#include "Implicit.hpp"

double ImplicitSurface::operator()(const Point& pt) const {
    return operator()(pt.x, pt.y, pt.z);
}

Point ImplicitSurface::normal_at(const Point& pt) const {
    // this is simply the gradient.
    static const double d_dist = 1e-8;

    Point normal(
            (operator()(pt.x + d_dist, pt.y, pt.z) -
             operator()(pt.x - d_dist, pt.y, pt.z)) / (2. * d_dist),
            (operator()(pt.x, pt.y + d_dist, pt.z) -
             operator()(pt.x, pt.y - d_dist, pt.z)) / (2. * d_dist),
            (operator()(pt.x, pt.y, pt.z + d_dist) -
             operator()(pt.x, pt.y, pt.z - d_dist)) / (2. * d_dist));
    normal.normalize();
    return normal;
}