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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 "Wm5DistLine3Rectangle3.h"
#include "Wm5DistLine3Segment3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
DistLine3Rectangle3<Real>::DistLine3Rectangle3 (const Line3<Real>& line,
const Rectangle3<Real>& rectangle)
:
mLine(&line),
mRectangle(&rectangle)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Line3<Real>& DistLine3Rectangle3<Real>::GetLine () const
{
return *mLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Rectangle3<Real>& DistLine3Rectangle3<Real>::GetRectangle () const
{
return *mRectangle;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Rectangle3<Real>::Get ()
{
return Math<Real>::Sqrt(GetSquared());
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Rectangle3<Real>::GetSquared ()
{
// Test if line intersects rectangle. If so, the squared distance is
// zero.
Vector3<Real> N = mRectangle->Axis[0].Cross(mRectangle->Axis[1]);
Real NdD = N.Dot(mLine->Direction);
if (Math<Real>::FAbs(NdD) > Math<Real>::ZERO_TOLERANCE)
{
// The line and rectangle are not parallel, so the line intersects
// the plane of the rectangle.
Vector3<Real> diff = mLine->Origin - mRectangle->Center;
Vector3<Real> U, V;
Vector3<Real>::GenerateComplementBasis(U, V, mLine->Direction);
Real UdD0 = U.Dot(mRectangle->Axis[0]);
Real UdD1 = U.Dot(mRectangle->Axis[1]);
Real UdPmC = U.Dot(diff);
Real VdD0 = V.Dot(mRectangle->Axis[0]);
Real VdD1 = V.Dot(mRectangle->Axis[1]);
Real VdPmC = V.Dot(diff);
Real invDet = ((Real)1)/(UdD0*VdD1 - UdD1*VdD0);
// Rectangle coordinates for the point of intersection.
Real s0 = (VdD1*UdPmC - UdD1*VdPmC)*invDet;
Real s1 = (UdD0*VdPmC - VdD0*UdPmC)*invDet;
if (Math<Real>::FAbs(s0) <= mRectangle->Extent[0]
&& Math<Real>::FAbs(s1) <= mRectangle->Extent[1])
{
// Line parameter for the point of intersection.
Real DdD0 = mLine->Direction.Dot(mRectangle->Axis[0]);
Real DdD1 = mLine->Direction.Dot(mRectangle->Axis[1]);
Real DdDiff = mLine->Direction.Dot(diff);
mLineParameter = s0*DdD0 + s1*DdD1 - DdDiff;
// Rectangle coordinates for the point of intersection.
mRectCoord[0] = s0;
mRectCoord[1] = s1;
// The intersection point is inside or on the rectangle.
mClosestPoint0 = mLine->Origin +
mLineParameter*mLine->Direction;
mClosestPoint1 = mRectangle->Center +
s0*mRectangle->Axis[0] + s1*mRectangle->Axis[1];
return (Real)0;
}
}
// Either (1) the line is not parallel to the rectangle and the point of
// intersection of the line and the plane of the rectangle is outside the
// rectangle or (2) the line and rectangle are parallel. Regardless, the
// closest point on the rectangle is on an edge of the rectangle. Compare
// the line to all four edges of the rectangle.
Real sqrDist = Math<Real>::MAX_REAL;
Vector3<Real> scaledDir[2] =
{
mRectangle->Extent[0]*mRectangle->Axis[0],
mRectangle->Extent[1]*mRectangle->Axis[1]
};
for (int i1 = 0; i1 < 2; ++i1)
{
for (int i0 = 0; i0 < 2; ++i0)
{
Segment3<Real> segment;
segment.Center = mRectangle->Center +
((Real)(2*i0-1))*scaledDir[i1];
segment.Direction = mRectangle->Axis[1-i1];
segment.Extent = mRectangle->Extent[1-i1];
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;
mRectCoord[0] = mRectangle->Extent[0]*((1-i1)*(2*i0-1) +
i1*ratio);
mRectCoord[1] = mRectangle->Extent[1]*((1-i0)*(2*i1-1) +
i0*ratio);
}
}
}
return sqrDist;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Rectangle3<Real>::Get (Real t,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Vector3<Real> movedOrigin = mLine->Origin + t*velocity0;
Vector3<Real> movedCenter = mRectangle->Center + t*velocity1;
Line3<Real> movedLine(movedOrigin, mLine->Direction);
Rectangle3<Real> movedRectangle(movedCenter, mRectangle->Axis,
mRectangle->Extent);
return DistLine3Rectangle3<Real>(movedLine, movedRectangle).Get();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Rectangle3<Real>::GetSquared (Real t,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Vector3<Real> movedOrigin = mLine->Origin + t*velocity0;
Vector3<Real> movedCenter = mRectangle->Center + t*velocity1;
Line3<Real> movedLine(movedOrigin, mLine->Direction);
Rectangle3<Real> movedRectangle(movedCenter, mRectangle->Axis,
mRectangle->Extent);
return DistLine3Rectangle3<Real>(movedLine, movedRectangle).GetSquared();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Rectangle3<Real>::GetLineParameter () const
{
return mLineParameter;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistLine3Rectangle3<Real>::GetRectangleCoordinate (int i) const
{
return mRectCoord[i];
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class DistLine3Rectangle3<float>;
template WM5_MATHEMATICS_ITEM
class DistLine3Rectangle3<double>;
//----------------------------------------------------------------------------
}
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