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Diffstat (limited to '')
| -rw-r--r-- | src/2geom/sbasis-2d.cpp | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/src/2geom/sbasis-2d.cpp b/src/2geom/sbasis-2d.cpp new file mode 100644 index 0000000..53b09cd --- /dev/null +++ b/src/2geom/sbasis-2d.cpp @@ -0,0 +1,202 @@ +#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 : |