distance_plane_sphere.hpp

#ifndef PASTELGEOMETRY_DISTANCE_PLANE_SPHERE_HPP
#define PASTELGEOMETRY_DISTANCE_PLANE_SPHERE_HPP

#include "pastel/geometry/distance/distance_plane_sphere.h"
#include "pastel/geometry/distance/distance_plane_point.h"

namespace Pastel
{

    template <typename Real, integer N>
    Real distance(
        const Plane<Real, N>& plane,
        const Sphere<Real, N>& sphere)
    {
        return std::sqrt(distance2(plane, sphere));
    }

    template <typename Real, integer N>
    Real distance2(
        const Plane<Real, N>& plane,
        const Sphere<Real, N>& sphere)
    {
        PENSURE_OP(plane.n(), ==, sphere.n());

        // Let
        // s = distance from sphere's center to the plane.
        // r = sphere's radius
        // Then the distance d is given by
        // d = s - r
        // Negative distance means overlapping,
        // so then zero distance is returned.
        // d < 0 <=> s - r < 0 <=> s < r <=> s^2 < r^2

        Real centerDistance2 =
            distance2(plane, sphere.position());
        if (centerDistance2 <= square(sphere.radius()))
        {
            return 0;
        }

        return square(std::sqrt(centerDistance2) - sphere.radius());
    }

}

#endif