Add intersections for path ops

src/pathops/SkDLineIntersection.cpp

+/*
+ * 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 "SkIntersections.h"
+#include "SkPathOpsLine.h"
+
+/* Determine the intersection point of two lines. This assumes the lines are not parallel,
+   and that that the lines are infinite.
+   From http://en.wikipedia.org/wiki/Line-line_intersection
+ */
+SkDPoint SkIntersections::Line(const SkDLine& a, const SkDLine& b) {
+    double axLen = a[1].fX - a[0].fX;
+    double ayLen = a[1].fY - a[0].fY;
+    double bxLen = b[1].fX - b[0].fX;
+    double byLen = b[1].fY - b[0].fY;
+    double denom = byLen * axLen - ayLen * bxLen;
+    SkASSERT(denom);
+    double term1 = a[1].fX * a[0].fY - a[1].fY * a[0].fX;
+    double term2 = b[1].fX * b[0].fY - b[1].fY * b[0].fX;
+    SkDPoint p;
+    p.fX = (term1 * bxLen - axLen * term2) / denom;
+    p.fY = (term1 * byLen - ayLen * term2) / denom;
+    return p;
+}
+
+int SkIntersections::computePoints(const SkDLine& line, int used) {
+    fPt[0] = line.xyAtT(fT[0][0]);
+    if ((fUsed = used) == 2) {
+        fPt[1] = line.xyAtT(fT[0][1]);
+    }
+    return fUsed;
+}
+
+/*
+   Determine the intersection point of two line segments
+   Return FALSE if the lines don't intersect
+   from: http://paulbourke.net/geometry/lineline2d/
+ */
+
+int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) {
+    double axLen = a[1].fX - a[0].fX;
+    double ayLen = a[1].fY - a[0].fY;
+    double bxLen = b[1].fX - b[0].fX;
+    double byLen = b[1].fY - b[0].fY;
+    /* Slopes match when denom goes to zero:
+                      axLen / ayLen ==                   bxLen / byLen
+    (ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
+             byLen  * axLen         ==  ayLen          * bxLen
+             byLen  * axLen         -   ayLen          * bxLen == 0 ( == denom )
+     */
+    double denom = byLen * axLen - ayLen * bxLen;
+    double ab0y = a[0].fY - b[0].fY;
+    double ab0x = a[0].fX - b[0].fX;
+    double numerA = ab0y * bxLen - byLen * ab0x;
+    double numerB = ab0y * axLen - ayLen * ab0x;
+    bool mayNotOverlap = (numerA < 0 && denom > numerA) || (numerA > 0 && denom < numerA)
+            || (numerB < 0 && denom > numerB) || (numerB > 0 && denom < numerB);
+    numerA /= denom;
+    numerB /= denom;
+    if ((!approximately_zero(denom) || (!approximately_zero_inverse(numerA)
+            && !approximately_zero_inverse(numerB))) && !sk_double_isnan(numerA)
+            && !sk_double_isnan(numerB)) {
+        if (mayNotOverlap) {
+            return fUsed = 0;
+        }
+        fT[0][0] = numerA;
+        fT[1][0] = numerB;
+        fPt[0] = a.xyAtT(numerA);
+        return computePoints(a, 1);
+    }
+   /* See if the axis intercepts match:
+              ay - ax * ayLen / axLen  ==          by - bx * ayLen / axLen
+     axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
+     axLen *  ay - ax * ayLen          == axLen *  by - bx * ayLen
+    */
+    // FIXME: need to use AlmostEqualUlps variant instead
+    if (!approximately_equal_squared(axLen * a[0].fY - ayLen * a[0].fX,
+            axLen * b[0].fY - ayLen * b[0].fX)) {
+        return fUsed = 0;
+    }
+    const double* aPtr;
+    const double* bPtr;
+    if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) {
+        aPtr = &a[0].fX;
+        bPtr = &b[0].fX;
+    } else {
+        aPtr = &a[0].fY;
+        bPtr = &b[0].fY;
+    }
+    double a0 = aPtr[0];
+    double a1 = aPtr[2];
+    double b0 = bPtr[0];
+    double b1 = bPtr[2];
+    // OPTIMIZATION: restructure to reject before the divide
+    // e.g., if ((a0 - b0) * (a0 - a1) < 0 || abs(a0 - b0) > abs(a0 - a1))
+    // (except efficient)
+    double aDenom = a0 - a1;
+    if (approximately_zero(aDenom)) {
+        if (!between(b0, a0, b1)) {
+            return fUsed = 0;
+        }
+        fT[0][0] = fT[0][1] = 0;
+    } else {
+        double at0 = (a0 - b0) / aDenom;
+        double at1 = (a0 - b1) / aDenom;
+        if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
+            return fUsed = 0;
+        }
+        fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
+        fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
+    }
+    double bDenom = b0 - b1;
+    if (approximately_zero(bDenom)) {
+        fT[1][0] = fT[1][1] = 0;
+    } else {
+        int bIn = aDenom * bDenom < 0;
+        fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / bDenom, 1.0), 0.0);
+        fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / bDenom, 1.0), 0.0);
+    }
+    bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
+    SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
+    return computePoints(a, 1 + second);
+}
+
+int SkIntersections::horizontal(const SkDLine& line, double y) {
+    double min = line[0].fY;
+    double max = line[1].fY;
+    if (min > max) {
+        SkTSwap(min, max);
+    }
+    if (min > y || max < y) {
+        return fUsed = 0;
+    }
+    if (AlmostEqualUlps(min, max)) {
+        fT[0][0] = 0;
+        fT[0][1] = 1;
+        return fUsed = 2;
+    }
+    fT[0][0] = (y - line[0].fY) / (line[1].fY - line[0].fY);
+    return fUsed = 1;
+}
+
+// OPTIMIZATION  Given: dy = line[1].fY - line[0].fY
+// and: xIntercept / (y - line[0].fY) == (line[1].fX - line[0].fX) / dy
+// then: xIntercept * dy == (line[1].fX - line[0].fX) * (y - line[0].fY)
+// Assuming that dy is always > 0, the line segment intercepts if:
+//   left * dy <= xIntercept * dy <= right * dy
+// thus: left * dy <= (line[1].fX - line[0].fX) * (y - line[0].fY) <= 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 SkIntersections::horizontal(const SkDLine& line, double left, double right, double y) {
+    int result = horizontal(line, y);
+    if (result != 1) {
+        SkASSERT(result == 0); // FIXME: this is incorrect if result == 2
+        return result;
+    }
+    double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
+    if (xIntercept > right || xIntercept < left) {
+        return fUsed = 0;
+    }
+    return result;
+}
+
+int SkIntersections::horizontal(const SkDLine& line, double left, double right,
+                                double y, bool flipped) {
+    int result = horizontal(line, y);
+    switch (result) {
+        case 0:
+            break;
+        case 1: {
+            double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
+            if (xIntercept > right || xIntercept < left) {
+                return fUsed = 0;
+            }
+            fT[1][0] = (xIntercept - left) / (right - left);
+            break;
+        }
+        case 2:
+            double a0 = line[0].fX;
+            double a1 = line[1].fX;
+            double b0 = flipped ? right : left;
+            double b1 = flipped ? left : right;
+            // FIXME: share common code below
+            double at0 = (a0 - b0) / (a0 - a1);
+            double at1 = (a0 - b1) / (a0 - a1);
+            if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
+                return fUsed = 0;
+            }
+            fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
+            fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
+            int bIn = (a0 - a1) * (b0 - b1) < 0;
+            fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), 1.0), 0.0);
+            fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), 1.0), 0.0);
+            bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
+            SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
+            return computePoints(line, 1 + second);
+    }
+    if (flipped) {
+        // OPTIMIZATION: instead of swapping, pass original line, use [1].fX - [0].fX
+        for (int index = 0; index < result; ++index) {
+            fT[1][index] = 1 - fT[1][index];
+        }
+    }
+    return computePoints(line, result);
+}
+
+int SkIntersections::vertical(const SkDLine& line, double x) {
+    double min = line[0].fX;
+    double max = line[1].fX;
+    if (min > max) {
+        SkTSwap(min, max);
+    }
+    if (min > x || max < x) {
+        return fUsed = 0;
+    }
+    if (AlmostEqualUlps(min, max)) {
+        fT[0][0] = 0;
+        fT[0][1] = 1;
+        return fUsed = 2;
+    }
+    fT[0][0] = (x - line[0].fX) / (line[1].fX - line[0].fX);
+    return fUsed = 1;
+}
+
+int SkIntersections::vertical(const SkDLine& line, double top, double bottom,
+                              double x, bool flipped) {
+    int result = vertical(line, x);
+    switch (result) {
+        case 0:
+            break;
+        case 1: {
+            double yIntercept = line[0].fY + fT[0][0] * (line[1].fY - line[0].fY);
+            if (yIntercept > bottom || yIntercept < top) {
+                return fUsed = 0;
+            }
+            fT[1][0] = (yIntercept - top) / (bottom - top);
+            break;
+        }
+        case 2:
+            double a0 = line[0].fY;
+            double a1 = line[1].fY;
+            double b0 = flipped ? bottom : top;
+            double b1 = flipped ? top : bottom;
+            // FIXME: share common code above
+            double at0 = (a0 - b0) / (a0 - a1);
+            double at1 = (a0 - b1) / (a0 - a1);
+            if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
+                return fUsed = 0;
+            }
+            fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
+            fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
+            int bIn = (a0 - a1) * (b0 - b1) < 0;
+            fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), 1.0), 0.0);
+            fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), 1.0), 0.0);
+            bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
+            SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
+            return computePoints(line, 1 + second);
+            break;
+    }
+    if (flipped) {
+        // OPTIMIZATION: instead of swapping, pass original line, use [1].fY - [0].fY
+        for (int index = 0; index < result; ++index) {
+            fT[1][index] = 1 - fT[1][index];
+        }
+    }
+    return computePoints(line, result);
+}
+
+// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
+// 4 subs, 2 muls, 1 cmp
+static bool ccw(const SkDPoint& A, const SkDPoint& B, const SkDPoint& C) {
+    return (C.fY - A.fY) * (B.fX - A.fX) > (B.fY - A.fY) * (C.fX - A.fX);
+}
+
+// 16 subs, 8 muls, 6 cmps
+bool SkIntersections::Test(const SkDLine& a, const SkDLine& b) {
+    return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1])
+            && ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]);
+}