GteDistRayRay.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

#include <Mathematics/GteDCPQuery.h>
#include <Mathematics/GteRay.h>

namespace gte
{

template <int N, typename Real>
class DCPQuery<Real, Ray<N, Real>, Ray<N, Real>>
{
public:
    struct Result
    {
        Real distance, sqrDistance;
        Real parameter[2];
        Vector<N, Real> closestPoint[2];
    };

    Result operator()(Ray<N, Real> const& ray0, Ray<N, Real> const& ray1);
};

// Template aliases for convenience.
template <int N, typename Real>
using DCPRayRay = DCPQuery<Real, Ray<N, Real>, Ray<N, Real>>;

template <typename Real>
using DCPRay2Ray2 = DCPRayRay<2, Real>;

template <typename Real>
using DCPRay3Ray3 = DCPRayRay<3, Real>;


template <int N, typename Real>
typename DCPQuery<Real, Ray<N, Real>, Ray<N, Real>>::Result
DCPQuery<Real, Ray<N, Real>, Ray<N, Real>>::operator()(
    Ray<N, Real> const& ray0, Ray<N, Real> const& ray1)
{
    Result result;

    Vector<N, Real> diff = ray0.origin - ray1.origin;
    Real a01 = -Dot(ray0.direction, ray1.direction);
    Real b0 = Dot(diff, ray0.direction), b1;
    Real s0, s1;

    if (std::abs(a01) < (Real)1)
    {
        // Rays are not parallel.
        b1 = -Dot(diff, ray1.direction);
        s0 = a01 * b1 - b0;
        s1 = a01 * b0 - b1;

        if (s0 >= (Real)0)
        {
            if (s1 >= (Real)0)  // region 0 (interior)
            {
                // Minimum at two interior points of rays.
                Real det = (Real)1 - a01 * a01;
                s0 /= det;
                s1 /= det;
            }
            else  // region 3 (side)
            {
                s1 = (Real)0;
                if (b0 >= (Real)0)
                {
                    s0 = (Real)0;
                }
                else
                {
                    s0 = -b0;
                }
            }
        }
        else
        {
            if (s1 >= (Real)0)  // region 1 (side)
            {
                s0 = (Real)0;
                if (b1 >= (Real)0)
                {
                    s1 = (Real)0;
                }
                else
                {
                    s1 = -b1;
                }
            }
            else  // region 2 (corner)
            {
                if (b0 < (Real)0)
                {
                    s0 = -b0;
                    s1 = (Real)0;
                }
                else
                {
                    s0 = (Real)0;
                    if (b1 >= (Real)0)
                    {
                        s1 = (Real)0;
                    }
                    else
                    {
                        s1 = -b1;
                    }
                }
            }
        }
    }
    else
    {
        // Rays are parallel.
        if (a01 > (Real)0)
        {
            // Opposite direction vectors.
            s1 = (Real)0;
            if (b0 >= (Real)0)
            {
                s0 = (Real)0;
            }
            else
            {
                s0 = -b0;
            }
        }
        else
        {
            // Same direction vectors.
            if (b0 >= (Real)0)
            {
                b1 = -Dot(diff, ray1.direction);
                s0 = (Real)0;
                s1 = -b1;
            }
            else
            {
                s0 = -b0;
                s1 = (Real)0;
            }
        }
    }

    result.parameter[0] = s0;
    result.parameter[1] = s1;
    result.closestPoint[0] = ray0.origin + s0 * ray0.direction;
    result.closestPoint[1] = ray1.origin + s1 * ray1.direction;
    diff = result.closestPoint[0] - result.closestPoint[1];
    result.sqrDistance = Dot(diff, diff);
    result.distance = sqrt(result.sqrDistance);
    return result;
}


}