Add base types for path ops

Paths contain lines, quads, and cubics, which are
collectively curves.

To work with path intersections, intermediary curves
are constructed. For now, those intermediates use
doubles to guarantee sufficient precision.

The DVector, DPoint, DLine, DQuad, and DCubic
structs encapsulate these intermediate curves.

The DRect and DTriangle structs are created to
describe intersectable areas of interest.

The Bounds struct inherits from SkRect to create
a SkScalar-based rectangle that intersects shared
edges.

This also includes common math equalities and
debugging that the remainder of path ops builds on,
as well as a temporary top-level interface in
include/pathops/SkPathOps.h.
Review URL: https://codereview.chromium.org/12827020

git-svn-id: http://skia.googlecode.com/svn/trunk@8551 2bbb7eff-a529-9590-31e7-b0007b416f81

1 files changed, 430 insertions, 0 deletions

diff --git a/src/pathops/SkAddIntersections.cpp b/src/pathops/SkAddIntersections.cpp
new file mode 100644
index 0000000000..9efd4d63eb
--- /dev/null
+++ b/src/pathops/SkAddIntersections.cpp
@@ -0,0 +1,430 @@
+/*
+ * Copyright 2012 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+#include "SkAddIntersections.h"
+#include "SkPathOpsBounds.h"
+
+#if DEBUG_ADD_INTERSECTING_TS
+
+static void debugShowLineIntersection(int pts, const SkIntersectionHelper& wt,
+                                      const SkIntersectionHelper& wn, const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no intersect " LINE_DEBUG_STR " " LINE_DEBUG_STR "\n",
+                __FUNCTION__, LINE_DEBUG_DATA(wt.pts()), LINE_DEBUG_DATA(wn.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " LINE_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], LINE_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    if (pts == 2) {
+        SkDebugf(" " T_DEBUG_STR(wtTs, 1) " " PT_DEBUG_STR, i[0][1], PT_DEBUG_DATA(i, 1));
+    }
+    SkDebugf(" wnTs[0]=%g " LINE_DEBUG_STR, i[1][0], LINE_DEBUG_DATA(wn.pts()));
+    if (pts == 2) {
+        SkDebugf(" " T_DEBUG_STR(wnTs, 1), i[1][1]);
+    }
+    SkDebugf("\n");
+}
+
+static void debugShowQuadLineIntersection(int pts, const SkIntersectionHelper& wt,
+                                          const SkIntersectionHelper& wn,
+                                          const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no intersect " QUAD_DEBUG_STR " " LINE_DEBUG_STR "\n",
+                __FUNCTION__, QUAD_DEBUG_DATA(wt.pts()), LINE_DEBUG_DATA(wn.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " QUAD_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], QUAD_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wtTs) " " PT_DEBUG_STR, n, i[0][n], PT_DEBUG_DATA(i, n));
+    }
+    SkDebugf(" wnTs[0]=%g " LINE_DEBUG_STR, i[1][0], LINE_DEBUG_DATA(wn.pts()));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wnTs), n, i[1][n]);
+    }
+    SkDebugf("\n");
+}
+
+static void debugShowQuadIntersection(int pts, const SkIntersectionHelper& wt,
+        const SkIntersectionHelper& wn, const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no intersect " QUAD_DEBUG_STR " " QUAD_DEBUG_STR "\n",
+                __FUNCTION__, QUAD_DEBUG_DATA(wt.pts()), QUAD_DEBUG_DATA(wn.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " QUAD_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], QUAD_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wtTs) " " PT_DEBUG_STR, n, i[0][n], PT_DEBUG_DATA(i, n));
+    }
+    SkDebugf(" wnTs[0]=%g " QUAD_DEBUG_STR, i[1][0], QUAD_DEBUG_DATA(wn.pts()));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wnTs), n, i[1][n]);
+    }
+    SkDebugf("\n");
+}
+
+static void debugShowCubicLineIntersection(int pts, const SkIntersectionHelper& wt,
+        const SkIntersectionHelper& wn, const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no intersect " CUBIC_DEBUG_STR " " LINE_DEBUG_STR "\n",
+                __FUNCTION__, CUBIC_DEBUG_DATA(wt.pts()), LINE_DEBUG_DATA(wn.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " CUBIC_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], CUBIC_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wtTs) " " PT_DEBUG_STR, n, i[0][n], PT_DEBUG_DATA(i, n));
+    }
+    SkDebugf(" wnTs[0]=%g " LINE_DEBUG_STR, i[1][0], LINE_DEBUG_DATA(wn.pts()));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wnTs), n, i[1][n]);
+    }
+    SkDebugf("\n");
+}
+
+static void debugShowCubicQuadIntersection(int pts, const SkIntersectionHelper& wt,
+        const SkIntersectionHelper& wn, const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no intersect " CUBIC_DEBUG_STR " " QUAD_DEBUG_STR "\n",
+                __FUNCTION__, CUBIC_DEBUG_DATA(wt.pts()), QUAD_DEBUG_DATA(wn.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " CUBIC_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], CUBIC_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wtTs) " " PT_DEBUG_STR, n, i[0][n], PT_DEBUG_DATA(i, n));
+    }
+    SkDebugf(" wnTs[0]=%g " QUAD_DEBUG_STR, i[1][0], QUAD_DEBUG_DATA(wn.pts()));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wnTs), n, i[1][n]);
+    }
+    SkDebugf("\n");
+}
+
+static void debugShowCubicIntersection(int pts, const SkIntersectionHelper& wt,
+        const SkIntersectionHelper& wn, const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no intersect " CUBIC_DEBUG_STR " " CUBIC_DEBUG_STR "\n",
+                __FUNCTION__, CUBIC_DEBUG_DATA(wt.pts()), CUBIC_DEBUG_DATA(wn.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " CUBIC_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], CUBIC_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wtTs) " " PT_DEBUG_STR, n, i[0][n], PT_DEBUG_DATA(i, n));
+    }
+    SkDebugf(" wnTs[0]=%g " CUBIC_DEBUG_STR, i[1][0], CUBIC_DEBUG_DATA(wn.pts()));
+    for (int n = 1; n < pts; ++n) {
+        SkDebugf(" " TX_DEBUG_STR(wnTs), n, i[1][n]);
+    }
+    SkDebugf("\n");
+}
+
+static void debugShowCubicIntersection(int pts, const SkIntersectionHelper& wt,
+        const SkIntersections& i) {
+    SkASSERT(i.used() == pts);
+    if (!pts) {
+        SkDebugf("%s no self intersect " CUBIC_DEBUG_STR "\n", __FUNCTION__,
+                CUBIC_DEBUG_DATA(wt.pts()));
+        return;
+    }
+    SkDebugf("%s " T_DEBUG_STR(wtTs, 0) " " CUBIC_DEBUG_STR " " PT_DEBUG_STR, __FUNCTION__,
+            i[0][0], CUBIC_DEBUG_DATA(wt.pts()), PT_DEBUG_DATA(i, 0));
+    SkDebugf(" " T_DEBUG_STR(wtTs, 1), i[1][0]);
+    SkDebugf("\n");
+}
+
+#else
+static void debugShowLineIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersectionHelper& , const SkIntersections& ) {
+}
+
+static void debugShowQuadLineIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersectionHelper& , const SkIntersections& ) {
+}
+
+static void debugShowQuadIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersectionHelper& , const SkIntersections& ) {
+}
+
+static void debugShowCubicLineIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersectionHelper& , const SkIntersections& ) {
+}
+
+static void debugShowCubicQuadIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersectionHelper& , const SkIntersections& ) {
+}
+
+static void debugShowCubicIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersectionHelper& , const SkIntersections& ) {
+}
+
+static void debugShowCubicIntersection(int , const SkIntersectionHelper& ,
+        const SkIntersections& ) {
+}
+#endif
+
+bool AddIntersectTs(SkOpContour* test, SkOpContour* next) {
+    if (test != next) {
+        if (test->bounds().fBottom < next->bounds().fTop) {
+            return false;
+        }
+        if (!SkPathOpsBounds::Intersects(test->bounds(), next->bounds())) {
+            return true;
+        }
+    }
+    SkIntersectionHelper wt;
+    wt.init(test);
+    bool foundCommonContour = test == next;
+    do {
+        SkIntersectionHelper wn;
+        wn.init(next);
+        if (test == next && !wn.startAfter(wt)) {
+            continue;
+        }
+        do {
+            if (!SkPathOpsBounds::Intersects(wt.bounds(), wn.bounds())) {
+                continue;
+            }
+            int pts = 0;
+            SkIntersections ts;
+            bool swap = false;
+            switch (wt.segmentType()) {
+                case SkIntersectionHelper::kHorizontalLine_Segment:
+                    swap = true;
+                    switch (wn.segmentType()) {
+                        case SkIntersectionHelper::kHorizontalLine_Segment:
+                        case SkIntersectionHelper::kVerticalLine_Segment:
+                        case SkIntersectionHelper::kLine_Segment: {
+                            pts = ts.lineHorizontal(wn.pts(), wt.left(),
+                                    wt.right(), wt.y(), wt.xFlipped());
+                            debugShowLineIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kQuad_Segment: {
+                            pts = ts.quadHorizontal(wn.pts(), wt.left(),
+                                    wt.right(), wt.y(), wt.xFlipped());
+                            debugShowQuadLineIntersection(pts, wn, wt, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kCubic_Segment: {
+                            pts = ts.cubicHorizontal(wn.pts(), wt.left(),
+                                    wt.right(), wt.y(), wt.xFlipped());
+                            debugShowCubicLineIntersection(pts, wn, wt, ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case SkIntersectionHelper::kVerticalLine_Segment:
+                    swap = true;
+                    switch (wn.segmentType()) {
+                        case SkIntersectionHelper::kHorizontalLine_Segment:
+                        case SkIntersectionHelper::kVerticalLine_Segment:
+                        case SkIntersectionHelper::kLine_Segment: {
+                            pts = ts.lineVertical(wn.pts(), wt.top(),
+                                    wt.bottom(), wt.x(), wt.yFlipped());
+                            debugShowLineIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kQuad_Segment: {
+                            pts = ts.quadVertical(wn.pts(), wt.top(),
+                                    wt.bottom(), wt.x(), wt.yFlipped());
+                            debugShowQuadLineIntersection(pts, wn, wt, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kCubic_Segment: {
+                            pts = ts.cubicVertical(wn.pts(), wt.top(),
+                                    wt.bottom(), wt.x(), wt.yFlipped());
+                            debugShowCubicLineIntersection(pts, wn, wt, ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case SkIntersectionHelper::kLine_Segment:
+                    switch (wn.segmentType()) {
+                        case SkIntersectionHelper::kHorizontalLine_Segment:
+                            pts = ts.lineHorizontal(wt.pts(), wn.left(),
+                                    wn.right(), wn.y(), wn.xFlipped());
+                            debugShowLineIntersection(pts, wt, wn, ts);
+                            break;
+                        case SkIntersectionHelper::kVerticalLine_Segment:
+                            pts = ts.lineVertical(wt.pts(), wn.top(),
+                                    wn.bottom(), wn.x(), wn.yFlipped());
+                            debugShowLineIntersection(pts, wt, wn, ts);
+                            break;
+                        case SkIntersectionHelper::kLine_Segment: {
+                            pts = ts.lineLine(wt.pts(), wn.pts());
+                            debugShowLineIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kQuad_Segment: {
+                            swap = true;
+                            pts = ts.quadLine(wn.pts(), wt.pts());
+                            debugShowQuadLineIntersection(pts, wn, wt, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kCubic_Segment: {
+                            swap = true;
+                            pts = ts.cubicLine(wn.pts(), wt.pts());
+                            debugShowCubicLineIntersection(pts, wn, wt,  ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case SkIntersectionHelper::kQuad_Segment:
+                    switch (wn.segmentType()) {
+                        case SkIntersectionHelper::kHorizontalLine_Segment:
+                            pts = ts.quadHorizontal(wt.pts(), wn.left(),
+                                    wn.right(), wn.y(), wn.xFlipped());
+                            debugShowQuadLineIntersection(pts, wt, wn, ts);
+                            break;
+                        case SkIntersectionHelper::kVerticalLine_Segment:
+                            pts = ts.quadVertical(wt.pts(), wn.top(),
+                                    wn.bottom(), wn.x(), wn.yFlipped());
+                            debugShowQuadLineIntersection(pts, wt, wn, ts);
+                            break;
+                        case SkIntersectionHelper::kLine_Segment: {
+                            pts = ts.quadLine(wt.pts(), wn.pts());
+                            debugShowQuadLineIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kQuad_Segment: {
+                            pts = ts.quadQuad(wt.pts(), wn.pts());
+                            debugShowQuadIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kCubic_Segment: {
+                            swap = true;
+                            pts = ts.cubicQuad(wn.pts(), wt.pts());
+                            debugShowCubicQuadIntersection(pts, wn, wt, ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case SkIntersectionHelper::kCubic_Segment:
+                    switch (wn.segmentType()) {
+                        case SkIntersectionHelper::kHorizontalLine_Segment:
+                            pts = ts.cubicHorizontal(wt.pts(), wn.left(),
+                                    wn.right(), wn.y(), wn.xFlipped());
+                            debugShowCubicLineIntersection(pts, wt, wn, ts);
+                            break;
+                        case SkIntersectionHelper::kVerticalLine_Segment:
+                            pts = ts.cubicVertical(wt.pts(), wn.top(),
+                                    wn.bottom(), wn.x(), wn.yFlipped());
+                            debugShowCubicLineIntersection(pts, wt, wn, ts);
+                            break;
+                        case SkIntersectionHelper::kLine_Segment: {
+                            pts = ts.cubicLine(wt.pts(), wn.pts());
+                            debugShowCubicLineIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kQuad_Segment: {
+                            pts = ts.cubicQuad(wt.pts(), wn.pts());
+                            debugShowCubicQuadIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        case SkIntersectionHelper::kCubic_Segment: {
+                            pts = ts.cubicCubic(wt.pts(), wn.pts());
+                            debugShowCubicIntersection(pts, wt, wn, ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                default:
+                    SkASSERT(0);
+            }
+            if (!foundCommonContour && pts > 0) {
+                test->addCross(next);
+                next->addCross(test);
+                foundCommonContour = true;
+            }
+            // in addition to recording T values, record matching segment
+            if (pts == 2) {
+                if (wn.segmentType() <= SkIntersectionHelper::kLine_Segment
+                        && wt.segmentType() <= SkIntersectionHelper::kLine_Segment) {
+                    wt.addCoincident(wn, ts, swap);
+                    continue;
+                }
+                if (wn.segmentType() >= SkIntersectionHelper::kQuad_Segment
+                        && wt.segmentType() >= SkIntersectionHelper::kQuad_Segment
+                        && ts.isCoincident(0)) {
+                    SkASSERT(ts.coincidentUsed() == 2);
+                    wt.addCoincident(wn, ts, swap);
+                    continue;
+                }
+            }
+            for (int pt = 0; pt < pts; ++pt) {
+                SkASSERT(ts[0][pt] >= 0 && ts[0][pt] <= 1);
+                SkASSERT(ts[1][pt] >= 0 && ts[1][pt] <= 1);
+                SkPoint point = ts.pt(pt).asSkPoint();
+                int testTAt = wt.addT(wn, point, ts[swap][pt]);
+                int nextTAt = wn.addT(wt, point, ts[!swap][pt]);
+                wt.addOtherT(testTAt, ts[!swap][pt], nextTAt);
+                wn.addOtherT(nextTAt, ts[swap][pt], testTAt);
+            }
+        } while (wn.advance());
+    } while (wt.advance());
+    return true;
+}
+
+void AddSelfIntersectTs(SkOpContour* test) {
+    SkIntersectionHelper wt;
+    wt.init(test);
+    do {
+        if (wt.segmentType() != SkIntersectionHelper::kCubic_Segment) {
+            continue;
+        }
+        SkIntersections ts;
+        int pts = ts.cubic(wt.pts());
+        debugShowCubicIntersection(pts, wt, ts);
+        if (!pts) {
+            continue;
+        }
+        SkASSERT(pts == 1);
+        SkASSERT(ts[0][0] >= 0 && ts[0][0] <= 1);
+        SkASSERT(ts[1][0] >= 0 && ts[1][0] <= 1);
+        SkPoint point = ts.pt(0).asSkPoint();
+        int testTAt = wt.addSelfT(wt, point, ts[0][0]);
+        int nextTAt = wt.addT(wt, point, ts[1][0]);
+        wt.addOtherT(testTAt, ts[1][0], nextTAt);
+        wt.addOtherT(nextTAt, ts[0][0], testTAt);
+    } while (wt.advance());
+}
+
+// resolve any coincident pairs found while intersecting, and
+// see if coincidence is formed by clipping non-concident segments
+void CoincidenceCheck(SkTDArray<SkOpContour*>* contourList, int total) {
+    int contourCount = (*contourList).count();
+    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
+        SkOpContour* contour = (*contourList)[cIndex];
+        contour->addCoincidentPoints();
+    }
+    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
+        SkOpContour* contour = (*contourList)[cIndex];
+        contour->calcCoincidentWinding();
+    }
+    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
+        SkOpContour* contour = (*contourList)[cIndex];
+        contour->findTooCloseToCall();
+    }
+}