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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// 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: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5DistLine3Triangle3.h"
#include "Wm5DistLine3Segment3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
DistLine3Triangle3<Real>::DistLine3Triangle3 (const Line3<Real>& rkLine,
const Triangle3<Real>& rkTriangle)
:
mLine(&rkLine),
mTriangle(&rkTriangle)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Line3<Real>& DistLine3Triangle3<Real>::GetLine () const
{
return *mLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Triangle3<Real>& DistLine3Triangle3<Real>::GetTriangle () const
{
return *mTriangle;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Triangle3<Real>::Get ()
{
return Math<Real>::Sqrt(GetSquared());
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Triangle3<Real>::GetSquared ()
{
// Test if line intersects triangle. If so, the squared distance is zero.
Vector3<Real> edge0 = mTriangle->V[1] - mTriangle->V[0];
Vector3<Real> edge1 = mTriangle->V[2] - mTriangle->V[0];
Vector3<Real> normal = edge0.UnitCross(edge1);
Real NdD = normal.Dot(mLine->Direction);
if (Math<Real>::FAbs(NdD) > Math<Real>::ZERO_TOLERANCE)
{
// The line and triangle are not parallel, so the line intersects
// the plane of the triangle.
Vector3<Real> diff = mLine->Origin - mTriangle->V[0];
Vector3<Real> U, V;
Vector3<Real>::GenerateComplementBasis(U, V, mLine->Direction);
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 = ((Real)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 = (Real)1 - b1 - b2;
if (b0 >= (Real)0 && b1 >= (Real)0 && b2 >= (Real)0)
{
// Line parameter for the point of intersection.
Real DdE0 = mLine->Direction.Dot(edge0);
Real DdE1 = mLine->Direction.Dot(edge1);
Real DdDiff = mLine->Direction.Dot(diff);
mLineParameter = b1*DdE0 + b2*DdE1 - DdDiff;
// Barycentric coordinates for the point of intersection.
mTriangleBary[0] = b0;
mTriangleBary[1] = b1;
mTriangleBary[2] = b2;
// The intersection point is inside or on the triangle.
mClosestPoint0 = mLine->Origin +
mLineParameter*mLine->Direction;
mClosestPoint1 = mTriangle->V[0] + b1*edge0 + b2*edge1;
return (Real)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 = Math<Real>::MAX_REAL;
for (int i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
{
Segment3<Real> segment;
segment.Center = ((Real)0.5)*(mTriangle->V[i0] +
mTriangle->V[i1]);
segment.Direction = mTriangle->V[i1] - mTriangle->V[i0];
segment.Extent = ((Real)0.5)*segment.Direction.Normalize();
segment.ComputeEndPoints();
DistLine3Segment3<Real> queryLS(*mLine, segment);
Real sqrDistTmp = queryLS.GetSquared();
if (sqrDistTmp < sqrDist)
{
mClosestPoint0 = queryLS.GetClosestPoint0();
mClosestPoint1 = queryLS.GetClosestPoint1();
sqrDist = sqrDistTmp;
mLineParameter = queryLS.GetLineParameter();
Real ratio = queryLS.GetSegmentParameter()/segment.Extent;
mTriangleBary[i0] = ((Real)0.5)*((Real)1 - ratio);
mTriangleBary[i1] = (Real)1 - mTriangleBary[i0];
mTriangleBary[3-i0-i1] = (Real)0;
}
}
return sqrDist;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Triangle3<Real>::Get (Real t, const Vector3<Real>& velocity0,
const Vector3<Real>& velocity1)
{
Vector3<Real> movedOrigin = mLine->Origin + t*velocity0;
Vector3<Real> movedV0 = mTriangle->V[0] + t*velocity1;
Vector3<Real> movedV1 = mTriangle->V[1] + t*velocity1;
Vector3<Real> movedV2 = mTriangle->V[2] + t*velocity1;
Line3<Real> movedLine(movedOrigin, mLine->Direction);
Triangle3<Real> movedTriangle(movedV0, movedV1, movedV2);
return DistLine3Triangle3<Real>(movedLine, movedTriangle).Get();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Triangle3<Real>::GetSquared (Real t,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Vector3<Real> movedOrigin = mLine->Origin + t*velocity0;
Vector3<Real> movedV0 = mTriangle->V[0] + t*velocity1;
Vector3<Real> movedV1 = mTriangle->V[1] + t*velocity1;
Vector3<Real> movedV2 = mTriangle->V[2] + t*velocity1;
Line3<Real> movedLine(movedOrigin, mLine->Direction);
Triangle3<Real> movedTriangle(movedV0, movedV1, movedV2);
return DistLine3Triangle3<Real>(movedLine, movedTriangle).GetSquared();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Triangle3<Real>::GetLineParameter () const
{
return mLineParameter;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Triangle3<Real>::GetTriangleBary (int i) const
{
return mTriangleBary[i];
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class DistLine3Triangle3<float>;
template WM5_MATHEMATICS_ITEM
class DistLine3Triangle3<double>;
//----------------------------------------------------------------------------
}
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