int leftScanlineIntersections(const TQuadratic &q, double t0, double t1,
bool &ascending)
{
const TPointD &p0 = q.getP0(), &p1 = q.getP1(), &p2 = q.getP2();
double y1_y0 = y(p1) - y(p0),
accel = y(p2) - y(p1) - y1_y0;
// Fallback to segment case whenever we have too flat quads
if (std::fabs(accel) < m_tol)
return leftScanlineIntersections(TSegment(q.getPoint(t0), q.getPoint(t1)), ascending);
// Calculate new ascension
int ascends = isAscending(q, t1, t0 < t1);
bool wasAscending = ascending;
ascending = (ascends > 0) ? true
: (ascends < 0) ? false
: (wasAscending = !ascending, ascending); // Couples with the cusps check below
// In case the y coords are not in range, quit
int solIdx[2];
if (!areInYRange(q, t0, t1, solIdx))
return 0;
// Identify coordinates for which q(t) == y
double poly[3] = {y(p0) - m_y, 2.0 * y1_y0, accel},
s[2];
int sCount = tcg::poly_ops::solve_2(poly, s); // Tolerance dealt at the first bailout above
if (sCount == 2) {
// Calculate result
int result = 0;
if (solIdx[0] >= 0) {
result += int(getX(q, s[solIdx[0]]) < m_x && (getY(q, t0) != m_y || ascending == wasAscending)); // Cusp check
}
if (solIdx[1] >= 0)
result += int(getX(q, s[solIdx[1]]) < m_x);
return result;
}
return (assert(sCount == 0), 0); // Should never happen, since m_y is in range. If it ever happens,
// it must be close to the extremal - so quit with no intersections.
}
int intersect(const TQuadratic &q, const TSegment &s,
std::vector<DoublePair> &intersections, bool firstIsQuad) {
int solutionNumber = 0;
// Note the line `a*x+b*y+c = 0` we search for solutions
// di a*x(t)+b*y(t)+c=0 in [0,1]
double a = s.getP0().y - s.getP1().y, b = s.getP1().x - s.getP0().x,
c = -(a * s.getP0().x + b * s.getP0().y);
// se il segmento e' un punto
if (0.0 == a && 0.0 == b) {
double outParForQuad = q.getT(s.getP0());
if (areAlmostEqual(q.getPoint(outParForQuad), s.getP0())) {
if (firstIsQuad)
intersections.push_back(DoublePair(outParForQuad, 0));
else
intersections.push_back(DoublePair(0, outParForQuad));
return 1;
}
return 0;
}
if (q.getP2() - q.getP1() ==
q.getP1() - q.getP0()) { // the second is a segment....
if (firstIsQuad)
return intersect(TSegment(q.getP0(), q.getP2()), s, intersections);
else
return intersect(s, TSegment(q.getP0(), q.getP2()), intersections);
}
std::vector<TPointD> bez, pol;
bez.push_back(q.getP0());
bez.push_back(q.getP1());
bez.push_back(q.getP2());
bezier2poly(bez, pol);
std::vector<double> poly_1(3, 0), sol;
poly_1[0] = a * pol[0].x + b * pol[0].y + c;
poly_1[1] = a * pol[1].x + b * pol[1].y;
poly_1[2] = a * pol[2].x + b * pol[2].y;
if (!(rootFinding(poly_1, sol))) return 0;
double segmentPar, solution;
TPointD v10(s.getP1() - s.getP0());
for (UINT i = 0; i < sol.size(); ++i) {
solution = sol[i];
if ((0.0 <= solution && solution <= 1.0) ||
areAlmostEqual(solution, 0.0, 1e-6) ||
areAlmostEqual(solution, 1.0, 1e-6)) {
segmentPar = (q.getPoint(solution) - s.getP0()) * v10 / (v10 * v10);
if ((0.0 <= segmentPar && segmentPar <= 1.0) ||
areAlmostEqual(segmentPar, 0.0, 1e-6) ||
areAlmostEqual(segmentPar, 1.0, 1e-6)) {
TPointD p1 = q.getPoint(solution);
TPointD p2 = s.getPoint(segmentPar);
assert(areAlmostEqual(p1, p2, 1e-1));
if (firstIsQuad)
intersections.push_back(DoublePair(solution, segmentPar));
else
intersections.push_back(DoublePair(segmentPar, solution));
solutionNumber++;
}
}
}
return solutionNumber;
}
int intersect(const TQuadratic &c0, const TQuadratic &c1,
std::vector<DoublePair> &intersections, bool checksegments) {
int ret;
// Works baddly, sometimes patch intersections...
if (checksegments) {
ret = intersectCloseControlPoints(c0, c1, intersections);
if (ret != -2) return ret;
}
double a = c0.getP0().x - 2 * c0.getP1().x + c0.getP2().x;
double b = 2 * (c0.getP1().x - c0.getP0().x);
double d = c0.getP0().y - 2 * c0.getP1().y + c0.getP2().y;
double e = 2 * (c0.getP1().y - c0.getP0().y);
double coeff = b * d - a * e;
int i = 0;
if (areAlmostEqual(coeff, 0.0)) // c0 is a Segment, or a single point!!!
{
TSegment s = TSegment(c0.getP0(), c0.getP2());
ret = intersect(s, c1, intersections);
if (a == 0 && d == 0) // values of t in s coincide with values of t in c0
return ret;
for (i = intersections.size() - ret; i < (int)intersections.size(); i++) {
intersections[i].first = c0.getT(s.getPoint(intersections[i].first));
}
return ret;
}
double c = c0.getP0().x;
double f = c0.getP0().y;
double g = c1.getP0().x - 2 * c1.getP1().x + c1.getP2().x;
double h = 2 * (c1.getP1().x - c1.getP0().x);
double k = c1.getP0().x;
double m = c1.getP0().y - 2 * c1.getP1().y + c1.getP2().y;
double p = 2 * (c1.getP1().y - c1.getP0().y);
double q = c1.getP0().y;
if (areAlmostEqual(h * m - g * p,
0.0)) // c1 is a Segment, or a single point!!!
{
TSegment s = TSegment(c1.getP0(), c1.getP2());
ret = intersect(c0, s, intersections);
if (g == 0 && m == 0) // values of t in s coincide with values of t in c0
return ret;
for (i = intersections.size() - ret; i < (int)intersections.size(); i++) {
intersections[i].second = c1.getT(s.getPoint(intersections[i].second));
}
return ret;
}
double a2 = (g * d - a * m);
double b2 = (h * d - a * p);
double c2 = ((k - c) * d + (f - q) * a);
coeff = 1.0 / coeff;
double A = (a * a + d * d) * coeff * coeff;
double aux = A * c2 + (a * b + d * e) * coeff;
std::vector<double> t;
std::vector<double> solutions;
t.push_back(aux * c2 + a * c + d * f - k * a - d * q);
aux += A * c2;
t.push_back(aux * b2 - h * a - d * p);
t.push_back(aux * a2 + A * b2 * b2 - g * a - d * m);
t.push_back(2 * A * a2 * b2);
t.push_back(A * a2 * a2);
rootFinding(t, solutions);
// solutions.push_back(0.0); //per convenzione; un valore vale l'altro....
for (i = 0; i < (int)solutions.size(); i++) {
if (solutions[i] < 0) {
if (areAlmostEqual(solutions[i], 0, 1e-6))
solutions[i] = 0;
else
continue;
} else if (solutions[i] > 1) {
if (areAlmostEqual(solutions[i], 1, 1e-6))
solutions[i] = 1;
else
continue;
}
DoublePair tt;
tt.second = solutions[i];
tt.first = coeff * (tt.second * (a2 * tt.second + b2) + c2);
if (tt.first < 0) {
if (areAlmostEqual(tt.first, 0, 1e-6))
tt.first = 0;
else
continue;
} else if (tt.first > 1) {
if (areAlmostEqual(tt.first, 1, 1e-6))
tt.first = 1;
else
continue;
}
intersections.push_back(tt);
assert(areAlmostEqual(c0.getPoint(tt.first), c1.getPoint(tt.second), 1e-1));
}
return intersections.size();
}
