Adding upstream version 1.3.upstream/1.3upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 728 insertions, 0 deletions

diff --git a/src/2geom/path-intersection.cpp b/src/2geom/path-intersection.cpp
new file mode 100644
index 0000000..280d7ba
--- /dev/null
+++ b/src/2geom/path-intersection.cpp
@@ -0,0 +1,728 @@
+#include <2geom/path-intersection.h>
+
+#include <2geom/ord.h>
+
+//for path_direction:
+#include <2geom/sbasis-geometric.h>
+#include <2geom/line.h>
+#ifdef HAVE_GSL
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_multiroots.h>
+#endif
+
+namespace Geom {
+
+/// Compute winding number of the path at the specified point
+int winding(Path const &path, Point const &p) {
+    return path.winding(p);
+}
+
+/**
+ * This function should only be applied to simple paths (regions), as otherwise
+ * a boolean winding direction is undefined.  It returns true for fill, false for
+ * hole.  Defaults to using the sign of area when it reaches funny cases.
+ */
+bool path_direction(Path const &p) {
+    if(p.empty()) return false;
+
+    /*goto doh;
+    //could probably be more efficient, but this is a quick job
+    double y = p.initialPoint()[Y];
+    double x = p.initialPoint()[X];
+    Cmp res = cmp(p[0].finalPoint()[Y], y);
+    for(unsigned i = 1; i < p.size(); i++) {
+        Cmp final_to_ray = cmp(p[i].finalPoint()[Y], y);
+        Cmp initial_to_ray = cmp(p[i].initialPoint()[Y], y);
+        // if y is included, these will have opposite values, giving order.
+        Cmp c = cmp(final_to_ray, initial_to_ray);
+        if(c != EQUAL_TO) {
+            std::vector<double> rs = p[i].roots(y, Y);
+            for(unsigned j = 0; j < rs.size(); j++) {
+                double nx = p[i].valueAt(rs[j], X);
+                if(nx > x) {
+                    x = nx;
+                    res = c;
+                }
+            }
+        } else if(final_to_ray == EQUAL_TO) goto doh;
+    }
+    return res < 0;
+    
+    doh:*/
+        //Otherwise fallback on area
+        
+        Piecewise<D2<SBasis> > pw = p.toPwSb();
+        double area;
+        Point centre;
+        Geom::centroid(pw, centre, area);
+        return area > 0;
+}
+
+//pair intersect code based on njh's pair-intersect
+
+/** A little sugar for appending a list to another */
+template<typename T>
+void append(T &a, T const &b) {
+    a.insert(a.end(), b.begin(), b.end());
+}
+
+/**
+ * Finds the intersection between the lines defined by A0 & A1, and B0 & B1.
+ * Returns through the last 3 parameters, returning the t-values on the lines
+ * and the cross-product of the deltas (a useful byproduct).  The return value
+ * indicates if the time values are within their proper range on the line segments.
+ */
+bool
+linear_intersect(Point const &A0, Point const &A1, Point const &B0, Point const &B1,
+                 double &tA, double &tB, double &det) {
+    bool both_lines_non_zero = (!are_near(A0, A1)) && (!are_near(B0, B1));
+
+    // Cramer's rule as cross products
+    Point Ad = A1 - A0,
+          Bd = B1 - B0,
+           d = B0 - A0;
+    det = cross(Ad, Bd);
+
+    double det_rel = det; // Calculate the determinant of the normalized vectors
+    if (both_lines_non_zero) {
+        det_rel /= Ad.length();
+        det_rel /= Bd.length();
+    }
+
+    if( fabs(det_rel) < 1e-12 ) { // If the cross product is NEARLY zero,
+        // Then one of the linesegments might have length zero
+        if (both_lines_non_zero) {
+            // If that's not the case, then we must have either:
+            // - parallel lines, with no intersections, or
+            // - coincident lines, with an infinite number of intersections
+            // Either is quite useless, so we'll just bail out
+            return false;
+        } // Else, one of the linesegments is zero, and we might still be able to calculate a single intersection point
+    } // Else we haven't bailed out, and we'll try to calculate the intersections
+
+    double detinv = 1.0 / det;
+    tA = cross(d, Bd) * detinv;
+    tB = cross(d, Ad) * detinv;
+    return (tA >= 0.) && (tA <= 1.) && (tB >= 0.) && (tB <= 1.);
+}
+
+
+#if 0
+typedef union dbl_64{
+    long long i64;
+    double d64;
+};
+
+static double EpsilonOf(double value)
+{
+    dbl_64 s;
+    s.d64 = value;
+    if(s.i64 == 0)
+    {
+        s.i64++;
+        return s.d64 - value;
+    }
+    else if(s.i64-- < 0)
+        return s.d64 - value;
+    else
+        return value - s.d64;
+}
+#endif
+
+#ifdef HAVE_GSL
+struct rparams {
+    Curve const &A;
+    Curve const &B;
+};
+
+static int
+intersect_polish_f (const gsl_vector * x, void *params,
+                    gsl_vector * f)
+{
+    const double x0 = gsl_vector_get (x, 0);
+    const double x1 = gsl_vector_get (x, 1);
+     
+    Geom::Point dx = ((struct rparams *) params)->A(x0) - 
+        ((struct rparams *) params)->B(x1);
+     
+    gsl_vector_set (f, 0, dx[0]);
+    gsl_vector_set (f, 1, dx[1]);
+     
+    return GSL_SUCCESS;
+}
+#endif
+
+static void 
+intersect_polish_root (Curve const &A, double &s, Curve const &B, double &t)
+{
+    std::vector<Point> as, bs;
+    as = A.pointAndDerivatives(s, 2);
+    bs = B.pointAndDerivatives(t, 2);
+    Point F = as[0] - bs[0];
+    double best = dot(F, F);
+    
+    for(int i = 0; i < 4; i++) {
+        
+        /**
+           we want to solve
+           J*(x1 - x0) = f(x0)
+           
+           |dA(s)[0]  -dB(t)[0]|  (X1 - X0) = A(s) - B(t)
+           |dA(s)[1]  -dB(t)[1]| 
+        **/
+
+        // We're using the standard transformation matricies, which is numerically rather poor.  Much better to solve the equation using elimination.
+
+        Affine jack(as[1][0], as[1][1],
+                    -bs[1][0], -bs[1][1],
+                    0, 0);
+        Point soln = (F)*jack.inverse();
+        double ns = s - soln[0];
+        double nt = t - soln[1];
+
+        if (ns<0) ns=0;
+        else if (ns>1) ns=1;
+        if (nt<0) nt=0;
+        else if (nt>1) nt=1;
+        
+        as = A.pointAndDerivatives(ns, 2);
+        bs = B.pointAndDerivatives(nt, 2);
+        F = as[0] - bs[0];
+        double trial = dot(F, F);
+        if (trial > best*0.1) // we have standards, you know
+            // At this point we could do a line search
+            break;
+        best = trial;
+        s = ns;
+        t = nt;
+    }
+
+#ifdef HAVE_GSL
+    if(0) { // the GSL version is more accurate, but taints this with GPL
+        int status;
+        size_t iter = 0;
+        const size_t n = 2;
+        struct rparams p = {A, B};
+        gsl_multiroot_function f = {&intersect_polish_f, n, &p};
+     
+        double x_init[2] = {s, t};
+        gsl_vector *x = gsl_vector_alloc (n);
+     
+        gsl_vector_set (x, 0, x_init[0]);
+        gsl_vector_set (x, 1, x_init[1]);
+     
+        const gsl_multiroot_fsolver_type *T = gsl_multiroot_fsolver_hybrids;
+        gsl_multiroot_fsolver *sol = gsl_multiroot_fsolver_alloc (T, 2);
+        gsl_multiroot_fsolver_set (sol, &f, x);
+     
+        do
+        {
+            iter++;
+            status = gsl_multiroot_fsolver_iterate (sol);
+     
+            if (status)   /* check if solver is stuck */
+                break;
+     
+            status =
+                gsl_multiroot_test_residual (sol->f, 1e-12);
+        }
+        while (status == GSL_CONTINUE && iter < 1000);
+    
+        s = gsl_vector_get (sol->x, 0);
+        t = gsl_vector_get (sol->x, 1);
+    
+        gsl_multiroot_fsolver_free (sol);
+        gsl_vector_free (x);
+    }
+#endif
+}
+
+/**
+ * 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);
+}
+
+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;
+}
+
+/** 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;
+}
+
+
+//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);
+}
+
+Crossings mono_intersect(Curve const & A, Interval const &Ad,
+                         Curve const & B, Interval const &Bd) {
+    Crossings ret;
+    mono_intersect(A, Ad.min(), Ad.max(), B, Bd.min(), Bd.max(), ret);
+    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)
+    Rect Ar = Rect(A0, A1), Br = Rect(B0, B1);
+    if(!Ar.intersects(Br) || A0 == A1 || B0 == B1) return;
+
+    if(depth > 12 || (Ar.maxExtent() < 0.1 && Ar.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);
+}
+
+/** This returns the times when the x or y derivative is 0 in the curve. */
+std::vector<double> curve_mono_splits(Curve const &d) {
+    Curve* deriv = d.derivative();
+    std::vector<double> rs = deriv->roots(0, X);
+    append(rs, deriv->roots(0, Y));
+    delete deriv;
+    std::sort(rs.begin(), rs.end());
+    return rs;
+}
+
+/** Convenience function to add a value to each entry in a vector of doubles. */
+std::vector<double> offset_doubles(std::vector<double> const &x, double offs) {
+    std::vector<double> ret;
+    for(double i : x) {
+        ret.push_back(i + offs);
+    }
+    return ret;
+}
+
+/**
+ * Finds all the monotonic splits for a path.  Only includes the split between
+ * curves if they switch derivative directions at that point.
+ */
+std::vector<double> path_mono_splits(Path const &p) {
+    std::vector<double> ret;
+    if(p.empty()) return ret;
+    
+    int pdx = 2, pdy = 2; // Previous derivative direction
+    for(unsigned i = 0; i < p.size(); i++) {
+        std::vector<double> spl = offset_doubles(curve_mono_splits(p[i]), i);
+        int dx = p[i].initialPoint()[X] > (spl.empty() ? p[i].finalPoint()[X] : p.valueAt(spl.front(), X)) ? 1 : 0;
+        int dy = p[i].initialPoint()[Y] > (spl.empty() ? p[i].finalPoint()[Y] : p.valueAt(spl.front(), Y)) ? 1 : 0;
+        //The direction changed, include the split time
+        if(dx != pdx || dy != pdy) {
+            ret.push_back(i);
+            pdx = dx; pdy = dy;
+        }
+        append(ret, spl);
+    }
+    return ret;
+}
+
+/**
+ * Applies path_mono_splits to multiple paths, and returns the results such that 
+ * time-set i corresponds to Path i.
+ */
+std::vector<std::vector<double> > paths_mono_splits(PathVector const &ps) {
+    std::vector<std::vector<double> > ret;
+    for(const auto & p : ps)
+        ret.push_back(path_mono_splits(p));
+    return ret;
+}
+
+/**
+ * Processes the bounds for a list of paths and a list of splits on them, yielding a list of rects for each.
+ * Each entry i corresponds to path i of the input.  The number of rects in each entry is guaranteed to be the
+ * number of splits for that path, subtracted by one.
+ */
+std::vector<std::vector<Rect> > split_bounds(PathVector const &p, std::vector<std::vector<double> > splits) {
+    std::vector<std::vector<Rect> > ret;
+    for(unsigned i = 0; i < p.size(); i++) {
+        std::vector<Rect> res;
+        for(unsigned j = 1; j < splits[i].size(); j++)
+            res.emplace_back(p[i].pointAt(splits[i][j-1]), p[i].pointAt(splits[i][j]));
+        ret.push_back(res);
+    }
+    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(PathVector const &a, PathVector 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(auto & i : bounds_a) bounds_a_union.push_back(union_list(i));
+    for(auto & i : bounds_b) bounds_b_union.push_back(union_list(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(auto & re : res) { re.a = i; re.b = jc; }
+            
+            merge_crossings(results[i], res, i);
+            merge_crossings(results[i], res, jc);
+        }
+    }
+
+    return results;
+}
+
+/* This function is similar codewise to the MonoCrosser, the main difference is that it deals with
+ * only one set of paths and includes self intersection
+CrossingSet crossings_among(PathVector const &p) {
+    CrossingSet results(p.size(), Crossings());
+    if(p.empty()) return results;
+    
+    std::vector<std::vector<double> > splits = paths_mono_splits(p);
+    std::vector<std::vector<Rect> > prs = split_bounds(p, splits);
+    std::vector<Rect> rs;
+    for(unsigned i = 0; i < prs.size(); i++) rs.push_back(union_list(prs[i]));
+    
+    std::vector<std::vector<unsigned> > cull = sweep_bounds(rs);
+    
+    //we actually want to do the self-intersections, so add em in:
+    for(unsigned i = 0; i < cull.size(); i++) cull[i].push_back(i);
+    
+    for(unsigned i = 0; i < cull.size(); i++) {
+        for(unsigned jx = 0; jx < cull[i].size(); jx++) {
+            unsigned j = cull[i][jx];
+            Crossings res;
+            
+            //Sweep of the monotonic portions
+            std::vector<std::vector<unsigned> > cull2 = sweep_bounds(prs[i], prs[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(p[i], splits[i][k-1], splits[i][k],
+                              p[j], splits[j][l-1], splits[j][l],
+                              res, .1);
+                }
+            }
+            
+            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;
+}
+*/
+
+
+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;
+}
+
+/*
+void mono_curve_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";
+    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_curve_intersect(B, Bl, mid,
+                         A, Al, Ah,
+                         ret, depth+1);
+    mono_curve_intersect(B, mid, Bh,
+                         A, Al, Ah,
+                         ret, depth+1);
+}
+
+std::vector<std::vector<double> > curves_mono_splits(Path const &p) {
+    std::vector<std::vector<double> > ret;
+    for(unsigned i = 0; i <= p.size(); i++) {
+        std::vector<double> spl;
+        spl.push_back(0);
+        append(spl, curve_mono_splits(p[i]));
+        spl.push_back(1);
+        ret.push_back(spl);
+    }
+}
+
+std::vector<std::vector<Rect> > curves_split_bounds(Path const &p, std::vector<std::vector<double> > splits) {
+    std::vector<std::vector<Rect> > ret;
+    for(unsigned i = 0; i < splits.size(); i++) {
+        std::vector<Rect> res;
+        for(unsigned j = 1; j < splits[i].size(); j++)
+            res.push_back(Rect(p.pointAt(splits[i][j-1]+i), p.pointAt(splits[i][j]+i)));
+        ret.push_back(res);
+    }
+    return ret;
+}
+
+Crossings path_self_crossings(Path const &p) {
+    Crossings ret;
+    std::vector<std::vector<unsigned> > cull = sweep_bounds(bounds(p));
+    std::vector<std::vector<double> > spl = curves_mono_splits(p);
+    std::vector<std::vector<Rect> > bnds = curves_split_bounds(p, spl);
+    for(unsigned i = 0; i < cull.size(); i++) {
+        Crossings res;
+        for(unsigned k = 1; k < spl[i].size(); k++)
+            for(unsigned l = k+1; l < spl[i].size(); l++)
+                mono_curve_intersect(p[i], spl[i][k-1], spl[i][k], p[i], spl[i][l-1], spl[i][l], res);
+        offset_crossings(res, i, i);
+        append(ret, res);
+        for(unsigned jx = 0; jx < cull[i].size(); jx++) {
+            unsigned j = cull[i][jx];
+            res.clear();
+            
+            std::vector<std::vector<unsigned> > cull2 = sweep_bounds(bnds[i], bnds[j]);
+            for(unsigned k = 0; k < cull2.size(); k++) {
+                for(unsigned lx = 0; lx < cull2[k].size(); lx++) {
+                    unsigned l = cull2[k][lx];
+                    mono_curve_intersect(p[i], spl[i][k-1], spl[i][k], p[j], spl[j][l-1], spl[j][l], 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) {
+                        res.push_back(res[k]);
+                    }
+                }
+                res = res2;
+            //}
+            offset_crossings(res, i, j);
+            append(ret, res);
+        }
+    }
+    return ret;
+}
+*/
+
+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(auto & re : res) {
+                    if(re.ta != 0 && re.ta != 1 && re.tb != 0 && re.tb != 1) {
+                        res2.push_back(re);
+                    }
+                }
+                res = res2;
+            //}
+            offset_crossings(res, i, j);
+            append(ret, res);
+        }
+    }
+    return ret;
+}
+
+void flip_crossings(Crossings &crs) {
+    for(auto & cr : crs)
+        cr = Crossing(cr.tb, cr.ta, cr.b, cr.a, !cr.dir);
+}
+
+CrossingSet crossings_among(PathVector 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(auto & re : res) { re.a = re.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(auto & re : res) { re.a = i; re.b = j; }
+            merge_crossings(results[i], res, i);
+            merge_crossings(results[j], res, j);
+        }
+    }
+    return results;
+}
+
+}
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+  indent-tabs-mode:nil
+  fill-column:99
+  End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :