GteDistTriangle3Rectangle3.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/GteDistSegment3Rectangle3.h>
#include <Mathematics/GteDistSegment3Triangle3.h>

namespace gte
{

template <typename Real>
class DCPQuery<Real, Triangle3<Real>, Rectangle3<Real>>
{
public:
    struct Result
    {
        Real distance, sqrDistance;
        Real triangleParameter[3], rectangleParameter[2];
        Vector3<Real> closestPoint[2];
    };

    Result operator()(Triangle3<Real> const& triangle,
        Rectangle3<Real> const& rectangle);
};


template <typename Real>
typename DCPQuery<Real, Triangle3<Real>, Rectangle3<Real>>::Result
DCPQuery<Real, Triangle3<Real>, Rectangle3<Real>>::operator()(
    Triangle3<Real> const& triangle, Rectangle3<Real> const& rectangle)
{
    Result result;

    result.sqrDistance = std::numeric_limits<Real>::max();

    // Compare edges of triangle to the interior of rectangle.
    for (int i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
    {
        Vector3<Real> segCenter = ((Real)0.5)*(triangle.v[i0] +
            triangle.v[i1]);
        Vector3<Real> segDirection = triangle.v[i1] - triangle.v[i0];
        Real segExtent = ((Real)0.5)*Normalize(segDirection);
        Segment3<Real> edge(segCenter, segDirection, segExtent);

        DCPQuery<Real, Segment3<Real>, Rectangle3<Real>> srQuery;
        auto srResult = srQuery(edge, rectangle);
        if (srResult.sqrDistance < result.sqrDistance)
        {
            result.distance = srResult.distance;
            result.sqrDistance = srResult.sqrDistance;
            Real ratio = srResult.segmentParameter / segExtent;  // in [-1,1]
            result.triangleParameter[i0] = ((Real)0.5)*((Real)1 - ratio);
            result.triangleParameter[i1] =
                (Real)1 - result.triangleParameter[i0];
            result.triangleParameter[3 - i0 - i1] = (Real)0;
            result.rectangleParameter[0] = srResult.rectangleParameter[0];
            result.rectangleParameter[1] = srResult.rectangleParameter[1];
            result.closestPoint[0] = srResult.closestPoint[0];
            result.closestPoint[1] = srResult.closestPoint[1];
        }
    }

    // Compare edges of rectangle to the interior of triangle.
    for (int i1 = 0; i1 < 2; ++i1)
    {
        for (int i0 = -1; i0 <= 1; i0 += 2)
        {
            Real s = i0 * rectangle.extent[1 - i1];
            Vector3<Real> segCenter = rectangle.center +
                s * rectangle.axis[1 - i1];
            Segment3<Real> edge(segCenter, rectangle.axis[i1],
                rectangle.extent[i1]);

            DCPQuery<Real, Segment3<Real>, Triangle3<Real>> stQuery;
            auto stResult = stQuery(edge, triangle);
            if (stResult.sqrDistance < result.sqrDistance)
            {
                result.distance = stResult.distance;
                result.sqrDistance = stResult.sqrDistance;
                result.triangleParameter[0] = stResult.triangleParameter[0];
                result.triangleParameter[1] = stResult.triangleParameter[1];
                result.triangleParameter[2] = stResult.triangleParameter[2];
                result.rectangleParameter[i1] = s;
                result.rectangleParameter[1 - i1] = stResult.segmentParameter;
                result.closestPoint[0] = stResult.closestPoint[1];
                result.closestPoint[1] = stResult.closestPoint[0];
            }
        }
    }
    return result;
}


}