path ops near exact

src/pathops/SkDQuadLineIntersection.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"
 #include "SkPathOpsQuad.h"
 
@@ skipping 74 matching lines @@
        B = 2*(-(a -   b    ) + g'*(d  -   e    )      )
        C =   ( (a          ) - g'*(d           ) - h' )
  */
 
 
 class LineQuadraticIntersections {
 public:
     LineQuadraticIntersections(const SkDQuad& q, const SkDLine& l, SkIntersections* i)
         : quad(q)
         , line(l)
-        , intersections(i) {
+        , intersections(i)
+        , fAllowNear(true) {
+    }
+
+    void allowNear(bool allow) {
+        fAllowNear = allow;
     }
 
     int intersectRay(double roots[2]) {
     /*
         solve by rotating line+quad so line is horizontal, then finding the roots
         set up matrix to rotate quad to x-axis
         |cos(a) -sin(a)|
         |sin(a)  cos(a)|
         note that cos(a) = A(djacent) / Hypoteneuse
                   sin(a) = O(pposite) / Hypoteneuse
@@ skipping 13 matching lines @@
         }
         double A = r[2];
         double B = r[1];
         double C = r[0];
         A += C - 2 * B;  // A = a - 2*b + c
         B -= C;  // B = -(b - c)
         return SkDQuad::RootsValidT(A, 2 * B, C, roots);
     }
 
     int intersect() {
-        addEndPoints();
+        addExactEndPoints();
         double rootVals[2];
         int roots = intersectRay(rootVals);
         for (int index = 0; index < roots; ++index) {
             double quadT = rootVals[index];
             double lineT = findLineT(quadT);
             if (PinTs(&quadT, &lineT)) {
                 SkDPoint pt = line.xyAtT(lineT);
                 intersections->insert(quadT, lineT, pt);
             }
         }
+        if (fAllowNear) {
+            addNearEndPoints();
+        }
         return intersections->used();
     }
 
     int horizontalIntersect(double axisIntercept, double roots[2]) {
         double D = quad[2].fY;  // f
         double E = quad[1].fY;  // e
         double F = quad[0].fY;  // d
         D += F - 2 * E;         // D = d - 2*e + f
         E -= F;                 // E = -(d - e)
         F -= axisIntercept;
         return SkDQuad::RootsValidT(D, 2 * E, F, roots);
     }
 
     int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) {
-        addHorizontalEndPoints(left, right, axisIntercept);
+        addExactHorizontalEndPoints(left, right, axisIntercept);
         double rootVals[2];
         int roots = horizontalIntersect(axisIntercept, rootVals);
         for (int index = 0; index < roots; ++index) {
             double quadT = rootVals[index];
             SkDPoint pt = quad.xyAtT(quadT);
             double lineT = (pt.fX - left) / (right - left);
             if (PinTs(&quadT, &lineT)) {
                 intersections->insert(quadT, lineT, pt);
             }
         }
+        if (fAllowNear) {
+            addNearHorizontalEndPoints(left, right, axisIntercept);
+        }
         if (flipped) {
             intersections->flip();
         }
         return intersections->used();
     }
 
     int verticalIntersect(double axisIntercept, double roots[2]) {
         double D = quad[2].fX;  // f
         double E = quad[1].fX;  // e
         double F = quad[0].fX;  // d
         D += F - 2 * E;         // D = d - 2*e + f
         E -= F;                 // E = -(d - e)
         F -= axisIntercept;
         return SkDQuad::RootsValidT(D, 2 * E, F, roots);
     }
 
     int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) {
-        addVerticalEndPoints(top, bottom, axisIntercept);
+        addExactVerticalEndPoints(top, bottom, axisIntercept);
         double rootVals[2];
         int roots = verticalIntersect(axisIntercept, rootVals);
         for (int index = 0; index < roots; ++index) {
             double quadT = rootVals[index];
             SkDPoint pt = quad.xyAtT(quadT);
             double lineT = (pt.fY - top) / (bottom - top);
             if (PinTs(&quadT, &lineT)) {
                 intersections->insert(quadT, lineT, pt);
             }
         }
+        if (fAllowNear) {
+            addNearVerticalEndPoints(top, bottom, axisIntercept);
+        }
         if (flipped) {
             intersections->flip();
         }
         return intersections->used();
     }
 
 protected:
     // add endpoints first to get zero and one t values exactly
-    void addEndPoints() {
+    void addExactEndPoints() {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
-            bool foundEnd = false;
-            for (int lIndex = 0; lIndex < 2; lIndex++) {
-                if (quad[qIndex] == line[lIndex]) {
-                    intersections->insert(qIndex >> 1, lIndex, line[lIndex]);
-                    foundEnd = true;
-                }
-            }
-            if (foundEnd) {
+            double lineT = line.exactPoint(quad[qIndex]);
+            if (lineT < 0) {
                 continue;
             }
-            // See if the quad end touches the line.
-            double dist = line.isLeft(quad[qIndex]); // this distance isn't cartesian
-            SkDVector lineLen = line[1] - line[0]; // the x/y magnitudes of the line
-            // compute the ULPS of the larger of the x/y deltas
-            double larger = SkTMax(SkTAbs(lineLen.fX), SkTAbs(lineLen.fY));
-            if (!RoughlyEqualUlps(larger, larger + dist)) { // is the dist within ULPS tolerance?
-                continue;
-            }
-            double lineT = findLineT(qIndex >> 1);
-            if (!between(0, lineT, 1)) {
-                continue;
-            }
-            SkDPoint linePt = line.xyAtT(lineT);
-            if (linePt.approximatelyEqual(quad[qIndex])) {
-                intersections->insert(qIndex >> 1, lineT, quad[qIndex]);
-            }
+            double quadT = (double) (qIndex >> 1);
+            intersections->insert(quadT, lineT, quad[qIndex]);
         }
     }
 
-    void addHorizontalEndPoints(double left, double right, double y) {
+    void addNearEndPoints() {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
-            if (!AlmostEqualUlps(quad[qIndex].fY, y)) {
+            double quadT = (double) (qIndex >> 1);
+            if (intersections->hasT(quadT)) {
                 continue;
             }
-            double x = quad[qIndex].fX;
-            if (between(left, x, right)) {
-                double t = (x - left) / (right - left);
-                intersections->insert(qIndex >> 1, t, quad[qIndex]);
+            double lineT = line.nearPoint(quad[qIndex]);
+            if (lineT < 0) {
+                continue;
             }
+            intersections->insert(quadT, lineT, quad[qIndex]);
+        }
+        // FIXME: see if line end is nearly on quad
+    }
+
+    void addExactHorizontalEndPoints(double left, double right, double y) {
+        for (int qIndex = 0; qIndex < 3; qIndex += 2) {
+            double lineT = SkDLine::ExactPointH(quad[qIndex], left, right, y);
+            if (lineT < 0) {
+                continue;
+            }
+            double quadT = (double) (qIndex >> 1);
+            intersections->insert(quadT, lineT, quad[qIndex]);
         }
     }
 
-    void addVerticalEndPoints(double top, double bottom, double x) {
+    void addNearHorizontalEndPoints(double left, double right, double y) {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
-            if (!AlmostEqualUlps(quad[qIndex].fX, x)) {
+            double quadT = (double) (qIndex >> 1);
+            if (intersections->hasT(quadT)) {
                 continue;
             }
-            double y = quad[qIndex].fY;
-            if (between(top, y, bottom)) {
-                double t = (y - top) / (bottom - top);
-                intersections->insert(qIndex >> 1, t, quad[qIndex]);
+            double lineT = SkDLine::NearPointH(quad[qIndex], left, right, y);
+            if (lineT < 0) {
+                continue;
             }
+            intersections->insert(quadT, lineT, quad[qIndex]);
         }
+        // FIXME: see if line end is nearly on quad
+    }
+
+    void addExactVerticalEndPoints(double top, double bottom, double x) {
+        for (int qIndex = 0; qIndex < 3; qIndex += 2) {
+            double lineT = SkDLine::ExactPointV(quad[qIndex], top, bottom, x);
+            if (lineT < 0) {
+                continue;
+            }
+            double quadT = (double) (qIndex >> 1);
+            intersections->insert(quadT, lineT, quad[qIndex]);
+        }
+    }
+
+    void addNearVerticalEndPoints(double top, double bottom, double x) {
+        for (int qIndex = 0; qIndex < 3; qIndex += 2) {
+            double quadT = (double) (qIndex >> 1);
+            if (intersections->hasT(quadT)) {
+                continue;
+            }
+            double lineT = SkDLine::NearPointV(quad[qIndex], top, bottom, x);
+            if (lineT < 0) {
+                continue;
+            }
+            intersections->insert(quadT, lineT, quad[qIndex]);
+        }
+        // FIXME: see if line end is nearly on quad
     }
 
     double findLineT(double t) {
         SkDPoint xy = quad.xyAtT(t);
         double dx = line[1].fX - line[0].fX;
         double dy = line[1].fY - line[0].fY;
-#if 0
-        if (fabs(dx) > fabs(dy)) {
-            return (xy.fX - line[0].fX) / dx;
-        }
-        return (xy.fY - line[0].fY) / dy;
-#else
         double dxT = (xy.fX - line[0].fX) / dx;
         double dyT = (xy.fY - line[0].fY) / dy;
         if (!between(FLT_EPSILON, dxT, 1 - FLT_EPSILON) && between(0, dyT, 1)) {
             return dyT;
         }
         if (!between(FLT_EPSILON, dyT, 1 - FLT_EPSILON) && between(0, dxT, 1)) {
             return dxT;
         }
         return fabs(dx) > fabs(dy) ? dxT : dyT;
-#endif
     }
 
     static bool PinTs(double* quadT, double* lineT) {
         if (!approximately_one_or_less(*lineT)) {
             return false;
         }
         if (!approximately_zero_or_more(*lineT)) {
             return false;
         }
-        if (precisely_less_than_zero(*quadT)) {
-            *quadT = 0;
-        } else if (precisely_greater_than_one(*quadT)) {
-            *quadT = 1;
-        }
-        if (precisely_less_than_zero(*lineT)) {
-            *lineT = 0;
-        } else if (precisely_greater_than_one(*lineT)) {
-            *lineT = 1;
-        }
+        *quadT = SkPinT(*quadT);
+        *lineT = SkPinT(*lineT);
         return true;
     }
 
 private:
     const SkDQuad& quad;
     const SkDLine& line;
     SkIntersections* intersections;
+    bool fAllowNear;
 };
 
 // utility for pairs of coincident quads
 static double horizontalIntersect(const SkDQuad& quad, const SkDPoint& pt) {
     LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)),
             static_cast<SkIntersections*>(0));
     double rootVals[2];
     int roots = q.horizontalIntersect(pt.fY, rootVals);
     for (int index = 0; index < roots; ++index) {
         double t = rootVals[index];
@@ skipping 34 matching lines @@
 }
 
 int SkIntersections::vertical(const SkDQuad& quad, double top, double bottom, double x,
                               bool flipped) {
     LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), this);
     return q.verticalIntersect(x, top, bottom, flipped);
 }
 
 int SkIntersections::intersect(const SkDQuad& quad, const SkDLine& line) {
     LineQuadraticIntersections q(quad, line, this);
+    q.allowNear(fAllowNear);
     return q.intersect();
 }
 
 int SkIntersections::intersectRay(const SkDQuad& quad, const SkDLine& line) {
     LineQuadraticIntersections q(quad, line, this);
     fUsed = q.intersectRay(fT[0]);
     for (int index = 0; index < fUsed; ++index) {
         fPt[index] = quad.xyAtT(fT[0][index]);
     }
     return fUsed;
 }