/** Compute the sqrt of a function.
\param f function
*/
Piecewise<SBasis> sqrt(Piecewise<SBasis> const &f, double tol, int order){
Piecewise<SBasis> result;
Piecewise<SBasis> zero = Piecewise<SBasis>(Linear(tol*tol));
zero.setDomain(f.domain());
Piecewise<SBasis> ff=max(f,zero);
for (unsigned i=0; i<ff.size(); i++){
Piecewise<SBasis> sqrtfi = sqrt_internal(ff.segs[i],tol,order);
sqrtfi.setDomain(Interval(ff.cuts[i],ff.cuts[i+1]));
result.concat(sqrtfi);
}
return result;
}
/** Return a function which gives the angle of vect at each point.
\param vect a piecewise parameteric curve.
\param tol the maximum error allowed.
\param order the maximum degree to use for approximation
\relates Piecewise
*/
Piecewise<SBasis>
Geom::atan2(Piecewise<D2<SBasis> > const &vect, double tol, unsigned order){
Piecewise<SBasis> result;
Piecewise<D2<SBasis> > v = cutAtRoots(vect,tol);
result.cuts.push_back(v.cuts.front());
for (unsigned i=0; i<v.size(); i++){
D2<SBasis> vi = RescaleForNonVanishingEnds(v.segs[i]);
SBasis x=vi[0], y=vi[1];
Piecewise<SBasis> angle;
angle = divide (x*derivative(y)-y*derivative(x), x*x+y*y, tol, order);
//TODO: I don't understand this - sign.
angle = integral(-angle);
Point vi0 = vi.at0();
angle += -std::atan2(vi0[1],vi0[0]) - angle[0].at0();
//TODO: deal with 2*pi jumps form one seg to the other...
//TODO: not exact at t=1 because of the integral.
//TODO: force continuity?
angle.setDomain(Interval(v.cuts[i],v.cuts[i+1]));
result.concat(angle);
}
return result;
}
/** Compute the cosine of a function.
\param f function
\param tol maximum error
\param order maximum degree polynomial to use
*/
Piecewise<SBasis> cos(Piecewise<SBasis> const &f, double tol, int order){
Piecewise<SBasis> result;
for (unsigned i=0; i<f.size(); i++){
Piecewise<SBasis> cosfi = cos(f.segs[i],tol,order);
cosfi.setDomain(Interval(f.cuts[i],f.cuts[i+1]));
result.concat(cosfi);
}
return result;
}