bool isLinear(const Cubic& cubic, int startIndex, int endIndex) {
LineParameters lineParameters;
lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
// FIXME: maybe it's possible to avoid this and compare non-normalized
lineParameters.normalize();
double distance = lineParameters.controlPtDistance(cubic, 1);
if (!approximately_zero(distance)) {
return false;
}
distance = lineParameters.controlPtDistance(cubic, 2);
return approximately_zero(distance);
}
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;
}
void LineParameter_Test() {
for (size_t index = firstLineParameterTest; index < tests_count; ++index) {
LineParameters lineParameters;
const Cubic& cubic = tests[index];
lineParameters.cubicEndPoints(cubic);
double denormalizedDistance[2];
denormalizedDistance[0] = lineParameters.controlPtDistance(cubic, 1);
denormalizedDistance[1] = lineParameters.controlPtDistance(cubic, 2);
double normalSquared = lineParameters.normalSquared();
size_t inner;
for (inner = 0; inner < 2; ++inner) {
double distSq = denormalizedDistance[inner];
distSq *= distSq;
double answersSq = answers[index][inner];
answersSq *= answersSq;
if (AlmostEqualUlps(distSq, normalSquared * answersSq)) {
continue;
}
SkDebugf("%s [%d,%d] denormalizedDistance:%g != answer:%g"
" distSq:%g answerSq:%g normalSquared:%g\n",
__FUNCTION__, (int)index, (int)inner,
denormalizedDistance[inner], answers[index][inner],
distSq, answersSq, normalSquared);
}
lineParameters.normalize();
double normalizedDistance[2];
normalizedDistance[0] = lineParameters.controlPtDistance(cubic, 1);
normalizedDistance[1] = lineParameters.controlPtDistance(cubic, 2);
for (inner = 0; inner < 2; ++inner) {
if (AlmostEqualUlps(fabs(normalizedDistance[inner]), answers[index][inner])) {
continue;
}
SkDebugf("%s [%d,%d] normalizedDistance:%1.10g != answer:%g\n",
__FUNCTION__, (int)index, (int)inner,
normalizedDistance[inner], answers[index][inner]);
}
}
}
static int check_linear(const Cubic& cubic, Cubic& reduction,
int minX, int maxX, int minY, int maxY) {
int startIndex = 0;
int endIndex = 3;
while (cubic[startIndex].approximatelyEqual(cubic[endIndex])) {
--endIndex;
if (endIndex == 0) {
printf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
assert(0);
}
}
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 * SquaredEpsilon;
int index;
for (index = 0; index < 2; ++index) {
double distSq = distance[index];
distSq *= distSq;
if (distSq > limit) {
return 0;
}
}
// four are colinear: return line formed by outside
reduction[0] = cubic[0];
reduction[1] = cubic[3];
int sameSide1;
int sameSide2;
bool useX = cubic[maxX].x - cubic[minX].x >= cubic[maxY].y - cubic[minY].y;
if (useX) {
sameSide1 = sign(cubic[0].x - cubic[1].x) + sign(cubic[3].x - cubic[1].x);
sameSide2 = sign(cubic[0].x - cubic[2].x) + sign(cubic[3].x - cubic[2].x);
} else {
sameSide1 = sign(cubic[0].y - cubic[1].y) + sign(cubic[3].y - cubic[1].y);
sameSide2 = sign(cubic[0].y - cubic[2].y) + sign(cubic[3].y - cubic[2].y);
}
if (sameSide1 == sameSide2 && (sameSide1 & 3) != 2) {
return 2;
}
double tValues[2];
int roots;
if (useX) {
roots = SkFindCubicExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
} else {
roots = SkFindCubicExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
}
for (index = 0; index < roots; ++index) {
_Point extrema;
extrema.x = interp_cubic_coords(&cubic[0].x, tValues[index]);
extrema.y = interp_cubic_coords(&cubic[0].y, tValues[index]);
// sameSide > 0 means mid is smaller than either [0] or [3], so replace smaller
int replace;
if (useX) {
if (extrema.x < cubic[0].x ^ extrema.x < cubic[3].x) {
continue;
}
replace = (extrema.x < cubic[0].x | extrema.x < cubic[3].x)
^ cubic[0].x < cubic[3].x;
} else {
if (extrema.y < cubic[0].y ^ extrema.y < cubic[3].y) {
continue;
}
replace = (extrema.y < cubic[0].y | extrema.y < cubic[3].y)
^ cubic[0].y < cubic[3].y;
}
reduction[replace] = extrema;
}
return 2;
}
// 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
}
