void subdiv_sbasis(SBasis const & s,
std::vector<double> & roots,
double left, double right) {
Interval bs = bounds_fast(s);
if(bs.min() > 0 || bs.max() < 0)
return; // no roots here
if(s.tailError(1) < 1e-7) {
double t = s[0][0] / (s[0][0] - s[0][1]);
roots.push_back(left*(1-t) + t*right);
return;
}
double middle = (left + right)/2;
subdiv_sbasis(compose(s, Linear(0, 0.5)), roots, left, middle);
subdiv_sbasis(compose(s, Linear(0.5, 1.)), roots, middle, right);
}
//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>(Linear(A[X],B[X]),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];
}
Piecewise<SBasis> reciprocal(Piecewise<SBasis> const &f, double tol, int order){
Piecewise<SBasis> reciprocal_fn=reciprocalOnDomain(*bounds_fast(f), tol);
Piecewise<SBasis> result=compose(reciprocal_fn,f);
truncateResult(result,order);
return(result);
}