distance_plane_point.hpp

#ifndef PASTELGEOMETRY_DISTANCE_PLANE_POINT_HPP
#define PASTELGEOMETRY_DISTANCE_PLANE_POINT_HPP

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

#include "pastel/sys/vector/vector_tools.h"
#include "pastel/sys/math_functions.h"

namespace Pastel
{

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

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

        // Let
        // D = plane.position() - point
        //
        // The length of the projection of D onto the
        // plane normal is
        // 
        // |D_proj| 
        // = |D| cos(alpha))
        // = (|plane.normal()| |D| cos(alpha)) / |plane.normal()|
        // = dot(plane.normal(), D) / |plane.normal()|
        //
        // where alpha is the angle between the plane normal
        // and D.
        //
        // It then follows that:
        // |D_proj|^2 = dot^2(plane.normal(), D) / dot(plane.normal())

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

}

#endif