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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 "Wm5IntrLine3Torus3.h"
#include "Wm5PolynomialRoots.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrLine3Torus3<Real>::IntrLine3Torus3 (const Line3<Real>& line,
const Torus3<Real>& torus)
:
mLine(&line),
mTorus(&torus)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Line3<Real>& IntrLine3Torus3<Real>::GetLine () const
{
return *mLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Torus3<Real>& IntrLine3Torus3<Real>::GetTorus () const
{
return *mTorus;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine3Torus3<Real>::Find ()
{
// Compute coefficients of quartic polynomial.
Real ro2 = mTorus->OuterRadius*mTorus->OuterRadius;
Real ri2 = mTorus->InnerRadius*mTorus->InnerRadius;
Real dd = mLine->Direction.Dot(mLine->Direction);
Real de = mLine->Origin.Dot(mLine->Direction);
Real value = mLine->Origin.Dot(mLine->Origin) - (ro2 + ri2);
Polynomial1<Real> poly(4);
Real zOrigin = mLine->Origin.Z();
Real zDir = mLine->Direction.Z();
poly[0] = value*value - ((Real)4)*ro2*(ri2 - zOrigin*zOrigin);
poly[1] = ((Real)4)*de*value + ((Real)8)*ro2*zDir*zOrigin;
poly[2] = ((Real)2)*dd*value + ((Real)4)*de*de + ((Real)4)*ro2*zDir*zDir;
poly[3] = ((Real)4)*dd*de;
poly[4] = dd*dd;
// Solve the quartic.
PolynomialRoots<Real> proots(Math<Real>::ZERO_TOLERANCE);
proots.FindB(poly, 6);
mQuantity = proots.GetCount();
const Real* root = proots.GetRoots();
// Get the intersection points.
for (int i = 0; i < mQuantity; ++i)
{
mPoint[i] = mLine->Origin + root[i]*mLine->Direction;
}
mIntersectionType = (mQuantity > 0 ? IT_POINT : IT_EMPTY);
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrLine3Torus3<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrLine3Torus3<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrLine3Torus3<float>;
template WM5_MATHEMATICS_ITEM
class IntrLine3Torus3<double>;
//----------------------------------------------------------------------------
}
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