text: /*
   * 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 "CurveIntersection.h"
  #include "CurveUtilities.h"
  #include "LineParameters.h"
  
  // return false if unable to clip (e.g., unable to create implicit line)
  // caller should subdivide, or create degenerate if the values are too small
  bool bezier_clip(const Cubic& cubic1, const Cubic& cubic2, double& minT, double& maxT) {
      minT = 1;
      maxT = 0;
      // determine normalized implicit line equation for pt[0] to pt[3]
      //   of the form ax + by + c = 0, where a*a + b*b == 1
  
      // find the implicit line equation parameters
      LineParameters endLine;
      endLine.cubicEndPoints(cubic1);
      if (!endLine.normalize()) {
          printf("line cannot be normalized: need more code here\n");
          return false;
      }
  
      double distance[2];
      distance[0] = endLine.controlPtDistance(cubic1, 1);
      distance[1] = endLine.controlPtDistance(cubic1, 2);
  
      // find fat line
      double top = distance[0];
      double bottom = distance[1];
      if (top > bottom) {
          SkTSwap(top, bottom);
      }
      if (top * bottom >= 0) {
          const double scale = 3/4.0; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf (13)
          if (top < 0) {
              top *= scale;
              bottom = 0;
          } else {
              top = 0;
              bottom *= scale;
          }
      } else {
          const double scale = 4/9.0; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf (15)
          top *= scale;
          bottom *= scale;
      }
  
      // compute intersecting candidate distance
      Cubic distance2y; // points with X of (0, 1/3, 2/3, 1)
      endLine.cubicDistanceY(cubic2, distance2y);
  
      int flags = 0;
      if (approximately_lesser_or_equal(distance2y[0].y, top)) {
          flags |= kFindTopMin;
      } else if (approximately_greater_or_equal(distance2y[0].y, bottom)) {
          flags |= kFindBottomMin;
      } else {
          minT = 0;
      }
  
      if (approximately_lesser_or_equal(distance2y[3].y, top)) {
          flags |= kFindTopMax;
      } else if (approximately_greater_or_equal(distance2y[3].y, bottom)) {
          flags |= kFindBottomMax;
      } else {
          maxT = 1;
      }
      // Find the intersection of distance convex hull and fat line.
      char to_0[2];
      char to_3[2];
      bool do_1_2_edge = convex_x_hull(distance2y, to_0, to_3);
      x_at(distance2y[0], distance2y[to_0[0]], top, bottom, flags, minT, maxT);
      if (to_0[0] != to_0[1]) {
          x_at(distance2y[0], distance2y[to_0[1]], top, bottom, flags, minT, maxT);
      }
      x_at(distance2y[to_3[0]], distance2y[3], top, bottom, flags, minT, maxT);
      if (to_3[0] != to_3[1]) {
          x_at(distance2y[to_3[1]], distance2y[3], top, bottom, flags, minT, maxT);
      }
      if (do_1_2_edge) {
          x_at(distance2y[1], distance2y[2], top, bottom, flags, minT, maxT);
      }
  
      return minT < maxT; // returns false if distance shows no intersection
  }
  