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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 "Wm5DistCircle3Circle3.h"
#include "Wm5PolynomialRoots.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
DistCircle3Circle3<Real>::DistCircle3Circle3 (const Circle3<Real>& circle0,
const Circle3<Real>& circle1)
:
mCircle0(&circle0),
mCircle1(&circle1)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Circle3<Real>& DistCircle3Circle3<Real>::GetCircle0 () const
{
return *mCircle0;
}
//----------------------------------------------------------------------------
template <typename Real>
const Circle3<Real>& DistCircle3Circle3<Real>::GetCircle1 () const
{
return *mCircle1;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistCircle3Circle3<Real>::Get ()
{
return Math<Real>::Sqrt(GetSquared());
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistCircle3Circle3<Real>::GetSquared ()
{
Vector3<Real> diff = mCircle1->Center - mCircle0->Center;
Real u0u1 = mCircle0->Direction0.Dot(mCircle1->Direction0);
Real u0v1 = mCircle0->Direction0.Dot(mCircle1->Direction1);
Real v0u1 = mCircle0->Direction1.Dot(mCircle1->Direction0);
Real v0v1 = mCircle0->Direction1.Dot(mCircle1->Direction1);
Real a0 = -diff.Dot(mCircle0->Direction0);
Real a1 = -mCircle1->Radius*u0u1;
Real a2 = -mCircle1->Radius*u0v1;
Real a3 = diff.Dot(mCircle0->Direction1);
Real a4 = mCircle1->Radius*v0u1;
Real a5 = mCircle1->Radius*v0v1;
Real b0 = -diff.Dot(mCircle1->Direction0);
Real b1 = mCircle0->Radius*u0u1;
Real b2 = mCircle0->Radius*v0u1;
Real b3 = diff.Dot(mCircle1->Direction1);
Real b4 = -mCircle0->Radius*u0v1;
Real b5 = -mCircle0->Radius*v0v1;
// Compute polynomial p0 = p00+p01*z+p02*z^2.
Polynomial1<Real> p0(2);
p0[0] = a2*b1 - a5*b2;
p0[1] = a0*b4 - a3*b5;
p0[2] = a5*b2 - a2*b1 + a1*b4 - a4*b5;
// Compute polynomial p1 = p10+p11*z.
Polynomial1<Real> p1(1);
p1[0] = a0*b1 - a3*b2;
p1[1] = a1*b1 - a5*b5 + a2*b4 - a4*b2;
// Compute polynomial q0 = q00+q01*z+q02*z^2.
Polynomial1<Real> q0(2);
q0[0] = a0*a0 + a2*a2 + a3*a3 + a5*a5;
q0[1] = ((Real)2)*(a0*a1 + a3*a4);
q0[2] = a1*a1 - a2*a2 + a4*a4 - a5*a5;
// Compute polynomial q1 = q10+q11*z.
Polynomial1<Real> q1(1);
q1[0] = ((Real)2)*(a0*a2 + a3*a5);
q1[1] = ((Real)2)*(a1*a2 + a4*a5);
// Compute coefficients of r0 = r00+r02*z^2.
Polynomial1<Real> r0(2);
r0[0] = b0*b0;
r0[1] = (Real)0;
r0[2] = b3*b3 - b0*b0;
// Compute polynomial r1 = r11*z.
Polynomial1<Real> r1(1);
r1[0] = (Real)0;
r1[1] = ((Real)2)*b0*b3;
// Compute polynomial g0 = g00+g01*z+g02*z^2+g03*z^3+g04*z^4.
Polynomial1<Real> g0(4);
g0[0] = p0[0]*p0[0] + p1[0]*p1[0] - q0[0]*r0[0];
g0[1] = ((Real)2)*(p0[0]*p0[1] + p1[0]*p1[1]) - q0[1]*r0[0] - q1[0]*r1[1];
g0[2] = p0[1]*p0[1] + ((Real)2)*p0[0]*p0[2] - p1[0]*p1[0] +
p1[1]*p1[1] - q0[2]*r0[0] - q0[0]*r0[2] - q1[1]*r1[1];
g0[3] = ((Real)2)*(p0[1]*p0[2] - p1[0]*p1[1]) - q0[1]*r0[2] + q1[0]*r1[1];
g0[4] = p0[2]*p0[2] - p1[1]*p1[1] - q0[2]*r0[2] + q1[1]*r1[1];
// Compute polynomial g1 = g10+g11*z+g12*z^2+g13*z^3.
Polynomial1<Real> g1(3);
g1[0] = ((Real)2)*p0[0]*p1[0] - q1[0]*r0[0];
g1[1] = ((Real)2)*(p0[1]*p1[0] + p0[0]*p1[1]) - q1[1]*r0[0] - q0[0]*r1[1];
g1[2] = ((Real)2)*(p0[2]*p1[0] + p0[1]*p1[1]) - q1[0]*r0[2] - q0[1]*r1[1];
g1[3] = ((Real)2)*p0[2]*p1[1] - q1[1]*r0[2] - q0[2]*r1[1];
// Compute polynomial h = sum_{i=0}^8 h_i z^i.
Polynomial1<Real> h(8);
h[0] = g0[0]*g0[0] - g1[0]*g1[0];
h[1] = ((Real)2)*(g0[0]*g0[1] - g1[0]*g1[1]);
h[2] = g0[1]*g0[1] + g1[0]*g1[0] - g1[1]*g1[1] +
((Real)2)*(g0[0]*g0[2] - g1[0]*g1[2]);
h[3] = ((Real)2)*(g0[1]*g0[2] + g0[0]*g0[3] + g1[0]*g1[1] -
g1[1]*g1[2] - g1[0]*g1[3]);
h[4] = g0[2]*g0[2] + g1[1]*g1[1] - g1[2]*g1[2] +
((Real)2)*(g0[1]*g0[3] + g0[0]*g0[4] + g1[0]*g1[2] -
g1[1]*g1[3]);
h[5] = ((Real)2)*(g0[2]*g0[3] + g0[1]*g0[4] + g1[1]*g1[2] +
g1[0]*g1[3] - g1[2]*g1[3]);
h[6] = g0[3]*g0[3] + g1[2]*g1[2] - g1[3]*g1[3] +
((Real)2)*(g0[2]*g0[4] + g1[1]*g1[3]);
h[7] = ((Real)2)*(g0[3]*g0[4] + g1[2]*g1[3]);
h[8] = g0[4]*g0[4] + g1[3]*g1[3];
PolynomialRoots<Real> polyroots(Math<Real>::ZERO_TOLERANCE);
polyroots.FindB(h, (Real)-1.01, (Real)1.01, 6);
int count = polyroots.GetCount();
const Real* roots = polyroots.GetRoots();
Real minSqrDist = Math<Real>::MAX_REAL;
Real cs0, sn0, cs1, sn1;
for (int i = 0; i < count; ++i)
{
cs1 = roots[i];
if (cs1 < (Real)-1)
{
cs1 = (Real)-1;
}
else if (cs1 > (Real)1)
{
cs1 = (Real)1;
}
// You can also try sn1 = -g0(cs1)/g1(cs1) to avoid the sqrt call,
// but beware when g1 is nearly zero. For now I use g0 and g1 to
// determine the sign of sn1.
sn1 = Math<Real>::Sqrt(Math<Real>::FAbs((Real)1 - cs1*cs1));
Real g0cs1 = g0(cs1);
Real g1cs1 = g1(cs1);
Real product = g0cs1*g1cs1;
if (product > (Real)0)
{
sn1 = -sn1;
}
else if (product < (Real)0)
{
// sn1 already has correct sign
}
else if (g1cs1 != (Real)0)
{
// g0 == 0.0
// assert( sn1 == 0.0 );
}
else // g1 == 0.0
{
// TO DO: When g1 = 0, there is no constraint on sn1.
// What should be done here? In this case, cs1 is a root
// to the quartic equation g0(cs1) = 0. Is there some
// geometric significance?
assertion(false, "Unexpected case\n");
}
Real m00 = a0 + a1*cs1 + a2*sn1;
Real m01 = a3 + a4*cs1 + a5*sn1;
Real m10 = b2*sn1 + b5*cs1;
Real m11 = b1*sn1 + b4*cs1;
Real det = m00*m11 - m01*m10;
if (Math<Real>::FAbs(det) >= Math<Real>::ZERO_TOLERANCE)
{
Real invDet = ((Real)1)/det;
Real lambda = -(b0*sn1 + b3*cs1);
cs0 = lambda*m00*invDet;
sn0 = -lambda*m01*invDet;
// Unitize in case of numerical error. Remove if you feel
// confident of the accuracy for cs0 and sn0.
Real tmp = Math<Real>::InvSqrt(cs0*cs0 + sn0*sn0);
cs0 *= tmp;
sn0 *= tmp;
Vector3<Real> closest0 = mCircle0->Center +
mCircle0->Radius*(cs0*mCircle0->Direction0 +
sn0*mCircle0->Direction1);
Vector3<Real> closest1 = mCircle1->Center +
mCircle1->Radius*(cs1*mCircle1->Direction0 +
sn1*mCircle1->Direction1);
diff = closest1 - closest0;
Real sqrDist = diff.SquaredLength();
if (sqrDist < minSqrDist)
{
minSqrDist = sqrDist;
mClosestPoint0 = closest0;
mClosestPoint1 = closest1;
}
}
else
{
// TO DO: Handle this case. Is there some geometric
// significance?
assertion(false, "Unexpected case\n");
}
}
return minSqrDist;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistCircle3Circle3<Real>::Get (Real t,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Vector3<Real> movedCenter0 = mCircle0->Center + t*velocity0;
Vector3<Real> movedCenter1 = mCircle1->Center + t*velocity1;
Circle3<Real> movedCircle0(movedCenter0, mCircle0->Direction0,
mCircle0->Direction1, mCircle0->Normal, mCircle0->Radius);
Circle3<Real> movedCircle1(movedCenter1, mCircle1->Direction0,
mCircle1->Direction1, mCircle1->Normal, mCircle1->Radius);
return DistCircle3Circle3<Real>(movedCircle0, movedCircle1).Get();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistCircle3Circle3<Real>::GetSquared (Real t,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
Vector3<Real> movedCenter0 = mCircle0->Center + t*velocity0;
Vector3<Real> movedCenter1 = mCircle1->Center + t*velocity1;
Circle3<Real> movedCircle0(movedCenter0, mCircle0->Direction0,
mCircle0->Direction1, mCircle0->Normal, mCircle0->Radius);
Circle3<Real> movedCircle1(movedCenter1, mCircle1->Direction0,
mCircle1->Direction1, mCircle1->Normal, mCircle1->Radius);
return DistCircle3Circle3<Real>(movedCircle0, movedCircle1).GetSquared();
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class DistCircle3Circle3<float>;
template WM5_MATHEMATICS_ITEM
class DistCircle3Circle3<double>;
//----------------------------------------------------------------------------
}
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