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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 "Wm5IntrRay3Ellipsoid3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrRay3Ellipsoid3<Real>::IntrRay3Ellipsoid3 (const Ray3<Real>& rkRay,
const Ellipsoid3<Real>& rkEllipsoid)
:
mRay(&rkRay),
mEllipsoid(&rkEllipsoid)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Ray3<Real>& IntrRay3Ellipsoid3<Real>::GetRay () const
{
return *mRay;
}
//----------------------------------------------------------------------------
template <typename Real>
const Ellipsoid3<Real>& IntrRay3Ellipsoid3<Real>::GetEllipsoid () const
{
return *mEllipsoid;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrRay3Ellipsoid3<Real>::Test ()
{
// The ellipsoid is (X-K)^T*M*(X-K)-1 = 0 and the ray is X = P+t*D.
// Substitute the ray 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 = mRay->Origin - mEllipsoid->Center;
Vector3<Real> matDir = M*mRay->Direction;
Vector3<Real> matDiff = M*diff;
Real a2 = mRay->Direction.Dot(matDir);
Real a1 = mRay->Direction.Dot(matDiff);
Real a0 = diff.Dot(matDiff) - (Real)1;
// No intersection if Q(t) has no real roots.
Real discr = a1*a1 - a0*a2;
if (discr < (Real)0)
{
return false;
}
// Test whether ray origin is inside ellipsoid.
if (a0 <= (Real)0)
{
return true;
}
// At this point, Q(0) = a0 > 0 and Q(t) has real roots. It is also
// the case that a2 > 0, since M is positive definite, implying that
// D^T*M*D > 0 for any nonzero vector D. Thus, an intersection occurs
// only when Q'(0) < 0.
return a1 < (Real)0;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrRay3Ellipsoid3<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 = mRay->Origin - mEllipsoid->Center;
Vector3<Real> matDir = M*mRay->Direction;
Vector3<Real> matDiff = M*diff;
Real a2 = mRay->Direction.Dot(matDir);
Real a1 = mRay->Direction.Dot(matDiff);
Real a0 = diff.Dot(matDiff) - (Real)1;
// Intersection occurs if Q(t) has real roots with t >= 0.
Real discr = a1*a1 - a0*a2;
Real t[2];
if (discr < (Real)0)
{
mIntersectionType = IT_EMPTY;
mQuantity = 0;
}
else if (discr > (Real)0)
{
Real root = Math<Real>::Sqrt(discr);
Real inv = ((Real)1)/a2;
t[0] = (-a1 - root)*inv;
t[1] = (-a1 + root)*inv;
if (t[0] >= (Real)0)
{
mIntersectionType = IT_SEGMENT;
mQuantity = 2;
mPoint[0] = mRay->Origin + t[0]*mRay->Direction;
mPoint[1] = mRay->Origin + t[1]*mRay->Direction;
}
else if (t[1] >= (Real)0)
{
mIntersectionType = IT_POINT;
mQuantity = 1;
mPoint[0] = mRay->Origin + t[1]*mRay->Direction;
t[0] = t[1];
}
else
{
mIntersectionType = IT_EMPTY;
mQuantity = 0;
}
}
else
{
t[0] = -a1/a2;
if (t[0] >= (Real)0)
{
mIntersectionType = IT_POINT;
mQuantity = 1;
mPoint[0] = mRay->Origin + t[0]*mRay->Direction;
}
else
{
mIntersectionType = IT_EMPTY;
mQuantity = 0;
}
}
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrRay3Ellipsoid3<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrRay3Ellipsoid3<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrRay3Ellipsoid3<float>;
template WM5_MATHEMATICS_ITEM
class IntrRay3Ellipsoid3<double>;
//----------------------------------------------------------------------------
}
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