Crossings self_crossings(Path const &p) {
Crossings ret;
std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds(p));
for(unsigned i = 0; i < cull.size(); i++) {
Crossings res = curve_self_crossings(p[i]);
offset_crossings(res, i, i);
append(ret, res);
for(unsigned jx = 0; jx < cull[i].size(); jx++) {
unsigned j = cull[i][jx];
res.clear();
pair_intersect(p[i], 0, 1, p[j], 0, 1, res);
//if(fabs(int(i)-j) == 1 || fabs(int(i)-j) == p.size()-1) {
Crossings res2;
for(unsigned k = 0; k < res.size(); k++) {
if(res[k].ta != 0 && res[k].ta != 1 && res[k].tb != 0 && res[k].tb != 1) {
res2.push_back(res[k]);
}
}
res = res2;
//}
offset_crossings(res, i, j);
append(ret, res);
}
}
return ret;
}
Crossings curve_self_crossings(Curve const &a) {
Crossings res;
std::vector<double> spl;
spl.push_back(0);
append(spl, curve_mono_splits(a));
spl.push_back(1);
for(unsigned i = 1; i < spl.size(); i++)
for(unsigned j = i+1; j < spl.size(); j++)
pair_intersect(a, spl[i-1], spl[i], a, spl[j-1], spl[j], res);
return res;
}
/**
* This uses the local bounds functions of curves to generically intersect two.
* It passes in the curves, time intervals, and keeps track of depth, while
* returning the results through the Crossings parameter.
*/
void pair_intersect(Curve const & A, double Al, double Ah,
Curve const & B, double Bl, double Bh,
Crossings &ret, unsigned depth=0) {
// std::cout << depth << "(" << Al << ", " << Ah << ")\n";
OptRect Ar = A.boundsLocal(Interval(Al, Ah));
if (!Ar) return;
OptRect Br = B.boundsLocal(Interval(Bl, Bh));
if (!Br) return;
if(! Ar->intersects(*Br)) return;
//Checks the general linearity of the function
if((depth > 12)) { // || (A.boundsLocal(Interval(Al, Ah), 1).maxExtent() < 0.1
//&& B.boundsLocal(Interval(Bl, Bh), 1).maxExtent() < 0.1)) {
double tA, tB, c;
if(linear_intersect(A.pointAt(Al), A.pointAt(Ah),
B.pointAt(Bl), B.pointAt(Bh),
tA, tB, c)) {
tA = tA * (Ah - Al) + Al;
tB = tB * (Bh - Bl) + Bl;
intersect_polish_root(A, tA,
B, tB);
if(depth % 2)
ret.push_back(Crossing(tB, tA, c < 0));
else
ret.push_back(Crossing(tA, tB, c > 0));
return;
}
}
if(depth > 12) return;
double mid = (Bl + Bh)/2;
pair_intersect(B, Bl, mid,
A, Al, Ah,
ret, depth+1);
pair_intersect(B, mid, Bh,
A, Al, Ah,
ret, depth+1);
}
/** A simple wrapper around pair_intersect */
Crossings SimpleCrosser::crossings(Curve const &a, Curve const &b) {
Crossings ret;
pair_intersect(a, 0, 1, b, 0, 1, ret);
return ret;
}
Crossings pair_intersect(Curve const & A, Interval const &Ad,
Curve const & B, Interval const &Bd) {
Crossings ret;
pair_intersect(A, Ad.min(), Ad.max(), B, Bd.min(), Bd.max(), ret);
return ret;
}
