// suggested by Sederberg.
double Bernsteins::horner(Bezier bz, double t)
{
double u, tn, tmp;
u = 1.0 - t;
tn = 1.0;
tmp = bz.at0() * u;
for(size_t i = 1; i < bz.degree(); ++i)
{
tn *= t;
tmp = (tmp + tn*choose<double>(bz.order(), (unsigned)i)*bz[i]) * u;
}
return (tmp + tn*t*bz.at1());
}
void
Bezier::find_bezier_roots(std::vector<double> &solutions,
double left_t, double right_t) const {
Bezier bz = *this;
//convex_hull_marching(bz, bz, solutions, left_t, right_t);
//return;
// a constant bezier, even if identically zero, has no roots
if (bz.isConstant()) {
return;
}
while(bz[0] == 0) {
debug(std::cout << "deflate\n");
bz = bz.deflate();
solutions.push_back(0);
}
if (bz.degree() == 1) {
debug(std::cout << "linear\n");
if (SGN(bz[0]) != SGN(bz[1])) {
double d = bz[0] - bz[1];
if(d != 0) {
double r = bz[0] / d;
if(0 <= r && r <= 1)
solutions.push_back(r);
}
}
return;
}
//std::cout << "initial = " << bz << std::endl;
Bernsteins B(solutions);
B.find_bernstein_roots(bz, 0, left_t, right_t);
//std::cout << solutions << std::endl;
}
