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-rw-r--r--src/2geom/sbasis-2d.cpp202
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diff --git a/src/2geom/sbasis-2d.cpp b/src/2geom/sbasis-2d.cpp
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+++ b/src/2geom/sbasis-2d.cpp
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+#include <2geom/sbasis-2d.h>
+#include <2geom/sbasis-geometric.h>
+
+namespace Geom{
+
+SBasis extract_u(SBasis2d const &a, double u) {
+ SBasis sb(a.vs, Linear());
+ double s = u*(1-u);
+
+ for(unsigned vi = 0; vi < a.vs; vi++) {
+ double sk = 1;
+ Linear bo(0,0);
+ for(unsigned ui = 0; ui < a.us; ui++) {
+ bo += (extract_u(a.index(ui, vi), u))*sk;
+ sk *= s;
+ }
+ sb[vi] = bo;
+ }
+
+ return sb;
+}
+
+SBasis extract_v(SBasis2d const &a, double v) {
+ SBasis sb(a.us, Linear());
+ double s = v*(1-v);
+
+ for(unsigned ui = 0; ui < a.us; ui++) {
+ double sk = 1;
+ Linear bo(0,0);
+ for(unsigned vi = 0; vi < a.vs; vi++) {
+ bo += (extract_v(a.index(ui, vi), v))*sk;
+ sk *= s;
+ }
+ sb[ui] = bo;
+ }
+
+ return sb;
+}
+
+SBasis compose(Linear2d const &a, D2<SBasis> const &p) {
+ D2<SBasis> omp(-p[X] + 1, -p[Y] + 1);
+ return multiply(omp[0], omp[1])*a[0] +
+ multiply(p[0], omp[1])*a[1] +
+ multiply(omp[0], p[1])*a[2] +
+ multiply(p[0], p[1])*a[3];
+}
+
+SBasis
+compose(SBasis2d const &fg, D2<SBasis> const &p) {
+ SBasis B;
+ SBasis s[2];
+ SBasis ss[2];
+ for(unsigned dim = 0; dim < 2; dim++)
+ s[dim] = p[dim]*(Linear(1) - p[dim]);
+ ss[1] = Linear(1);
+ for(unsigned vi = 0; vi < fg.vs; vi++) {
+ ss[0] = ss[1];
+ for(unsigned ui = 0; ui < fg.us; ui++) {
+ unsigned i = ui + vi*fg.us;
+ B += ss[0]*compose(fg[i], p);
+ ss[0] *= s[0];
+ }
+ ss[1] *= s[1];
+ }
+ return B;
+}
+
+D2<SBasis>
+compose_each(D2<SBasis2d> const &fg, D2<SBasis> const &p) {
+ return D2<SBasis>(compose(fg[X], p), compose(fg[Y], p));
+}
+
+SBasis2d partial_derivative(SBasis2d const &f, int dim) {
+ SBasis2d result;
+ for(unsigned i = 0; i < f.size(); i++) {
+ result.push_back(Linear2d(0,0,0,0));
+ }
+ result.us = f.us;
+ result.vs = f.vs;
+
+ for(unsigned i = 0; i < f.us; i++) {
+ for(unsigned j = 0; j < f.vs; j++) {
+ Linear2d lin = f.index(i,j);
+ Linear2d dlin(lin[1+dim]-lin[0], lin[1+2*dim]-lin[dim], lin[3-dim]-lin[2*(1-dim)], lin[3]-lin[2-dim]);
+ result[i+j*result.us] += dlin;
+ unsigned di = dim?j:i;
+ if (di>=1){
+ float motpi = dim?-1:1;
+ Linear2d ds_lin_low( lin[0], -motpi*lin[1], motpi*lin[2], -lin[3] );
+ result[(i+dim-1)+(j-dim)*result.us] += di*ds_lin_low;
+
+ Linear2d ds_lin_hi( lin[1+dim]-lin[0], lin[1+2*dim]-lin[dim], lin[3]-lin[2-dim], lin[3-dim]-lin[2-dim] );
+ result[i+j*result.us] += di*ds_lin_hi;
+ }
+ }
+ }
+ return result;
+}
+
+/**
+ * Finds a path which traces the 0 contour of f, traversing from A to B as a single d2<sbasis>.
+ * degmax specifies the degree (degree = 2*degmax-1, so a degmax of 2 generates a cubic fit).
+ * The algorithm is based on dividing out derivatives at each end point and does not use the curvature for fitting.
+ * It is less accurate than sb2d_cubic_solve, although this may be fixed in the future.
+ */
+D2<SBasis>
+sb2dsolve(SBasis2d const &f, Geom::Point const &A, Geom::Point const &B, unsigned degmax){
+ //g_warning("check f(A)= %f = f(B) = %f =0!", f.apply(A[X],A[Y]), f.apply(B[X],B[Y]));
+
+ SBasis2d dfdu = partial_derivative(f, 0);
+ SBasis2d dfdv = partial_derivative(f, 1);
+ Geom::Point dfA(dfdu.apply(A[X],A[Y]),dfdv.apply(A[X],A[Y]));
+ Geom::Point dfB(dfdu.apply(B[X],B[Y]),dfdv.apply(B[X],B[Y]));
+ Geom::Point nA = dfA/(dfA[X]*dfA[X]+dfA[Y]*dfA[Y]);
+ Geom::Point nB = dfB/(dfB[X]*dfB[X]+dfB[Y]*dfB[Y]);
+
+ D2<SBasis>result(SBasis(degmax, Linear()), SBasis(degmax, Linear()));
+ double fact_k=1;
+ double sign = 1.;
+ for(int dim = 0; dim < 2; dim++)
+ result[dim][0] = Linear(A[dim],B[dim]);
+ for(unsigned k=1; k<degmax; k++){
+ // these two lines make the solutions worse!
+ //fact_k *= k;
+ //sign = -sign;
+ SBasis f_on_curve = compose(f,result);
+ Linear reste = f_on_curve[k];
+ double ax = -reste[0]/fact_k*nA[X];
+ double ay = -reste[0]/fact_k*nA[Y];
+ double bx = -sign*reste[1]/fact_k*nB[X];
+ double by = -sign*reste[1]/fact_k*nB[Y];
+
+ result[X][k] = Linear(ax,bx);
+ result[Y][k] = Linear(ay,by);
+ //sign *= 3;
+ }
+ return result;
+}
+
+/**
+ * Finds a path which traces the 0 contour of f, traversing from A to B as a single cubic d2<sbasis>.
+ * The algorithm is based on matching direction and curvature at each end point.
+ */
+//TODO: handle the case when B is "behind" A for the natural orientation of the level set.
+//TODO: more generally, there might be up to 4 solutions. Choose the best one!
+D2<SBasis>
+sb2d_cubic_solve(SBasis2d const &f, Geom::Point const &A, Geom::Point const &B){
+ D2<SBasis>result;//(Linear(A[X],B[X]),Linear(A[Y],B[Y]));
+ //g_warning("check 0 = %f = %f!", f.apply(A[X],A[Y]), f.apply(B[X],B[Y]));
+
+ SBasis2d f_u = partial_derivative(f , 0);
+ SBasis2d f_v = partial_derivative(f , 1);
+ SBasis2d f_uu = partial_derivative(f_u, 0);
+ SBasis2d f_uv = partial_derivative(f_v, 0);
+ SBasis2d f_vv = partial_derivative(f_v, 1);
+
+ Geom::Point dfA(f_u.apply(A[X],A[Y]),f_v.apply(A[X],A[Y]));
+ Geom::Point dfB(f_u.apply(B[X],B[Y]),f_v.apply(B[X],B[Y]));
+
+ Geom::Point V0 = rot90(dfA);
+ Geom::Point V1 = rot90(dfB);
+
+ double D2fVV0 = f_uu.apply(A[X],A[Y])*V0[X]*V0[X]+
+ 2*f_uv.apply(A[X],A[Y])*V0[X]*V0[Y]+
+ f_vv.apply(A[X],A[Y])*V0[Y]*V0[Y];
+ double D2fVV1 = f_uu.apply(B[X],B[Y])*V1[X]*V1[X]+
+ 2*f_uv.apply(B[X],B[Y])*V1[X]*V1[Y]+
+ f_vv.apply(B[X],B[Y])*V1[Y]*V1[Y];
+
+ std::vector<D2<SBasis> > candidates = cubics_fitting_curvature(A,B,V0,V1,D2fVV0,D2fVV1);
+ if (candidates.empty()) {
+ return D2<SBasis>(SBasis(Linear(A[X],B[X])), SBasis(Linear(A[Y],B[Y])));
+ }
+ //TODO: I'm sure std algorithm could do that for me...
+ double error = -1;
+ unsigned best = 0;
+ for (unsigned i=0; i<candidates.size(); i++){
+ Interval bounds = *bounds_fast(compose(f,candidates[i]));
+ double new_error = (fabs(bounds.max())>fabs(bounds.min()) ? fabs(bounds.max()) : fabs(bounds.min()) );
+ if ( new_error < error || error < 0 ){
+ error = new_error;
+ best = i;
+ }
+ }
+ return candidates[best];
+}
+
+
+
+
+};
+
+/*
+ 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 :