bool isLinear(const Cubic& cubic, int startIndex, int endIndex) {
LineParameters lineParameters;
lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
double normalSquared = lineParameters.normalSquared();
double distance[2]; // distance is not normalized
int mask = other_two(startIndex, endIndex);
int inner1 = startIndex ^ mask;
int inner2 = endIndex ^ mask;
lineParameters.controlPtDistance(cubic, inner1, inner2, distance);
double limit = normalSquared;
int index;
for (index = 0; index < 2; ++index) {
double distSq = distance[index];
distSq *= distSq;
if (approximately_greater(distSq, limit)) {
return false;
}
}
return true;
}
// 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];
endLine.controlPtDistance(cubic1, distance);
// find fat line
double top = distance[0];
double bottom = distance[1];
if (top > bottom) {
std::swap(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(distance2y[0].y, top)) {
flags |= kFindTopMin;
} else if (approximately_greater(distance2y[0].y, bottom)) {
flags |= kFindBottomMin;
} else {
minT = 0;
}
if (approximately_lesser(distance2y[3].y, top)) {
flags |= kFindTopMax;
} else if (approximately_greater(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
}
// 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
}