GteDistPointSegment.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/GteSegment.h>

namespace gte
{

template <int N, typename Real>
class DCPQuery<Real, Vector<N, Real>, Segment<N, Real>>
{
public:
    struct Result
    {
        Real distance, sqrDistance;
        Real segmentParameter;  // t in [0,1]
        Vector<N, Real> segmentClosest;  // (1-t)*p[0] + t*p[1]
    };

    Result operator()(Vector<N, Real> const& point,
        Segment<N, Real> const& segment);
};

// Template aliases for convenience.
template <int N, typename Real>
using DCPPointSegment =
DCPQuery<Real, Vector<N, Real>, Segment<N, Real>>;

template <typename Real>
using DCPPoint2Segment2 = DCPPointSegment<2, Real>;

template <typename Real>
using DCPPoint3Segment3 = DCPPointSegment<3, Real>;


template <int N, typename Real>
typename DCPQuery<Real, Vector<N, Real>, Segment<N, Real>>::Result
DCPQuery<Real, Vector<N, Real>, Segment<N, Real>>::operator()(
    Vector<N, Real> const& point, Segment<N, Real> const& segment)
{
    Result result;

    // The direction vector is not unit length.  The normalization is deferred
    // until it is needed.
    Vector<N, Real> direction = segment.p[1] - segment.p[0];
    Vector<N, Real> diff = point - segment.p[1];
    Real t = Dot(direction, diff);
    if (t >= (Real)0)
    {
        result.segmentParameter = (Real)1;
        result.segmentClosest = segment.p[1];
    }
    else
    {
        diff = point - segment.p[0];
        t = Dot(direction, diff);
        if (t <= (Real)0)
        {
            result.segmentParameter = (Real)0;
            result.segmentClosest = segment.p[0];
        }
        else
        {
            Real sqrLength = Dot(direction, direction);
            if (sqrLength > (Real)0)
            {
                t /= sqrLength;
                result.segmentParameter = t;
                result.segmentClosest = segment.p[0] + t * direction;
            }
            else
            {
                result.segmentParameter = (Real)0;
                result.segmentClosest = segment.p[0];
            }
        }
    }

    diff = point - result.segmentClosest;
    result.sqrDistance = Dot(diff, diff);
    result.distance = sqrt(result.sqrDistance);

    return result;
}


}