void CubicCoincidence_Test() {
// split large quadratic
// upscale quadratics to cubics
// compare original, parts, to see if the are coincident
for (size_t index = firstCubicCoincidenceTest; index < quadratics_count; ++index) {
const Quadratic& test = quadratics[index];
QuadraticPair split;
chop_at(test, split, 0.5);
Quadratic midThird;
sub_divide(test, 1.0/3, 2.0/3, midThird);
Cubic whole, first, second, mid;
quad_to_cubic(test, whole);
quad_to_cubic(split.first(), first);
quad_to_cubic(split.second(), second);
quad_to_cubic(midThird, mid);
if (!implicit_matches(whole, first)) {
printf("%s-1 %d\n", __FUNCTION__, (int)index);
}
if (!implicit_matches(whole, second)) {
printf("%s-2 %d\n", __FUNCTION__, (int)index);
}
if (!implicit_matches(mid, first)) {
printf("%s-3 %d\n", __FUNCTION__, (int)index);
}
if (!implicit_matches(mid, second)) {
printf("%s-4 %d\n", __FUNCTION__, (int)index);
}
if (!implicit_matches(first, second)) {
printf("%s-5 %d\n", __FUNCTION__, (int)index);
}
}
}
bool intersect(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
if (implicit_matches(q1, q2)) {
// FIXME: compute T values
// compute the intersections of the ends to find the coincident span
bool useVertical = fabs(q1[0].x - q1[2].x) < fabs(q1[0].y - q1[2].y);
double t;
if ((t = axialIntersect(q1, q2[0], useVertical)) >= 0) {
i.addCoincident(t, 0);
}
if ((t = axialIntersect(q1, q2[2], useVertical)) >= 0) {
i.addCoincident(t, 1);
}
useVertical = fabs(q2[0].x - q2[2].x) < fabs(q2[0].y - q2[2].y);
if ((t = axialIntersect(q2, q1[0], useVertical)) >= 0) {
i.addCoincident(0, t);
}
if ((t = axialIntersect(q2, q1[2], useVertical)) >= 0) {
i.addCoincident(1, t);
}
assert(i.fCoincidentUsed <= 2);
return i.fCoincidentUsed > 0;
}
QuadraticIntersections q(q1, q2, i);
bool result = q.intersect();
// FIXME: partial coincidence detection is currently poor. For now, try
// to fix up the data after the fact. In the future, revisit the error
// term to try to avoid this kind of result in the first place.
if (i.fUsed && i.fCoincidentUsed) {
hackToFixPartialCoincidence(q1, q2, i);
}
return result;
}
void CubicParameterization_Test() {
for (size_t index = firstCubicParameterizationTest; index < cubics_count; ++index) {
for (size_t inner = 0; inner < 4; inner += 3) {
if (!point_on_parameterized_curve(cubics[index], cubics[index][inner])) {
printf("%s [%zu,%zu] 1 parameterization failed\n",
__FUNCTION__, index, inner);
}
if (!point_on_parameterized_curve(cubics[index], cubics[index ^ 1][inner])) {
printf("%s [%zu,%zu] 2 parameterization failed\n",
__FUNCTION__, index, inner);
}
}
if (!implicit_matches(cubics[index], cubics[index ^ 1])) {
printf("%s %d\n", __FUNCTION__, (int)index);
}
}
}
void CubicIntersection_Test() {
for (size_t index = firstCubicIntersectionTest; index < tests_count; ++index) {
const Cubic& cubic1 = tests[index][0];
const Cubic& cubic2 = tests[index][1];
Cubic reduce1, reduce2;
int order1 = reduceOrder(cubic1, reduce1, kReduceOrder_NoQuadraticsAllowed);
int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllowed);
if (order1 < 4) {
printf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order1);
continue;
}
if (order2 < 4) {
printf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order2);
continue;
}
if (implicit_matches(reduce1, reduce2)) {
printf("%s [%d] coincident\n", __FUNCTION__, (int) index);
continue;
}
Intersections tIntersections;
intersect(reduce1, reduce2, tIntersections);
if (!tIntersections.intersected()) {
printf("%s [%d] no intersection\n", __FUNCTION__, (int) index);
continue;
}
for (int pt = 0; pt < tIntersections.used(); ++pt) {
double tt1 = tIntersections.fT[0][pt];
double tx1, ty1;
xy_at_t(cubic1, tt1, tx1, ty1);
double tt2 = tIntersections.fT[1][pt];
double tx2, ty2;
xy_at_t(cubic2, tt2, tx2, ty2);
if (!AlmostEqualUlps(tx1, tx2)) {
printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
}
if (!AlmostEqualUlps(ty1, ty2)) {
printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
}
}
}
}