DistLine3Triangle3.h

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// Copyright Epic Games, Inc. All Rights Reserved.
 
// Port of geometry3Sharp DistLine3Triangle3
// which was ported from WildMagic 5 
 
#pragma once
 
#include "VectorTypes.h"
#include "TriangleTypes.h"
#include "SegmentTypes.h"
#include "DistLine3Segment3.h"
 
namespace UE
{
namespace Geometry
{
 
using namespace UE::Math;
 
template <typename Real>
class TDistLine3Triangle3
{
public:
    // Input
    TLine3<Real> Line;
    TTriangle3<Real> Triangle;
 
    // Output
    Real DistanceSquared = -1.0;
    Real LineParam;
    TVector<Real> LineClosest, TriangleClosest, TriangleBaryCoords;
 
 
    TDistLine3Triangle3(const TLine3<Real>& LineIn, const TTriangle3<Real>& TriangleIn) : Line(LineIn), Triangle(TriangleIn)
    {
    }
 
    Real Get()
    {
        return TMathUtil<Real>::Sqrt(ComputeResult());
    }
    Real GetSquared()
    {
        return ComputeResult();
    }
 
    Real ComputeResult()
    {
        if (DistanceSquared >= 0)
        {
            return DistanceSquared;
        }
 
        // Test if Line intersects Triangle.  If so, the squared distance is zero.
        TVector<Real> edge0 = Triangle.V[1] - Triangle.V[0];
        TVector<Real> edge1 = Triangle.V[2] - Triangle.V[0];
        TVector<Real> normal = edge0.Cross(edge1);
        Normalize(normal);
        Real NdD = normal.Dot(Line.Direction);
        if (TMathUtil<Real>::Abs(NdD) > TMathUtil<Real>::ZeroTolerance)
        {
            // The line and triangle are not parallel, so the line intersects
            // the plane of the triangle.
            TVector<Real> diff = Line.Origin - Triangle.V[0];
            TVector<Real> U, V;
            VectorUtil::MakePerpVectors(Line.Direction, U, V);
            Real UdE0 = U.Dot(edge0);
            Real UdE1 = U.Dot(edge1);
            Real UdDiff = U.Dot(diff);
            Real VdE0 = V.Dot(edge0);
            Real VdE1 = V.Dot(edge1);
            Real VdDiff = V.Dot(diff);
            Real invDet = (1) / (UdE0 * VdE1 - UdE1 * VdE0);
 
            // Barycentric coordinates for the point of intersection.
            Real b1 = (VdE1 * UdDiff - UdE1 * VdDiff) * invDet;
            Real b2 = (UdE0 * VdDiff - VdE0 * UdDiff) * invDet;
            Real b0 = 1 - b1 - b2;
 
            if (b0 >= 0 && b1 >= 0 && b2 >= 0)
            {
                // Line parameter for the point of intersection.
                Real DdE0 = Line.Direction.Dot(edge0);
                Real DdE1 = Line.Direction.Dot(edge1);
                Real DdDiff = Line.Direction.Dot(diff);
                LineParam = b1 * DdE0 + b2 * DdE1 - DdDiff;
 
                // Barycentric coordinates for the point of intersection.
                TriangleBaryCoords = TVector<Real>(b0, b1, b2);
 
                // The intersection point is inside or on the Triangle.
                LineClosest = Line.Origin + LineParam * Line.Direction;
                TriangleClosest = Triangle.V[0] + b1 * edge0 + b2 * edge1;
                DistanceSquared = 0;
                return 0;
            }
        }
 
        // Either (1) the Line is not parallel to the Triangle and the point of
        // intersection of the Line and the plane of the Triangle is outside the
        // Triangle or (2) the Line and Triangle are parallel.  Regardless, the
        // closest point on the Triangle is on an edge of the Triangle.  Compare
        // the Line to all three edges of the Triangle.
        Real sqrDist = TMathUtil<Real>::MaxReal;
        for (int i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
        {
            TSegment3<Real> segment(Triangle.V[i0], Triangle.V[i1]);
            TDistLine3Segment3<Real> queryLS(Line, segment);
            Real sqrDistTmp = queryLS.GetSquared();
            if (sqrDistTmp < sqrDist)
            {
                LineClosest = queryLS.LineClosest;
                TriangleClosest = queryLS.SegmentClosest;
                sqrDist = sqrDistTmp;
                LineParam = queryLS.LineParameter;
                Real ratio = queryLS.SegmentParameter / segment.Extent;
                TriangleBaryCoords[i0] = (0.5) * (1 - ratio);
                TriangleBaryCoords[i1] = 1 - TriangleBaryCoords[i0];
                TriangleBaryCoords[3 - i0 - i1] = 0;
            }
        }
 
        DistanceSquared = sqrDist;
        return DistanceSquared;
    }
};
 
typedef TDistLine3Triangle3<float> FDistLine3Triangle3f;
typedef TDistLine3Triangle3<double> FDistLine3Triangle3d;
 
} // end namespace UE::Geometry
} // end namespace UE