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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: 5.0.2 (2014/02/14)
#include "Wm5MathematicsPCH.h"
#include "Wm5IntrPlane3Cylinder3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrPlane3Cylinder3<Real>::IntrPlane3Cylinder3 (const Plane3<Real>& rkPlane,
const Cylinder3<Real>& rkCylinder)
:
mPlane(&rkPlane),
mCylinder(&rkCylinder)
{
mType = PC_EMPTY_SET;
}
//----------------------------------------------------------------------------
template <typename Real>
const Plane3<Real>& IntrPlane3Cylinder3<Real>::GetPlane () const
{
return *mPlane;
}
//----------------------------------------------------------------------------
template <typename Real>
const Cylinder3<Real>& IntrPlane3Cylinder3<Real>::GetCylinder () const
{
return *mCylinder;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Cylinder3<Real>::Test ()
{
// Compute extremes of signed distance Dot(N,X)-d for points on the
// cylinder. These are
// min = (Dot(N,C)-d) - r*sqrt(1-Dot(N,W)^2) - (h/2)*|Dot(N,W)|
// max = (Dot(N,C)-d) + r*sqrt(1-Dot(N,W)^2) + (h/2)*|Dot(N,W)|
Real sDist = mPlane->DistanceTo(mCylinder->Axis.Origin);
Real absNdW = Math<Real>::FAbs(mPlane->Normal.Dot(
mCylinder->Axis.Direction));
Real root = Math<Real>::Sqrt(Math<Real>::FAbs((Real)1 - absNdW*absNdW));
Real term = mCylinder->Radius*root +
((Real)0.5)*mCylinder->Height*absNdW;
// Intersection occurs if and only if 0 is in the interval [min,max].
return Math<Real>::FAbs(sDist) <= term;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Cylinder3<Real>::Find ()
{
Real sDist = mPlane->DistanceTo(mCylinder->Axis.Origin);
Vector3<Real> center = mCylinder->Axis.Origin -
sDist*mPlane->Normal;
Real cosTheta = mCylinder->Axis.Direction.Dot(mPlane->Normal);
Real absCosTheta = Math<Real>::FAbs(cosTheta);
if (absCosTheta > (Real)0)
{
// The cylinder axis intersects the plane in a unique point.
if (absCosTheta < (Real)1)
{
mType = PC_ELLIPSE;
mEllipse.Normal = mPlane->Normal;
mEllipse.Center = mCylinder->Axis.Origin -
(sDist/cosTheta)*mCylinder->Axis.Direction;
mEllipse.Major = mCylinder->Axis.Direction -
cosTheta*mPlane->Normal;
mEllipse.Minor = mPlane->Normal.Cross(mEllipse.Major);
mEllipse.MajorLength = mCylinder->Radius/absCosTheta;
mEllipse.MinorLength = mCylinder->Radius;
mEllipse.Major.Normalize();
mEllipse.Minor.Normalize();
return true;
}
else
{
mType = PC_CIRCLE;
mCircle.Normal = mPlane->Normal;
mCircle.Center = center;
mCircle.Radius = mCylinder->Radius;
return true;
}
}
else
{
// The cylinder is parallel to the plane.
Real absSDist = Math<Real>::FAbs(sDist);
if (absSDist < mCylinder->Radius)
{
mType = PC_TWO_LINES;
Vector3<Real> offset = mCylinder->Axis.Direction.Cross(
mPlane->Normal);
Real extent = Math<Real>::Sqrt(
mCylinder->Radius*mCylinder->Radius - sDist*sDist);
mLine0.Origin = center - extent*offset;
mLine0.Direction = mCylinder->Axis.Direction;
mLine1.Origin = center + extent*offset;
mLine1.Direction = mCylinder->Axis.Direction;
return true;
}
else if (absSDist == mCylinder->Radius)
{
mType = PC_ONE_LINE;
mLine0.Origin = center;
mLine0.Direction = mCylinder->Axis.Direction;
return true;
}
else
{
mType = PC_EMPTY_SET;
return false;
}
}
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrPlane3Cylinder3<Real>::CylinderIsCulled () const
{
// Compute extremes of signed distance Dot(N,X)-d for points on the
// cylinder. These are
// min = (Dot(N,C)-d) - r*sqrt(1-Dot(N,W)^2) - (h/2)*|Dot(N,W)|
// max = (Dot(N,C)-d) + r*sqrt(1-Dot(N,W)^2) + (h/2)*|Dot(N,W)|
Real sDist = mPlane->DistanceTo(mCylinder->Axis.Origin);
Real absNdW = Math<Real>::FAbs(mPlane->Normal.Dot(
mCylinder->Axis.Direction));
Real root = Math<Real>::Sqrt(Math<Real>::FAbs((Real)1 - absNdW*absNdW));
Real term = mCylinder->Radius*root +
((Real)0.5)*mCylinder->Height*absNdW;
// Culling occurs if and only if max <= 0.
return sDist + term <= (Real)0;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrPlane3Cylinder3<Real>::GetType () const
{
return mType;
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrPlane3Cylinder3<Real>::GetOneLine (Line3<Real>& line) const
{
line = mLine0;
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrPlane3Cylinder3<Real>::GetTwoLines (Line3<Real>& line0,
Line3<Real>& line1) const
{
line0 = mLine0;
line1 = mLine1;
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrPlane3Cylinder3<Real>::GetCircle (Circle3<Real>& circle) const
{
circle = mCircle;
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrPlane3Cylinder3<Real>::GetEllipse (Ellipse3<Real>& ellipse) const
{
ellipse = mEllipse;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrPlane3Cylinder3<float>;
template WM5_MATHEMATICS_ITEM
class IntrPlane3Cylinder3<double>;
//----------------------------------------------------------------------------
}
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