intersect_plane_sphere.h

// Description: Intersection between a plane and a sphere

#ifndef PASTELGEOMETRY_INTERSECT_PLANE_SPHERE_H
#define PASTELGEOMETRY_INTERSECT_PLANE_SPHERE_H

#include "pastel/geometry/intersect/intersect_line_plane.h"
#include "pastel/geometry/overlap/overlaps_plane_sphere.h"
#include "pastel/geometry/shape/line.h"
#include "pastel/sys/vector.h"

namespace Pastel
{

    //! Finds the intersection between a plane and a sphere.
    /*!
   The intersection of a sphere with a plane is a disk.
   We will use the sphere structure to return its center
   and radius. The disk's normal is the plane's normal.
   */
    template <typename Real, int N>
        bool intersect(
            const Plane<Real, N>& plane,
            const Sphere<Real, N>& sphere,
            Sphere<Real, N>& result)
    {
        Line<Real, N> line(
            sphere.position(),
            plane.normal());

        Real t(0);

        bool intersected = Pastel::intersect(line, plane, t);
        // There is no way to miss the plane.
        ASSERT(intersected);

        const Real radius2 = sphere.radius() * sphere.radius();

        // Let
        // P the center of the sphere
        // N be the (unit) normal of the plane

        // ||(P + t * N) - P||^2 == ||t * N||^2 = t^2
        const Real nearestDistance2 = t * t;

        if (radius2 < nearestDistance2)
        {
            // The sphere does not intersect the plane.
            return false;
        }

        result.setPosition(line.at(t));
        result.setRadius(
            std::sqrt(radius2 - nearestDistance2));

        return true;
    }

}

#endif