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;
}
