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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: 5.10.0 (2013/03/17)
#include "Wm5MathematicsPCH.h"
#include "Wm5DistPoint2Hyperbola2.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
static Real H (Real t, const Vector2<Real>& point, const Vector2<Real>& resqr)
{
Real ratio0 = point[0]/((Real)1 + t*resqr[0]);
Real ratio1 = point[1]/((Real)1 - t*resqr[1]);
return ratio0*ratio0 - ratio1*ratio1 - (Real)1;
}
//----------------------------------------------------------------------------
template <typename Real>
Real ComputeDistancePointToHyperbola (const Vector2<Real>& point,
const Vector2<Real>& extent, Vector2<Real>& closest)
{
assertion(extent[0] > (Real)0 && extent[1] > (Real)0, "Invalid inputs");
Vector2<Real> esqr(extent[0]*extent[0], extent[1]*extent[1]);
Vector2<Real> resqr(((Real)1)/esqr[0], ((Real)1)/esqr[1]);
// Initialize for bisection. It is not relevant that H(-a^2) = +infinity
// and H(b^2) = -infinity, so we need only initialize function values with
// accordingly signed numbers.
Real t0 = -esqr[0], t1 = esqr[1];
Real troot = ((Real)0.5)*(t0 + t1);
Real hroot = H(troot, point, resqr);
// Iterate until H(troot) is exactly zero or until one of the
// floating-point endpoints does not change anymore. The latter condition
// takes advantage of the nature of IEEE floating-point numbers, so the
// loop must terminate in a finite number of steps.
while (hroot != (Real)0 && troot != t0 && troot != t1)
{
if (hroot > (Real)0)
{
t0 = troot;
troot = ((Real)0.5)*(t0 + t1);
}
else // hroot < (Real)0
{
t1 = troot;
}
troot = ((Real)0.5)*(t0 + t1);
hroot = H(troot, point, resqr);
}
closest[0] = point[0]/((Real)1 + troot*resqr[0]);
closest[1] = point[1]/((Real)1 - troot*resqr[1]);
Vector2<Real> diff = point - closest;
Real distance = diff.Length();
return distance;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
float ComputeDistancePointToHyperbola<float> (const Vector2<float>&,
const Vector2<float>&, Vector2<float>&);
template WM5_MATHEMATICS_ITEM
double ComputeDistancePointToHyperbola<double> (const Vector2<double>&,
const Vector2<double>&, Vector2<double>&);
//----------------------------------------------------------------------------
}
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