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116 lines
5.0 KiB
116 lines
5.0 KiB
// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/DistLineSegment.h>
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#include <Mathematics/Triangle.h>
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#include <Mathematics/Vector3.h>
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namespace gte
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{
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template <typename Real>
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class DCPQuery<Real, Line3<Real>, Triangle3<Real>>
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{
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public:
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struct Result
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{
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Real distance, sqrDistance;
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Real lineParameter, triangleParameter[3];
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Vector3<Real> closestPoint[2];
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};
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Result operator()(Line3<Real> const& line, Triangle3<Real> const& triangle)
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{
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Result result;
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// Test if line intersects triangle. If so, the squared distance
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// is zero.
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Vector3<Real> edge0 = triangle.v[1] - triangle.v[0];
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Vector3<Real> edge1 = triangle.v[2] - triangle.v[0];
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Vector3<Real> normal = UnitCross(edge0, edge1);
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Real NdD = Dot(normal, line.direction);
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if (std::fabs(NdD) > (Real)0)
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{
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// The line and triangle are not parallel, so the line
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// intersects/ the plane of the triangle.
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Vector3<Real> diff = line.origin - triangle.v[0];
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Vector3<Real> basis[3]; // {D, U, V}
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basis[0] = line.direction;
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ComputeOrthogonalComplement<Real>(1, basis);
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Real UdE0 = Dot(basis[1], edge0);
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Real UdE1 = Dot(basis[1], edge1);
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Real UdDiff = Dot(basis[1], diff);
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Real VdE0 = Dot(basis[2], edge0);
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Real VdE1 = Dot(basis[2], edge1);
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Real VdDiff = Dot(basis[2], diff);
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Real invDet = ((Real)1) / (UdE0 * VdE1 - UdE1 * VdE0);
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// Barycentric coordinates for the point of intersection.
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Real b1 = (VdE1 * UdDiff - UdE1 * VdDiff) * invDet;
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Real b2 = (UdE0 * VdDiff - VdE0 * UdDiff) * invDet;
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Real b0 = (Real)1 - b1 - b2;
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if (b0 >= (Real)0 && b1 >= (Real)0 && b2 >= (Real)0)
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{
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// Line parameter for the point of intersection.
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Real DdE0 = Dot(line.direction, edge0);
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Real DdE1 = Dot(line.direction, edge1);
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Real DdDiff = Dot(line.direction, diff);
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result.lineParameter = b1 * DdE0 + b2 * DdE1 - DdDiff;
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// Barycentric coordinates for the point of intersection.
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result.triangleParameter[0] = b0;
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result.triangleParameter[1] = b1;
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result.triangleParameter[2] = b2;
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// The intersection point is inside or on the triangle.
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result.closestPoint[0] = line.origin + result.lineParameter * line.direction;
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result.closestPoint[1] = triangle.v[0] + b1 * edge0 + b2 * edge1;
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result.distance = (Real)0;
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result.sqrDistance = (Real)0;
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return result;
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}
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}
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// Either (1) the line is not parallel to the triangle and the
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// point of intersection of the line and the plane of the triangle
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// is outside the triangle or (2) the line and triangle are
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// parallel. Regardless, the closest point on the triangle is on
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// an edge of the triangle. Compare the line to all three edges
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// of the triangle.
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result.distance = std::numeric_limits<Real>::max();
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result.sqrDistance = std::numeric_limits<Real>::max();
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for (int i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
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{
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Vector3<Real> segCenter = (Real)0.5 * (triangle.v[i0] + triangle.v[i1]);
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Vector3<Real> segDirection = triangle.v[i1] - triangle.v[i0];
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Real segExtent = (Real)0.5 * Normalize(segDirection);
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Segment3<Real> segment(segCenter, segDirection, segExtent);
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DCPQuery<Real, Line3<Real>, Segment3<Real>> query;
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auto lsResult = query(line, segment);
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if (lsResult.sqrDistance < result.sqrDistance)
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{
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result.sqrDistance = lsResult.sqrDistance;
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result.distance = lsResult.distance;
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result.lineParameter = lsResult.parameter[0];
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result.triangleParameter[i0] = (Real)0.5 * ((Real)1 -
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lsResult.parameter[0] / segExtent);
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result.triangleParameter[i1] = (Real)1 -
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result.triangleParameter[i0];
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result.triangleParameter[3 - i0 - i1] = (Real)0;
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result.closestPoint[0] = lsResult.closestPoint[0];
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result.closestPoint[1] = lsResult.closestPoint[1];
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}
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}
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return result;
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}
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};
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}
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