/* if returning true, check contains true if cubic's hull collapsed, making the cubic linear
if returning false, check contains true if the the cubic pair have only the end point in common
*/
bool SkDCubic::hullIntersects(const SkDPoint* pts, int ptCount, bool* isLinear) const {
bool linear = true;
char hullOrder[4];
int hullCount = convexHull(hullOrder);
int end1 = hullOrder[0];
int hullIndex = 0;
const SkDPoint* endPt[2];
endPt[0] = &fPts[end1];
do {
hullIndex = (hullIndex + 1) % hullCount;
int end2 = hullOrder[hullIndex];
endPt[1] = &fPts[end2];
double origX = endPt[0]->fX;
double origY = endPt[0]->fY;
double adj = endPt[1]->fX - origX;
double opp = endPt[1]->fY - origY;
int oddManMask = other_two(end1, end2);
int oddMan = end1 ^ oddManMask;
double sign = (fPts[oddMan].fY - origY) * adj - (fPts[oddMan].fX - origX) * opp;
int oddMan2 = end2 ^ oddManMask;
double sign2 = (fPts[oddMan2].fY - origY) * adj - (fPts[oddMan2].fX - origX) * opp;
if (sign * sign2 < 0) {
continue;
}
if (approximately_zero(sign)) {
sign = sign2;
if (approximately_zero(sign)) {
continue;
}
}
linear = false;
bool foundOutlier = false;
for (int n = 0; n < ptCount; ++n) {
double test = (pts[n].fY - origY) * adj - (pts[n].fX - origX) * opp;
if (test * sign > 0 && !precisely_zero(test)) {
foundOutlier = true;
break;
}
}
if (!foundOutlier) {
return false;
}
endPt[0] = endPt[1];
end1 = end2;
} while (hullIndex);
*isLinear = linear;
return true;
}
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;
}
/* Given a cubic, find the convex hull described by the end and control points.
The hull may have 3 or 4 points. Cubics that degenerate into a point or line
are not considered.
The hull is computed by assuming that three points, if unique and non-linear,
form a triangle. The fourth point may replace one of the first three, may be
discarded if in the triangle or on an edge, or may be inserted between any of
the three to form a convex quadralateral.
The indices returned in order describe the convex hull.
*/
int convex_hull(const Cubic& cubic, char order[4]) {
size_t index;
// find top point
size_t yMin = 0;
for (index = 1; index < 4; ++index) {
if (cubic[yMin].y > cubic[index].y || (cubic[yMin].y == cubic[index].y
&& cubic[yMin].x > cubic[index].x)) {
yMin = index;
}
}
order[0] = yMin;
int midX = -1;
int backupYMin = -1;
for (int pass = 0; pass < 2; ++pass) {
for (index = 0; index < 4; ++index) {
if (index == yMin) {
continue;
}
// rotate line from (yMin, index) to axis
// see if remaining two points are both above or below
// use this to find mid
int mask = other_two(yMin, index);
int side1 = yMin ^ mask;
int side2 = index ^ mask;
Cubic rotPath;
if (!rotate(cubic, yMin, index, rotPath)) { // ! if cbc[yMin]==cbc[idx]
order[1] = side1;
order[2] = side2;
return 3;
}
int sides = side(rotPath[side1].y - rotPath[yMin].y);
sides ^= side(rotPath[side2].y - rotPath[yMin].y);
if (sides == 2) { // '2' means one remaining point <0, one >0
if (midX >= 0) {
printf("%s unexpected mid\n", __FUNCTION__); // there can be only one mid
}
midX = index;
} else if (sides == 0) { // '0' means both to one side or the other
backupYMin = index;
}
}
if (midX >= 0) {
break;
}
if (backupYMin < 0) {
break;
}
yMin = backupYMin;
backupYMin = -1;
}
if (midX < 0) {
midX = yMin ^ 3; // choose any other point
}
int mask = other_two(yMin, midX);
int least = yMin ^ mask;
int most = midX ^ mask;
order[0] = yMin;
order[1] = least;
// see if mid value is on same side of line (least, most) as yMin
Cubic midPath;
if (!rotate(cubic, least, most, midPath)) { // ! if cbc[least]==cbc[most]
order[2] = midX;
return 3;
}
int midSides = side(midPath[yMin].y - midPath[least].y);
midSides ^= side(midPath[midX].y - midPath[least].y);
if (midSides != 2) { // if mid point is not between
order[2] = most;
return 3; // result is a triangle
}
order[2] = midX;
order[3] = most;
return 4; // result is a quadralateral
}
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;
}
