closest_plane_point.h

// Description: Closest points between a plane and a point

#ifndef PASTELGEOMETRY_CLOSEST_PLANE_POINT_H
#define PASTELGEOMETRY_CLOSEST_PLANE_POINT_H

#include "pastel/geometry/shape/plane.h"

#include "pastel/sys/vector.h"

namespace Pastel
{

    //! Computes closest points between a plane and a point.
    /*!
   Preconditions:
   plane.n() == point.n()

   Returns:
   A parameter t such that 'point + t * plane.normal()' and
   'point' are closest points.
   */
    template <typename Real, int N>
    Real closest(
        const Plane<Real, N>& plane,
        const Vector<Real, N>& point)
    {
        PENSURE_OP(plane.n(), ==, point.n());

        // Let
        // N = the normal of the plane
        // D = a point on the plane
        // P = a point
        //
        // The plane equation is:
        // dot(N, X - D) = 0
        //
        // Let X = R(t) = P + t * N
        // => dot(N, (P - D) + t' * N) = 0
        // => t' = -dot(N, (P - D)) / dot(N, N)
        // => t' = dot(N, (D - P)) / dot(N, N)

        return dot(plane.normal(),
            plane.position() - point) /
            dot(plane.normal());
    }

}

#endif