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;
}
/**
* Takes two paths and time ranges on them, with the invariant that the
* paths are monotonic on the range. Splits A when the linear intersection
* doesn't exist or is inaccurate. Uses the fact that it is monotonic to
* do very fast local bounds.
*/
void mono_pair(Path const &A, double Al, double Ah,
Path const &B, double Bl, double Bh,
Crossings &ret, double /*tol*/, unsigned depth = 0) {
if( Al >= Ah || Bl >= Bh) return;
std::cout << " " << depth << "[" << Al << ", " << Ah << "]" << "[" << Bl << ", " << Bh << "]";
Point A0 = A.pointAt(Al), A1 = A.pointAt(Ah),
B0 = B.pointAt(Bl), B1 = B.pointAt(Bh);
//inline code that this implies? (without rect/interval construction)
if(!Rect(A0, A1).intersects(Rect(B0, B1)) || A0 == A1 || B0 == B1) 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(A0, A1, B0, B1,
tA, tB, c)) {
tA = tA * (Ah - Al) + Al;
tB = tB * (Bh - Bl) + Bl;
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;
mono_pair(B, Bl, mid,
A, Al, Ah,
ret, depth+1);
mono_pair(B, mid, Bh,
A, Al, Ah,
ret, depth+1);
}
CrossingSet reverse_tb(CrossingSet const &cr, unsigned split, std::vector<double> max) {
CrossingSet ret;
for(unsigned i = 0; i < cr.size(); i++) {
Crossings res = reverse_tb(cr[i], split, max);
if(i >= split) std::reverse(res.begin(), res.end());
ret.push_back(res);
}
return ret;
}
Crossings reverse_ta(Crossings const &cr, std::vector<double> max) {
Crossings ret;
for(Crossings::const_iterator i = cr.begin(); i != cr.end(); ++i) {
double mx = max[i->a];
ret.push_back(Crossing(i->ta > mx+0.01 ? (1 - (i->ta - mx) + mx) : mx - i->ta,
i->tb, !i->dir));
}
return ret;
}
Crossings reverse_tb(Crossings const &cr, unsigned split, std::vector<double> max) {
Crossings ret;
for(Crossings::const_iterator i = cr.begin(); i != cr.end(); ++i) {
double mx = max[i->b - split];
std::cout << i->b << "\n";
ret.push_back(Crossing(i->ta, i->tb > mx+0.01 ? (1 - (i->tb - mx) + mx) : mx - i->tb,
!i->dir));
}
return ret;
}
void merge_crossings(Crossings &a, Crossings &b, unsigned i) {
Crossings n;
sort_crossings(b, i);
n.resize(a.size() + b.size());
std::merge(a.begin(), a.end(), b.begin(), b.end(), n.begin(), CrossingOrder(i));
a = n;
}
void mark_crossings(cairo_t *cr, Shape const &a, Shape const &b) {
const Regions ac = a.getContent();
Crossings c = crossings(Path(a[0]), Path(b[0]));
//for(unsigned j = 0; j < cc.size(); j++) {
//Crossings c = cc[j];
for(Crossings::iterator i = c.begin(); i != c.end(); ++i) {
draw_cross(cr, Path(ac[i->a]).pointAt(i->ta));
cairo_stroke(cr);
//draw_text(cr, ac[i->a].getBoundary().pointAt(i->ta), i->dir ? "T" : "F");
}
//}
}
Edges edges(Path const &p, Crossings const &cr, unsigned ix) {
Edges ret = Edges();
EndPoint prev;
for(unsigned i = 0; i <= cr.size(); i++) {
double t = cr[i == cr.size() ? 0 : i].getTime(ix);
Point pnt = p.pointAt(t);
Point normal = p.pointAt(t+0.01) - pnt;
normal.normalize();
std::cout << pnt << "\n";
EndPoint cur(pnt, normal, t);
if(i == 0) { prev = cur; continue; }
ret.push_back(Edge(prev, cur, ix, false));
ret.push_back(Edge(prev, cur, ix, true));
prev = cur;
}
return ret;
}
/**
* This is the main routine of "MonoCrosser", and implements a monotonic strategy on multiple curves.
* Finds crossings between two sets of paths, yielding a CrossingSet. [0, a.size()) of the return correspond
* to the sorted crossings of a with paths of b. The rest of the return, [a.size(), a.size() + b.size()],
* corresponds to the sorted crossings of b with paths of a.
*
* This function does two sweeps, one on the bounds of each path, and after that cull, one on the curves within.
* This leads to a certain amount of code complexity, however, most of that is factored into the above functions
*/
CrossingSet MonoCrosser::crossings(std::vector<Path> const &a, std::vector<Path> const &b) {
if(b.empty()) return CrossingSet(a.size(), Crossings());
CrossingSet results(a.size() + b.size(), Crossings());
if(a.empty()) return results;
std::vector<std::vector<double> > splits_a = paths_mono_splits(a), splits_b = paths_mono_splits(b);
std::vector<std::vector<Rect> > bounds_a = split_bounds(a, splits_a), bounds_b = split_bounds(b, splits_b);
std::vector<Rect> bounds_a_union, bounds_b_union;
for(unsigned i = 0; i < bounds_a.size(); i++) bounds_a_union.push_back(union_list(bounds_a[i]));
for(unsigned i = 0; i < bounds_b.size(); i++) bounds_b_union.push_back(union_list(bounds_b[i]));
std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds_a_union, bounds_b_union);
Crossings n;
for(unsigned i = 0; i < cull.size(); i++) {
for(unsigned jx = 0; jx < cull[i].size(); jx++) {
unsigned j = cull[i][jx];
unsigned jc = j + a.size();
Crossings res;
//Sweep of the monotonic portions
std::vector<std::vector<unsigned> > cull2 = sweep_bounds(bounds_a[i], bounds_b[j]);
for(unsigned k = 0; k < cull2.size(); k++) {
for(unsigned lx = 0; lx < cull2[k].size(); lx++) {
unsigned l = cull2[k][lx];
mono_pair(a[i], splits_a[i][k-1], splits_a[i][k],
b[j], splits_b[j][l-1], splits_b[j][l],
res, .1);
}
}
for(unsigned k = 0; k < res.size(); k++) { res[k].a = i; res[k].b = jc; }
merge_crossings(results[i], res, i);
merge_crossings(results[i], res, jc);
}
}
return results;
}
/**
* 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);
}
//same as below but curves not paths
void mono_intersect(Curve const &A, double Al, double Ah,
Curve const &B, double Bl, double Bh,
Crossings &ret, double tol = 0.1, unsigned depth = 0) {
if( Al >= Ah || Bl >= Bh) return;
//std::cout << " " << depth << "[" << Al << ", " << Ah << "]" << "[" << Bl << ", " << Bh << "]";
Point A0 = A.pointAt(Al), A1 = A.pointAt(Ah),
B0 = B.pointAt(Bl), B1 = B.pointAt(Bh);
//inline code that this implies? (without rect/interval construction)
Rect Ar = Rect(A0, A1), Br = Rect(B0, B1);
if(!Ar.intersects(Br) || A0 == A1 || B0 == B1) return;
if(depth > 12 || (Ar.maxExtent() < tol && Ar.maxExtent() < tol)) {
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;
mono_intersect(B, Bl, mid,
A, Al, Ah,
ret, tol, depth+1);
mono_intersect(B, mid, Bh,
A, Al, Ah,
ret, tol, depth+1);
}
CrossingSet crossings_among(std::vector<Path> const &p) {
CrossingSet results(p.size(), Crossings());
if(p.empty()) return results;
SimpleCrosser cc;
std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds(p));
for(unsigned i = 0; i < cull.size(); i++) {
Crossings res = self_crossings(p[i]);
for(unsigned k = 0; k < res.size(); k++) { res[k].a = res[k].b = i; }
merge_crossings(results[i], res, i);
flip_crossings(res);
merge_crossings(results[i], res, i);
for(unsigned jx = 0; jx < cull[i].size(); jx++) {
unsigned j = cull[i][jx];
Crossings res = cc.crossings(p[i], p[j]);
for(unsigned k = 0; k < res.size(); k++) { res[k].a = i; res[k].b = j; }
merge_crossings(results[i], res, i);
merge_crossings(results[j], res, j);
}
}
return results;
}
void offset_crossings(Crossings &cr, double a, double b) {
for(unsigned i = 0; i < cr.size(); i++) {
cr[i].ta += a;
cr[i].tb += b;
}
}
void flip_crossings(Crossings &crs) {
for(unsigned i = 0; i < crs.size(); i++)
crs[i] = Crossing(crs[i].tb, crs[i].ta, crs[i].b, crs[i].a, !crs[i].dir);
}
