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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 "Wm5IntrSphere3Cone3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrSphere3Cone3<Real>::IntrSphere3Cone3 (const Sphere3<Real>& rkSphere,
const Cone3<Real>& rkCone)
:
mSphere(&rkSphere),
mCone(&rkCone)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Sphere3<Real>& IntrSphere3Cone3<Real>::GetSphere () const
{
return *mSphere;
}
//----------------------------------------------------------------------------
template <typename Real>
const Cone3<Real>& IntrSphere3Cone3<Real>::GetCone () const
{
return *mCone;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrSphere3Cone3<Real>::Test ()
{
Real invSin = ((Real)1)/mCone->SinAngle;
Real cosSqr = mCone->CosAngle*mCone->CosAngle;
Vector3<Real> CmV = mSphere->Center - mCone->Vertex;
Vector3<Real> D = CmV + (mSphere->Radius*invSin)*mCone->Axis;
Real DSqrLen = D.SquaredLength();
Real e = D.Dot(mCone->Axis);
if (e > (Real)0 && e*e >= DSqrLen*cosSqr)
{
Real sinSqr = mCone->SinAngle*mCone->SinAngle;
DSqrLen = CmV.SquaredLength();
e = -CmV.Dot(mCone->Axis);
if (e > (Real)0 && e*e >= DSqrLen*sinSqr)
{
Real rSqr = mSphere->Radius*mSphere->Radius;
return DSqrLen <= rSqr;
}
return true;
}
return false;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrSphere3Cone3<Real>::Find ()
{
// Test whether cone vertex is in sphere.
Vector3<Real> diff = mSphere->Center - mCone->Vertex;
Real rSqr = mSphere->Radius*mSphere->Radius;
Real lenSqr = diff.SquaredLength();
if (lenSqr <= rSqr)
{
return true;
}
// Test whether sphere center is in cone.
Real dot = diff.Dot(mCone->Axis);
Real dotSqr = dot*dot;
Real cosSqr = mCone->CosAngle*mCone->CosAngle;
if (dotSqr >= lenSqr*cosSqr && dot > (Real)0)
{
// Sphere center is inside cone, so sphere and cone intersect.
return true;
}
// Sphere center is outside cone. Problem now reduces to looking for
// an intersection between circle and ray in the plane containing
// cone vertex and spanned by cone axis and vector from vertex to
// sphere center.
// Ray is t*D+V (t >= 0) where |D| = 1 and dot(A,D) = cos(angle).
// Also, D = e*A+f*(C-V). Plugging ray equation into sphere equation
// yields R^2 = |t*D+V-C|^2, so the quadratic for intersections is
// t^2 - 2*dot(D,C-V)*t + |C-V|^2 - R^2 = 0. An intersection occurs
// if and only if the discriminant is nonnegative. This test becomes
//
// dot(D,C-V)^2 >= dot(C-V,C-V) - R^2
//
// Note that if the right-hand side is nonpositive, then the inequality
// is true (the sphere contains V). I have already ruled this out in
// the first block of code in this function.
Real uLen = Math<Real>::Sqrt(Math<Real>::FAbs(lenSqr-dotSqr));
Real test = mCone->CosAngle*dot + mCone->SinAngle*uLen;
Real discr = test*test - lenSqr + rSqr;
// compute point of intersection closest to vertex V
Real t = test - Math<Real>::Sqrt(discr);
Vector3<Real> B = diff - dot*mCone->Axis;
Real tmp = mCone->SinAngle/uLen;
mPoint = t*(mCone->CosAngle*mCone->Axis + tmp*B);
return discr >= (Real)0 && test >= (Real)0;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrSphere3Cone3<Real>::GetPoint () const
{
return mPoint;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrSphere3Cone3<float>;
template WM5_MATHEMATICS_ITEM
class IntrSphere3Cone3<double>;
//----------------------------------------------------------------------------
}
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