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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: 5.0.3 (2013/01/03)
#include "Wm5MathematicsPCH.h"
#include "Wm5DistPoint2Ellipse2.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
DistPoint2Ellipse2<Real>::DistPoint2Ellipse2 (const Vector2<Real>& point,
const Ellipse2<Real>& ellipse)
:
mPoint(&point),
mEllipse(&ellipse)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector2<Real>& DistPoint2Ellipse2<Real>::GetPoint () const
{
return *mPoint;
}
//----------------------------------------------------------------------------
template <typename Real>
const Ellipse2<Real>& DistPoint2Ellipse2<Real>::GetEllipse () const
{
return *mEllipse;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistPoint2Ellipse2<Real>::Get ()
{
return Math<Real>::Sqrt(GetSquared());
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistPoint2Ellipse2<Real>::GetSquared ()
{
// Compute coordinates of point in ellipse coordinate system.
Vector2<Real> diff = *mPoint - mEllipse->Center;
Vector2<Real> y(diff.Dot(mEllipse->Axis[0]), diff.Dot(mEllipse->Axis[1]));
Vector2<Real> x;
Real sqrDistance = SqrDistance(mEllipse->Extent, y, x);
mClosestPoint0 = *mPoint;
mClosestPoint1 = mEllipse->Center +
x[0]*mEllipse->Axis[0] +
x[1]*mEllipse->Axis[1];
return sqrDistance;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistPoint2Ellipse2<Real>::Get (Real t,
const Vector2<Real>& velocity0, const Vector2<Real>& velocity1)
{
Vector2<Real> movedPoint = *mPoint + t*velocity0;
Vector2<Real> movedCenter = mEllipse->Center + t*velocity1;
Ellipse2<Real> movedEllipse(movedCenter, mEllipse->Axis,
mEllipse->Extent);
return DistPoint2Ellipse2<Real>(movedPoint, movedEllipse).Get();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistPoint2Ellipse2<Real>::GetSquared (Real t,
const Vector2<Real>& velocity0, const Vector2<Real>& velocity1)
{
Vector2<Real> movedPoint = *mPoint + t*velocity0;
Vector2<Real> movedCenter = mEllipse->Center + t*velocity1;
Ellipse2<Real> movedEllipse(movedCenter, mEllipse->Axis,
mEllipse->Extent);
return DistPoint2Ellipse2<Real>(movedPoint, movedEllipse).GetSquared();
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistPoint2Ellipse2<Real>::SqrDistanceSpecial (const Real e[2],
const Real y[2], Real x[2])
{
Real sqrDistance;
if (y[1] > (Real)0)
{
if (y[0] > (Real)0)
{
// Bisect to compute the root of F(t) for t >= -e1*e1.
Real esqr[2] = { e[0]*e[0], e[1]*e[1] };
Real ey[2] = { e[0]*y[0], e[1]*y[1] };
Real t0 = -esqr[1] + ey[1];
Real t1 = -esqr[1] + sqrt(ey[0]*ey[0] + ey[1]*ey[1]);
Real t = t0;
const int imax = 2*std::numeric_limits<Real>::max_exponent;
for (int i = 0; i < imax; ++i)
{
t = ((Real)0.5)*(t0 + t1);
if (t == t0 || t == t1)
{
break;
}
Real r[2] = { ey[0]/(t + esqr[0]), ey[1]/(t + esqr[1]) };
Real f = r[0]*r[0] + r[1]*r[1] - (Real)1;
if (f > (Real)0)
{
t0 = t;
}
else if (f < (Real)0)
{
t1 = t;
}
else
{
break;
}
}
x[0] = esqr[0]*y[0]/(t + esqr[0]);
x[1] = esqr[1]*y[1]/(t + esqr[1]);
Real d[2] = { x[0] - y[0], x[1] - y[1] };
sqrDistance = d[0]*d[0] + d[1]*d[1];
}
else // y0 == 0
{
x[0] = (Real)0;
x[1] = e[1];
Real diff = y[1] - e[1];
sqrDistance = diff*diff;
}
}
else // y1 == 0
{
Real denom0 = e[0]*e[0] - e[1]*e[1];
Real e0y0 = e[0]*y[0];
if (e0y0 < denom0)
{
// y0 is inside the subinterval.
Real x0de0 = e0y0/denom0;
Real x0de0sqr = x0de0*x0de0;
x[0] = e[0]*x0de0;
x[1] = e[1]*sqrt(fabs((Real)1 - x0de0sqr));
Real d0 = x[0] - y[0];
sqrDistance = d0*d0 + x[1]*x[1];
}
else
{
// y0 is outside the subinterval. The closest ellipse point has
// x1 == 0 and is on the domain-boundary interval (x0/e0)^2 = 1.
x[0] = e[0];
x[1] = (Real)0;
Real diff = y[0] - e[0];
sqrDistance = diff*diff;
}
}
return sqrDistance;
}
//----------------------------------------------------------------------------
template <typename Real>
Real DistPoint2Ellipse2<Real>::SqrDistance (const Real e[2], const Real y[2],
Real x[2])
{
// Determine reflections for y to the first quadrant.
bool reflect[2];
int i, j;
for (i = 0; i < 2; ++i)
{
reflect[i] = (y[i] < (Real)0);
}
// Determine the axis order for decreasing extents.
int permute[2];
if (e[0] < e[1])
{
permute[0] = 1; permute[1] = 0;
}
else
{
permute[0] = 0; permute[1] = 1;
}
int invpermute[2];
for (i = 0; i < 2; ++i)
{
invpermute[permute[i]] = i;
}
Real locE[2], locY[2];
for (i = 0; i < 2; ++i)
{
j = permute[i];
locE[i] = e[j];
locY[i] = y[j];
if (reflect[j])
{
locY[i] = -locY[i];
}
}
Real locX[2];
Real sqrDistance = SqrDistanceSpecial(locE, locY, locX);
// Restore the axis order and reflections.
for (i = 0; i < 2; ++i)
{
j = invpermute[i];
if (reflect[i])
{
locX[j] = -locX[j];
}
x[i] = locX[j];
}
return sqrDistance;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class DistPoint2Ellipse2<float>;
template WM5_MATHEMATICS_ITEM
class DistPoint2Ellipse2<double>;
//----------------------------------------------------------------------------
}
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