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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 (2012/11/03)
#include "Wm5MathematicsPCH.h"
#include "Wm5IntrLine3Ellipsoid3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrLine3Ellipsoid3<Real>::IntrLine3Ellipsoid3 (const Line3<Real>& line,
const Ellipsoid3<Real>& ellipsoid)
:
mLine(&line),
mEllipsoid(&ellipsoid),
mNegativeThreshold((Real)0),
mPositiveThreshold((Real)0)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Line3<Real>& IntrLine3Ellipsoid3<Real>::GetLine () const
{
return *mLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Ellipsoid3<Real>& IntrLine3Ellipsoid3<Real>::GetEllipsoid () const
{
return *mEllipsoid;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine3Ellipsoid3<Real>::Test ()
{
// The ellipsoid is (X-K)^T*M*(X-K)-1 = 0 and the line is X = P+t*D.
// Substitute the line equation into the ellipsoid equation to obtain
// a quadratic equation
// Q(t) = a2*t^2 + 2*a1*t + a0 = 0
// where a2 = D^T*M*D, a1 = D^T*M*(P-K), and a0 = (P-K)^T*M*(P-K)-1.
Matrix3<Real> M;
mEllipsoid->GetM(M);
Vector3<Real> diff = mLine->Origin - mEllipsoid->Center;
Vector3<Real> matDir = M*mLine->Direction;
Vector3<Real> matDiff = M*diff;
Real a2 = mLine->Direction.Dot(matDir);
Real a1 = mLine->Direction.Dot(matDiff);
Real a0 = diff.Dot(matDiff) - (Real)1;
// Intersection occurs if Q(t) has real roots.
Real discr = a1*a1 - a0*a2;
return discr >= mNegativeThreshold;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine3Ellipsoid3<Real>::Find ()
{
// The ellipsoid is (X-K)^T*M*(X-K)-1 = 0 and the line is X = P+t*D.
// Substitute the line equation into the ellipsoid equation to obtain
// a quadratic equation
// Q(t) = a2*t^2 + 2*a1*t + a0 = 0
// where a2 = D^T*M*D, a1 = D^T*M*(P-K), and a0 = (P-K)^T*M*(P-K)-1.
Matrix3<Real> M;
mEllipsoid->GetM(M);
Vector3<Real> diff = mLine->Origin - mEllipsoid->Center;
Vector3<Real> matDir = M*mLine->Direction;
Vector3<Real> matDiff = M*diff;
Real a2 = mLine->Direction.Dot(matDir);
Real a1 = mLine->Direction.Dot(matDiff);
Real a0 = diff.Dot(matDiff) - (Real)1;
// Intersection occurs if Q(t) has real roots.
Real discr = a1*a1 - a0*a2;
Real t[2];
if (discr < mNegativeThreshold)
{
mIntersectionType = IT_EMPTY;
mQuantity = 0;
}
else if (discr > mPositiveThreshold)
{
mIntersectionType = IT_SEGMENT;
mQuantity = 2;
Real root = Math<Real>::Sqrt(discr);
Real inv = ((Real)1)/a2;
t[0] = (-a1 - root)*inv;
t[1] = (-a1 + root)*inv;
mPoint[0] = mLine->Origin + t[0]*mLine->Direction;
mPoint[1] = mLine->Origin + t[1]*mLine->Direction;
}
else
{
mIntersectionType = IT_POINT;
mQuantity = 1;
t[0] = -a1/a2;
mPoint[0] = mLine->Origin + t[0]*mLine->Direction;
}
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrLine3Ellipsoid3<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrLine3Ellipsoid3<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrLine3Ellipsoid3<Real>::SetNegativeThreshold (Real negThreshold)
{
if (negThreshold <= (Real)0)
{
mNegativeThreshold = negThreshold;
return;
}
assertion(false, "Negative threshold must be nonpositive.");
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntrLine3Ellipsoid3<Real>::GetNegativeThreshold () const
{
return mNegativeThreshold;
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrLine3Ellipsoid3<Real>::SetPositiveThreshold (Real posThreshold)
{
if (posThreshold >= (Real)0)
{
mPositiveThreshold = posThreshold;
return;
}
assertion(false, "Positive threshold must be nonnegative.");
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntrLine3Ellipsoid3<Real>::GetPositiveThreshold () const
{
return mPositiveThreshold;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrLine3Ellipsoid3<float>;
template WM5_MATHEMATICS_ITEM
class IntrLine3Ellipsoid3<double>;
//----------------------------------------------------------------------------
}
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