GteDistPointTriangleExact.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/GteTriangle.h>

namespace gte
{

template <int N, typename Rational>
class DistancePointTriangleExact
{
public:
    struct Result
    {
        Rational sqrDistance;
        Rational parameter[3];  // barycentric coordinates for triangle.v[3]
        Vector<N, Rational> closest;
    };

    Result operator()(Vector<N, Rational> const& point,
        Triangle<N, Rational> const& triangle);
};


template <int N, typename Rational>
typename DistancePointTriangleExact<N, Rational>::Result
DistancePointTriangleExact<N, Rational>::operator()(
    Vector<N, Rational> const& point, Triangle<N, Rational> const& triangle)
{
    Vector<N, Rational> diff = point - triangle.v[0];
    Vector<N, Rational> edge0 = triangle.v[1] - triangle.v[0];
    Vector<N, Rational> edge1 = triangle.v[2] - triangle.v[0];
    Rational a00 = Dot(edge0, edge0);
    Rational a01 = Dot(edge0, edge1);
    Rational a11 = Dot(edge1, edge1);
    Rational b0 = -Dot(diff, edge0);
    Rational b1 = -Dot(diff, edge1);
    Rational const zero = (Rational)0;
    Rational const one = (Rational)1;
    Rational det = a00 * a11 - a01 * a01;
    Rational t0 = a01 * b1 - a11 * b0;
    Rational t1 = a01 * b0 - a00 * b1;

    if (t0 + t1 <= det)
    {
        if (t0 < zero)
        {
            if (t1 < zero)  // region 4
            {
                if (b0 < zero)
                {
                    t1 = zero;
                    if (-b0 >= a00)  // V1
                    {
                        t0 = one;
                    }
                    else  // E01
                    {
                        t0 = -b0 / a00;
                    }
                }
                else
                {
                    t0 = zero;
                    if (b1 >= zero)  // V0
                    {
                        t1 = zero;
                    }
                    else if (-b1 >= a11)  // V2
                    {
                        t1 = one;
                    }
                    else  // E20
                    {
                        t1 = -b1 / a11;
                    }
                }
            }
            else  // region 3
            {
                t0 = zero;
                if (b1 >= zero)  // V0
                {
                    t1 = zero;
                }
                else if (-b1 >= a11)  // V2
                {
                    t1 = one;
                }
                else  // E20
                {
                    t1 = -b1 / a11;
                }
            }
        }
        else if (t1 < zero)  // region 5
        {
            t1 = zero;
            if (b0 >= zero)  // V0
            {
                t0 = zero;
            }
            else if (-b0 >= a00)  // V1
            {
                t0 = one;
            }
            else  // E01
            {
                t0 = -b0 / a00;
            }
        }
        else  // region 0, interior
        {
            Rational invDet = one / det;
            t0 *= invDet;
            t1 *= invDet;
        }
    }
    else
    {
        Rational tmp0, tmp1, numer, denom;

        if (t0 < zero)  // region 2
        {
            tmp0 = a01 + b0;
            tmp1 = a11 + b1;
            if (tmp1 > tmp0)
            {
                numer = tmp1 - tmp0;
                denom = a00 - ((Rational)2)*a01 + a11;
                if (numer >= denom)  // V1
                {
                    t0 = one;
                    t1 = zero;
                }
                else  // E12
                {
                    t0 = numer / denom;
                    t1 = one - t0;
                }
            }
            else
            {
                t0 = zero;
                if (tmp1 <= zero)  // V2
                {
                    t1 = one;
                }
                else if (b1 >= zero)  // V0
                {
                    t1 = zero;
                }
                else  // E20
                {
                    t1 = -b1 / a11;
                }
            }
        }
        else if (t1 < zero)  // region 6
        {
            tmp0 = a01 + b1;
            tmp1 = a00 + b0;
            if (tmp1 > tmp0)
            {
                numer = tmp1 - tmp0;
                denom = a00 - ((Rational)2)*a01 + a11;
                if (numer >= denom)  // V2
                {
                    t1 = one;
                    t0 = zero;
                }
                else  // E12
                {
                    t1 = numer / denom;
                    t0 = one - t1;
                }
            }
            else
            {
                t1 = zero;
                if (tmp1 <= zero)  // V1
                {
                    t0 = one;
                }
                else if (b0 >= zero)  // V0
                {
                    t0 = zero;
                }
                else  // E01
                {
                    t0 = -b0 / a00;
                }
            }
        }
        else  // region 1
        {
            numer = a11 + b1 - a01 - b0;
            if (numer <= zero)  // V2
            {
                t0 = zero;
                t1 = one;
            }
            else
            {
                denom = a00 - ((Rational)2)*a01 + a11;
                if (numer >= denom)  // V1
                {
                    t0 = one;
                    t1 = zero;
                }
                else  // 12
                {
                    t0 = numer / denom;
                    t1 = one - t0;
                }
            }
        }
    }

    Result result;
    result.parameter[0] = one - t0 - t1;
    result.parameter[1] = t0;
    result.parameter[2] = t1;
    result.closest = triangle.v[0] + t0 * edge0 + t1 * edge1;
    diff = point - result.closest;
    result.sqrDistance = Dot(diff, diff);
    return result;
}


}