);
+ path.close();
+ path.moveTo(0, 0);
+ path.lineTo(1, 0);
+ path.lineTo(0, 1);
+ path.close();
+ testSimplify(path, true, out);
+}
+
static void (*simplifyTests[])() = {
+ testSimplifySkinnyTriangle5,
+ testSimplifySkinnyTriangle4,
+ testSimplifySkinnyTriangle3,
+ testSimplifySkinnyTriangle2,
+ testSimplifySkinnyTriangle1,
+ testSimplifyTriangle24,
+ testSimplifyTriangle23,
+ testSimplifyTriangle22,
testSimplifyDegenerateTriangle2,
testSimplifyDegenerateTriangle1,
testSimplifyTriangle21,
@@ -560,7 +691,7 @@
static size_t simplifyTestsCount = sizeof(simplifyTests) / sizeof(simplifyTests[0]);
-static void (*firstTest)() = 0;
+static void (*firstTest)() = testSimplifySkinnyTriangle4;
void SimplifyPolygonPaths_Test() {
size_t index = 0;
@@ -569,8 +700,10 @@
++index;
}
}
+ bool firstTestComplete = false;
for ( ; index < simplifyTestsCount; ++index) {
(*simplifyTests[index])();
+ firstTestComplete = true;
}
}
diff --git a/experimental/Intersection/EdgeWalkerQuadralaterals_Test.cpp b/experimental/Intersection/EdgeWalkerQuadralaterals_Test.cpp
index b22e1a3..6cb2417 100644
--- a/experimental/Intersection/EdgeWalkerQuadralaterals_Test.cpp
+++ b/experimental/Intersection/EdgeWalkerQuadralaterals_Test.cpp
@@ -13,8 +13,82 @@
path.lineTo(1, 3);
path.lineTo(1, 3);
path.close();
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyQuad2() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(0, 2);
+ path.close();
+ path.moveTo(0, 1);
+ path.lineTo(0, 1);
+ path.lineTo(1, 1);
+ path.lineTo(0, 2);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyQuad3() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(1, 0);
+ path.lineTo(1, 2);
+ path.close();
+ path.moveTo(0, 1);
+ path.lineTo(1, 1);
+ path.lineTo(2, 1);
+ path.lineTo(0, 2);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyQuad4() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(1, 0);
+ path.lineTo(2, 2);
+ path.close();
+ path.moveTo(0, 0);
+ path.lineTo(2, 1);
+ path.lineTo(3, 1);
+ path.lineTo(3, 3);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyQuad5() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(0, 0);
+ path.lineTo(1, 0);
+ path.lineTo(3, 2);
+ path.close();
+ path.moveTo(0, 1);
+ path.lineTo(1, 1);
+ path.lineTo(2, 1);
+ path.lineTo(0, 2);
+ path.close();
+ testSimplify(path, true, out);
+}
+
+static void testSimplifyQuad6() {
+ SkPath path, out;
+ path.moveTo(0, 0);
+ path.lineTo(1, 0);
+ path.lineTo(1, 1);
+ path.lineTo(3, 3);
+ path.close();
+ path.moveTo(1, 1);
+ path.lineTo(1, 1);
+ path.lineTo(1, 1);
+ path.lineTo(2, 2);
+ path.close();
+ testSimplify(path, true, out);
}
static void testSimplify4x4Quadralaterals() {
@@ -41,7 +115,7 @@
for (int g = f ; g < 16; ++g) {
int gx = g & 0x03;
int gy = g >> 2;
- for (int h = g ; g < 16; ++g) {
+ for (int h = g ; h < 16; ++h) {
int hx = h & 0x03;
int hy = h >> 2;
SkPath path, out;
@@ -56,7 +130,7 @@
path.lineTo(gx, gy);
path.lineTo(hx, hy);
path.close();
- if (1) {
+ if (1) { // gdb: set print elements 400
char* str = pathStr;
str += sprintf(str, " path.moveTo(%d, %d);\n", ax, ay);
str += sprintf(str, " path.lineTo(%d, %d);\n", bx, by);
@@ -69,11 +143,15 @@
str += sprintf(str, " path.lineTo(%d, %d);\n", hx, hy);
str += sprintf(str, " path.close();");
}
- simplify(path, true, out);
- comparePaths(path, out);
+ if (!testSimplify(path, true, out)) {
+ SkDebugf("*/\n{ SkPath::kWinding_FillType, %d, %d, %d, %d, %d, %d, %d, %d },\n/*\n",
+ a, b, c, d, e, f, g, h);
+ }
path.setFillType(SkPath::kEvenOdd_FillType);
- simplify(path, true, out);
- comparePaths(path, out);
+ if (!testSimplify(path, true, out)) {
+ SkDebugf("*/\n{ SkPath::kEvenOdd_FillType, %d, %d, %d, %d, %d, %d, %d, %d },\n/*\n",
+ a, b, c, d, e, f, g, h);
+ }
}
}
}
@@ -87,6 +165,11 @@
static void (*simplifyTests[])() = {
+ testSimplifyQuad6,
+ testSimplifyQuad5,
+ testSimplifyQuad4,
+ testSimplifyQuad3,
+ testSimplifyQuad2,
testSimplifyQuad1,
testSimplify4x4Quadralaterals,
};
diff --git a/experimental/Intersection/EdgeWalkerRectangles_Test.cpp b/experimental/Intersection/EdgeWalkerRectangles_Test.cpp
index a42a970..8dc8627 100644
--- a/experimental/Intersection/EdgeWalkerRectangles_Test.cpp
+++ b/experimental/Intersection/EdgeWalkerRectangles_Test.cpp
@@ -1,6 +1,15 @@
#include "EdgeWalker_Test.h"
#include "Intersection_Tests.h"
+static void testSimplifyCoincidentInner() {
+ SkPath path, out;
+ path.setFillType(SkPath::kWinding_FillType);
+ path.addRect(10, 10, 60, 60, SkPath::kCCW_Direction);
+ path.addRect(20, 20, 50, 50, SkPath::kCW_Direction);
+ path.addRect(20, 30, 40, 40, SkPath::kCW_Direction);
+ testSimplify(path, true, out);
+}
+
static void testSimplifyCoincidentVertical() {
SkPath path, out;
path.setFillType(SkPath::kWinding_FillType);
@@ -295,8 +304,7 @@
SkPath path, out;
path.addRect(rect1, static_cast<SkPath::Direction>(dir));
path.addRect(rect2, static_cast<SkPath::Direction>(dir));
- simplify(path, true, out);
- comparePaths(path, out);
+ testSimplify(path, true, out);
}
}
}
@@ -409,6 +417,7 @@
}
static void (*simplifyTests[])() = {
+ testSimplifyCoincidentInner,
testSimplifyOverlapTiny,
testSimplifyDegenerate1,
testSimplifyCorner,
diff --git a/experimental/Intersection/EdgeWalker_Test.h b/experimental/Intersection/EdgeWalker_Test.h
index 3911004..c449d1a 100644
--- a/experimental/Intersection/EdgeWalker_Test.h
+++ b/experimental/Intersection/EdgeWalker_Test.h
@@ -3,7 +3,10 @@
#include "SkPath.h"
extern void contourBounds(const SkPath& path, SkTDArray<SkRect>& boundsArray);
-extern void comparePaths(const SkPath& one, const SkPath& two);
+extern bool comparePaths(const SkPath& one, const SkPath& two);
extern void comparePathsTiny(const SkPath& one, const SkPath& two);
+extern void drawAsciiPaths(const SkPath& one, const SkPath& two,
+ bool drawPaths);
extern void simplify(const SkPath& path, bool asFill, SkPath& simple);
-
+extern void showPath(const SkPath& path, const char* str = NULL);
+extern bool testSimplify(const SkPath& path, bool fill, SkPath& out);
diff --git a/experimental/Intersection/EdgeWalker_TestUtility.cpp b/experimental/Intersection/EdgeWalker_TestUtility.cpp
index eb1509e..84ca87f 100644
--- a/experimental/Intersection/EdgeWalker_TestUtility.cpp
+++ b/experimental/Intersection/EdgeWalker_TestUtility.cpp
@@ -4,32 +4,31 @@
#include "SkCanvas.h"
#include "SkPaint.h"
-static bool gDrawLastAsciiPaths = true;
+static bool gShowPath = false;
+static bool gDrawLastAsciiPaths = false;
static bool gDrawAllAsciiPaths = false;
-static bool gShowPath = true;
+static bool gShowAsciiPaths = false;
+static bool gComparePathsAssert = false;
-static void showPath(const char* str, const SkPath& path) {
- if (!gShowPath) {
- return;
- }
- SkDebugf("%s\n", str);
+void showPath(const SkPath& path, const char* str) {
+ SkDebugf("%s\n", str ? "original:" : str);
SkPath::Iter iter(path, true);
uint8_t verb;
SkPoint pts[4];
while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
switch (verb) {
case SkPath::kMove_Verb:
- SkDebugf("path.moveTo(%g, %g);\n", pts[0].fX, pts[0].fY);
+ SkDebugf("path.moveTo(%3.6g, %3.6g);\n", pts[0].fX, pts[0].fY);
continue;
case SkPath::kLine_Verb:
- SkDebugf("path.lineTo(%g, %g);\n", pts[1].fX, pts[1].fY);
+ SkDebugf("path.lineTo(%3.6g, %3.6g);\n", pts[1].fX, pts[1].fY);
break;
case SkPath::kQuad_Verb:
- SkDebugf("path.quadTo(%g, %g, %g, %g);\n",
+ SkDebugf("path.quadTo(%3.6g, %3.6g, %3.6g, %3.6g);\n",
pts[1].fX, pts[1].fY, pts[2].fX, pts[2].fY);
break;
case SkPath::kCubic_Verb:
- SkDebugf("path.cubicTo(%g, %g, %g, %g);\n",
+ SkDebugf("path.cubicTo(%3.6g, %3.6g, %3.6g, %3.6g);\n",
pts[1].fX, pts[1].fY, pts[2].fX, pts[2].fY,
pts[3].fX, pts[3].fY);
break;
@@ -77,14 +76,14 @@
return true;
}
-static void drawAsciiPaths(const SkPath& one, const SkPath& two,
+void drawAsciiPaths(const SkPath& one, const SkPath& two,
bool drawPaths) {
if (!drawPaths) {
return;
}
- if (0) {
- showPath("one:", one);
- showPath("two:", two);
+ if (gShowAsciiPaths) {
+ showPath(one, "one:");
+ showPath(two, "two:");
}
const SkRect& bounds1 = one.getBounds();
const SkRect& bounds2 = two.getBounds();
@@ -139,22 +138,25 @@
return false;
}
-void comparePaths(const SkPath& one, const SkPath& two) {
+bool comparePaths(const SkPath& one, const SkPath& two) {
if (pathsDrawTheSame(one, two)) {
- return;
+ return true;
}
drawAsciiPaths(one, two, gDrawAllAsciiPaths);
for (int x = 9; x <= 33; ++x) {
if (scaledDrawTheSame(one, two, x, x - (x >> 2), gDrawAllAsciiPaths)) {
- return;
+ return true;
}
}
if (!gDrawAllAsciiPaths) {
scaledDrawTheSame(one, two, 9, 7, gDrawLastAsciiPaths);
}
- showPath("original:", one);
- showPath("simplified:", two);
- SkASSERT(0);
+ if (gComparePathsAssert) {
+ showPath(one);
+ showPath(two, "simplified:");
+ SkASSERT(0);
+ }
+ return false;
}
// doesn't work yet
@@ -188,3 +190,10 @@
}
}
+bool testSimplify(const SkPath& path, bool fill, SkPath& out) {
+ if (gShowPath) {
+ showPath(path);
+ }
+ simplify(path, fill, out);
+ return comparePaths(path, out);
+}
diff --git a/experimental/Intersection/Intersection_Tests.cpp b/experimental/Intersection/Intersection_Tests.cpp
index 2a1620e..2cf9601 100644
--- a/experimental/Intersection/Intersection_Tests.cpp
+++ b/experimental/Intersection/Intersection_Tests.cpp
@@ -17,8 +17,8 @@
LineQuadraticIntersection_Test();
LineCubicIntersection_Test();
- SimplifyRectangularPaths_Test();
SimplifyPolygonPaths_Test();
+ SimplifyRectangularPaths_Test();
SimplifyQuadralateralPaths_Test();
QuadraticCoincidence_Test();
diff --git a/experimental/Intersection/LineIntersection.cpp b/experimental/Intersection/LineIntersection.cpp
index 4d80606..f5128ea 100644
--- a/experimental/Intersection/LineIntersection.cpp
+++ b/experimental/Intersection/LineIntersection.cpp
@@ -100,6 +100,28 @@
return 1;
}
+// OPTIMIZATION Given: dy = line[1].y - line[0].y
+// and: xIntercept / (y - line[0].y) == (line[1].x - line[0].x) / dy
+// then: xIntercept * dy == (line[1].x - line[0].x) * (y - line[0].y)
+// Assuming that dy is always > 0, the line segment intercepts if:
+// left * dy <= xIntercept * dy <= right * dy
+// thus: left * dy <= (line[1].x - line[0].x) * (y - line[0].y) <= right * dy
+// (clever as this is, it does not give us the t value, so may be useful only
+// as a quick reject -- and maybe not then; it takes 3 muls, 3 adds, 2 cmps)
+int horizontalLineIntersect(const _Line& line, double left, double right,
+ double y, double tRange[2]) {
+ int result = horizontalIntersect(line, y, tRange);
+ if (result != 1) {
+ return result;
+ }
+ // FIXME: this is incorrect if result == 2
+ double xIntercept = line[0].x + tRange[0] * (line[1].x - line[0].x);
+ if (xIntercept > right || xIntercept < left) {
+ return 0;
+ }
+ return result;
+}
+
// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
// 4 subs, 2 muls, 1 cmp
static bool ccw(const _Point& A, const _Point& B, const _Point& C) {
diff --git a/experimental/Intersection/LineIntersection.h b/experimental/Intersection/LineIntersection.h
index dfae7ef..687b77d 100644
--- a/experimental/Intersection/LineIntersection.h
+++ b/experimental/Intersection/LineIntersection.h
@@ -2,5 +2,7 @@
#include "DataTypes.h"
int horizontalIntersect(const _Line& line, double y, double tRange[2]);
+int horizontalLineIntersect(const _Line& line, double left, double right,
+ double y, double tRange[2]);
int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]);
bool testIntersect(const _Line& a, const _Line& b);
diff --git a/experimental/Intersection/edge.xcodeproj/project.pbxproj b/experimental/Intersection/edge.xcodeproj/project.pbxproj
index cf433c6..1b520f1 100644
--- a/experimental/Intersection/edge.xcodeproj/project.pbxproj
+++ b/experimental/Intersection/edge.xcodeproj/project.pbxproj
@@ -11,6 +11,7 @@
8D11072B0486CEB800E47090 /* InfoPlist.strings in Resources */ = {isa = PBXBuildFile; fileRef = 089C165CFE840E0CC02AAC07 /* InfoPlist.strings */; };
FE3201C8144DCC68006DDA67 /* skia_mac.mm in Sources */ = {isa = PBXBuildFile; fileRef = FE3201C6144DCC68006DDA67 /* skia_mac.mm */; };
FE3201C9144DCC68006DDA67 /* SkOSWindow_Mac.mm in Sources */ = {isa = PBXBuildFile; fileRef = FE3201C7144DCC68006DDA67 /* SkOSWindow_Mac.mm */; };
+ FE3DBAFE150E4A680006ADF4 /* junk.htm in Resources */ = {isa = PBXBuildFile; fileRef = FE3DBAFD150E4A680006ADF4 /* junk.htm */; };
FE7130A114CE0EEB0008E392 /* LineQuadraticIntersection.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FE7130A014CE0EEB0008E392 /* LineQuadraticIntersection.cpp */; };
FE7131C414CF5A960008E392 /* LineQuadraticIntersection_Test.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FE7131C314CF5A960008E392 /* LineQuadraticIntersection_Test.cpp */; };
FE7131EE14D03AED0008E392 /* LineCubicIntersection.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FE7131ED14D03AED0008E392 /* LineCubicIntersection.cpp */; };
@@ -59,6 +60,7 @@
FECAA6E114BDDF2D00B35E2C /* QuadraticReduceOrder_Test.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FECAA6E014BDDF2D00B35E2C /* QuadraticReduceOrder_Test.cpp */; };
FED53C391483CB9400F6359E /* Inline_Tests.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FED53C381483CB9400F6359E /* Inline_Tests.cpp */; };
FED865F915056A79006F4508 /* EdgeWalkerQuadralaterals_Test.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FED865F815056A79006F4508 /* EdgeWalkerQuadralaterals_Test.cpp */; };
+ FED866D715066642006F4508 /* EdgeWalkerPolygons_Mismatches.cpp in Sources */ = {isa = PBXBuildFile; fileRef = FED866D615066642006F4508 /* EdgeWalkerPolygons_Mismatches.cpp */; };
FEED7245144DD2250059E97B /* SkEventNotifier.mm in Sources */ = {isa = PBXBuildFile; fileRef = FEED723E144DD2250059E97B /* SkEventNotifier.mm */; };
FEED7292144DD4610059E97B /* libexperimental.a in Frameworks */ = {isa = PBXBuildFile; fileRef = FEED726E144DD4050059E97B /* libexperimental.a */; };
FEED7293144DD4620059E97B /* libskgr.a in Frameworks */ = {isa = PBXBuildFile; fileRef = FEED7276144DD4140059E97B /* libskgr.a */; };
@@ -237,6 +239,8 @@
8D1107320486CEB800E47090 /* edge.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = edge.app; sourceTree = BUILT_PRODUCTS_DIR; };
FE3201C6144DCC68006DDA67 /* skia_mac.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; name = skia_mac.mm; path = ../../src/utils/mac/skia_mac.mm; sourceTree = SOURCE_ROOT; };
FE3201C7144DCC68006DDA67 /* SkOSWindow_Mac.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; name = SkOSWindow_Mac.mm; path = ../../src/utils/mac/SkOSWindow_Mac.mm; sourceTree = SOURCE_ROOT; };
+ FE3DB8C9150A48320006ADF4 /* junk.txt */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text; path = junk.txt; sourceTree = "<group>"; };
+ FE3DBAFD150E4A680006ADF4 /* junk.htm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.html; name = junk.htm; path = ../../../../../junk.htm; sourceTree = SOURCE_ROOT; };
FE4FE7411492417500A12A34 /* IntersectionUtilities.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = IntersectionUtilities.cpp; sourceTree = "<group>"; };
FE7130A014CE0EEB0008E392 /* LineQuadraticIntersection.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = LineQuadraticIntersection.cpp; sourceTree = "<group>"; };
FE7131C314CF5A960008E392 /* LineQuadraticIntersection_Test.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = LineQuadraticIntersection_Test.cpp; sourceTree = "<group>"; };
@@ -301,6 +305,7 @@
FECAACA614BE1C6100B35E2C /* QuadraticParameterization_TestUtility.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = QuadraticParameterization_TestUtility.cpp; sourceTree = "<group>"; };
FED53C381483CB9400F6359E /* Inline_Tests.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = Inline_Tests.cpp; sourceTree = "<group>"; };
FED865F815056A79006F4508 /* EdgeWalkerQuadralaterals_Test.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = EdgeWalkerQuadralaterals_Test.cpp; sourceTree = "<group>"; };
+ FED866D615066642006F4508 /* EdgeWalkerPolygons_Mismatches.cpp */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; path = EdgeWalkerPolygons_Mismatches.cpp; sourceTree = "<group>"; };
FEED723C144DD2250059E97B /* SampleApp.xib */ = {isa = PBXFileReference; lastKnownFileType = file.xib; name = SampleApp.xib; path = ../../src/utils/mac/SampleApp.xib; sourceTree = SOURCE_ROOT; };
FEED723D144DD2250059E97B /* SampleAppDelegate.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; name = SampleAppDelegate.mm; path = ../../src/utils/mac/SampleAppDelegate.mm; sourceTree = SOURCE_ROOT; };
FEED723E144DD2250059E97B /* SkEventNotifier.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; name = SkEventNotifier.mm; path = ../../src/utils/mac/SkEventNotifier.mm; sourceTree = SOURCE_ROOT; };
@@ -476,6 +481,8 @@
FE71354F14D305FD0008E392 /* ShapeOps */ = {
isa = PBXGroup;
children = (
+ FE3DBAFD150E4A680006ADF4 /* junk.htm */,
+ FE3DB8C9150A48320006ADF4 /* junk.txt */,
FE71358514D309E90008E392 /* EdgeWalker.cpp */,
FE713C6114D9879B0008E392 /* TSearch.h */,
);
@@ -539,6 +546,7 @@
FEED764B144F29BD0059E97B /* TestUtilities.cpp */,
FE7413DB14F6926D00056D7B /* EdgeWalker_Test.h */,
FED865F815056A79006F4508 /* EdgeWalkerQuadralaterals_Test.cpp */,
+ FED866D615066642006F4508 /* EdgeWalkerPolygons_Mismatches.cpp */,
);
name = Tests;
sourceTree = "<group>";
@@ -890,6 +898,7 @@
8D11072B0486CEB800E47090 /* InfoPlist.strings in Resources */,
1DDD58160DA1D0A300B32029 /* MainMenu.xib in Resources */,
FEED72B0144DD5710059E97B /* SampleApp.xib in Resources */,
+ FE3DBAFE150E4A680006ADF4 /* junk.htm in Resources */,
);
runOnlyForDeploymentPostprocessing = 0;
};
@@ -952,6 +961,7 @@
FE7413D414F6915A00056D7B /* EdgeWalkerPolygons_Test.cpp in Sources */,
FE7413D814F691C200056D7B /* EdgeWalker_TestUtility.cpp in Sources */,
FED865F915056A79006F4508 /* EdgeWalkerQuadralaterals_Test.cpp in Sources */,
+ FED866D715066642006F4508 /* EdgeWalkerPolygons_Mismatches.cpp in Sources */,
);
runOnlyForDeploymentPostprocessing = 0;
};