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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 "Wm5IntrPlane3Plane3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrPlane3Plane3<Real>::IntrPlane3Plane3 (
const Plane3<Real>& rkPlane0, const Plane3<Real>& rkPlane1)
:
mPlane0(&rkPlane0),
mPlane1(&rkPlane1)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Plane3<Real>& IntrPlane3Plane3<Real>::GetPlane0 () const
{
return *mPlane0;
}
//----------------------------------------------------------------------------
template <typename Real>
const Plane3<Real>& IntrPlane3Plane3<Real>::GetPlane1 () const
{
return *mPlane1;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Plane3<Real>::Test ()
{
// If Cross(N0,N1) is zero, then either planes are parallel and separated
// or the same plane. In both cases, 'false' is returned. Otherwise, the
// planes intersect. To avoid subtle differences in reporting between
// Test() and Find(), the same parallel test is used. Mathematically,
// |Cross(N0,N1)|^2 = Dot(N0,N0)*Dot(N1,N1)-Dot(N0,N1)^2
// = 1 - Dot(N0,N1)^2
// The last equality is true since planes are required to have unit-length
// normal vectors. The test |Cross(N0,N1)| = 0 is the same as
// |Dot(N0,N1)| = 1. I test the latter condition in Test() and Find().
Real dot = mPlane0->Normal.Dot(mPlane1->Normal);
return Math<Real>::FAbs(dot) < (Real)1 - Math<Real>::ZERO_TOLERANCE;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Plane3<Real>::Find ()
{
// If N0 and N1 are parallel, either the planes are parallel and separated
// or the same plane. In both cases, 'false' is returned. Otherwise,
// the intersection line is
// L(t) = t*Cross(N0,N1)/|Cross(N0,N1)| + c0*N0 + c1*N1
// for some coefficients c0 and c1 and for t any real number (the line
// parameter). Taking dot products with the normals,
// d0 = Dot(N0,L) = c0*Dot(N0,N0) + c1*Dot(N0,N1) = c0 + c1*d
// d1 = Dot(N1,L) = c0*Dot(N0,N1) + c1*Dot(N1,N1) = c0*d + c1
// where d = Dot(N0,N1). These are two equations in two unknowns. The
// solution is
// c0 = (d0 - d*d1)/det
// c1 = (d1 - d*d0)/det
// where det = 1 - d^2.
Real dot = mPlane0->Normal.Dot(mPlane1->Normal);
if (Math<Real>::FAbs(dot) >= (Real)1 - Math<Real>::ZERO_TOLERANCE)
{
// The planes are parallel. Check if they are coplanar.
Real cDiff;
if (dot >= (Real)0)
{
// Normals are in same direction, need to look at c0-c1.
cDiff = mPlane0->Constant - mPlane1->Constant;
}
else
{
// Normals are in opposite directions, need to look at c0+c1.
cDiff = mPlane0->Constant + mPlane1->Constant;
}
if (Math<Real>::FAbs(cDiff) < Math<Real>::ZERO_TOLERANCE)
{
// Planes are coplanar.
mIntersectionType = IT_PLANE;
mIntrPlane = *mPlane0;
return true;
}
// Planes are parallel, but distinct.
mIntersectionType = IT_EMPTY;
return false;
}
Real invDet = ((Real)1)/((Real)1 - dot*dot);
Real c0 = (mPlane0->Constant - dot*mPlane1->Constant)*invDet;
Real c1 = (mPlane1->Constant - dot*mPlane0->Constant)*invDet;
mIntersectionType = IT_LINE;
mIntrLine.Origin = c0*mPlane0->Normal + c1*mPlane1->Normal;
mIntrLine.Direction = mPlane0->Normal.UnitCross(mPlane1->Normal);
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Plane3<Real>::Test (Real tmax,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Real dot = mPlane0->Normal.Dot(mPlane1->Normal);
if (Math<Real>::FAbs(dot) < (Real)1 - Math<Real>::ZERO_TOLERANCE)
{
// The planes are initially intersecting. Linear velocities will
// not change the fact that they are intersecting.
mContactTime = (Real)0;
mIntersectionType = IT_LINE;
return true;
}
// Check if planes are already coplanar.
Real cDiff;
if (dot >= (Real)0)
{
// Normals are in same direction, need to look at c0-c1.
cDiff = mPlane0->Constant - mPlane1->Constant;
}
else
{
// Normals are in opposite directions, need to look at c0+c1.
cDiff = mPlane0->Constant + mPlane1->Constant;
}
if (Math<Real>::FAbs(cDiff) < Math<Real>::ZERO_TOLERANCE)
{
// Planes are initially the same.
mContactTime = (Real)0;
mIntersectionType = IT_PLANE;
return true;
}
// The planes are parallel and separated. Determine when they will
// become coplanar.
Vector3<Real> relVelocity = velocity1 - velocity0;
dot = mPlane0->Normal.Dot(relVelocity);
if (Math<Real>::FAbs(dot) < Math<Real>::ZERO_TOLERANCE)
{
// The relative motion of the planes keeps them parallel.
mIntersectionType = IT_EMPTY;
return false;
}
mContactTime = cDiff/dot;
if ((Real)0 <= mContactTime && mContactTime <= tmax)
{
// The planes are moving towards each other and will meet within the
// specified time interval.
mIntersectionType = IT_PLANE;
return true;
}
mIntersectionType = IT_EMPTY;
return false;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Plane3<Real>::Find (Real tmax,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Real dot = mPlane0->Normal.Dot(mPlane1->Normal);
if (Math<Real>::FAbs(dot) < (Real)1 - Math<Real>::ZERO_TOLERANCE)
{
// The planes are initially intersecting. Linear velocities will
// not change the fact that they are intersecting.
mContactTime = (Real)0;
Real invDet = ((Real)1)/((Real)1 - dot*dot);
Real c0 = (mPlane0->Constant - dot*mPlane1->Constant)*invDet;
Real c1 = (mPlane1->Constant - dot*mPlane0->Constant)*invDet;
mIntersectionType = IT_LINE;
mIntrLine.Origin = c0*mPlane0->Normal + c1*mPlane1->Normal;
mIntrLine.Direction = mPlane0->Normal.UnitCross(mPlane1->Normal);
return true;
}
// Check if planes are already coplanar.
Real cDiff;
if (dot >= (Real)0)
{
// Normals are in same direction, need to look at c0-c1.
cDiff = mPlane0->Constant - mPlane1->Constant;
}
else
{
// Normals are in opposite directions, need to look at c0+c1.
cDiff = mPlane0->Constant + mPlane1->Constant;
}
if (Math<Real>::FAbs(cDiff) < Math<Real>::ZERO_TOLERANCE)
{
// Planes are initially the same.
mContactTime = (Real)0;
mIntersectionType = IT_PLANE;
mIntrPlane = *mPlane0;
return true;
}
// The planes are parallel and separated. Determine when they will
// become coplanar.
Vector3<Real> relVelocity = velocity1 - velocity0;
dot = mPlane0->Normal.Dot(relVelocity);
if (Math<Real>::FAbs(dot) < Math<Real>::ZERO_TOLERANCE)
{
// The relative motion of the planes keeps them parallel.
mIntersectionType = IT_EMPTY;
return false;
}
mContactTime = cDiff/dot;
if ((Real)0 <= mContactTime && mContactTime <= tmax)
{
// The planes are moving towards each other and will meet within the
// specified time interval.
mIntersectionType = IT_PLANE;
mIntrPlane.Normal = mPlane0->Normal;
mIntrPlane.Constant = mPlane0->Constant +
mContactTime*(mPlane0->Normal.Dot(velocity0));
return true;
}
mIntersectionType = IT_EMPTY;
return false;
}
//----------------------------------------------------------------------------
template <typename Real>
const Line3<Real>& IntrPlane3Plane3<Real>::GetIntersectionLine () const
{
return mIntrLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Plane3<Real>& IntrPlane3Plane3<Real>::GetIntersectionPlane () const
{
return mIntrPlane;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrPlane3Plane3<float>;
template WM5_MATHEMATICS_ITEM
class IntrPlane3Plane3<double>;
//----------------------------------------------------------------------------
}
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