bool isLinear(const Quadratic& quad, int startIndex, int endIndex) {
LineParameters lineParameters;
lineParameters.quadEndPoints(quad, startIndex, endIndex);
// FIXME: maybe it's possible to avoid this and compare non-normalized
lineParameters.normalize();
double distance = lineParameters.controlPtDistance(quad);
return approximately_zero(distance);
}
// 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 Quadratic& q1, const Quadratic& q2, 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.quadEndPoints(q1);
if (!endLine.normalize()) {
printf("line cannot be normalized: need more code here\n");
assert(0);
return false;
}
double distance = endLine.controlPtDistance(q1);
// find fat line
double top = 0;
double bottom = distance / 2; // http://students.cs.byu.edu/~tom/557/text/cic.pdf (7.6)
if (top > bottom) {
std::swap(top, bottom);
}
// compute intersecting candidate distance
Quadratic distance2y; // points with X of (0, 1/2, 1)
endLine.quadDistanceY(q2, distance2y);
int flags = 0;
if (approximately_lesser(distance2y[0].y, top)) {
flags |= kFindTopMin;
} else if (approximately_greater(distance2y[0].y, bottom)) {
flags |= kFindBottomMin;
} else {
minT = 0;
}
if (approximately_lesser(distance2y[2].y, top)) {
flags |= kFindTopMax;
} else if (approximately_greater(distance2y[2].y, bottom)) {
flags |= kFindBottomMax;
} else {
maxT = 1;
}
// Find the intersection of distance convex hull and fat line.
int idx = 0;
do {
int next = idx + 1;
if (next == 3) {
next = 0;
}
x_at(distance2y[idx], distance2y[next], top, bottom, flags, minT, maxT);
idx = next;
} while (idx);
#if DEBUG_BEZIER_CLIP
_Rect r1, r2;
r1.setBounds(q1);
r2.setBounds(q2);
_Point testPt = {0.487, 0.337};
if (r1.contains(testPt) && r2.contains(testPt)) {
printf("%s q1=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
" q2=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) minT=%1.9g maxT=%1.9g\n",
__FUNCTION__, q1[0].x, q1[0].y, q1[1].x, q1[1].y, q1[2].x, q1[2].y,
q2[0].x, q2[0].y, q2[1].x, q2[1].y, q2[2].x, q2[2].y, minT, maxT);
}
#endif
return minT < maxT; // returns false if distance shows no intersection
}
