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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 "Wm5ContLozenge3.h"
#include "Wm5ApprGaussPointsFit3.h"
#include "Wm5DistPoint3Line3.h"
#include "Wm5DistPoint3Rectangle3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Lozenge3<Real> ContLozenge (int numPoints, const Vector3<Real>* points)
{
// Fit with Gaussian. Axis(0) corresponds to the smallest eigenvalue.
Box3<Real> box = GaussPointsFit3<Real>(numPoints, points);
Vector3<Real> diff = points[0] - box.Center;
Real wMin = box.Axis[0].Dot(diff);
Real wMax = wMin;
Real w;
int i;
for (i = 1; i < numPoints; ++i)
{
diff = points[i] - box.Center;
w = box.Axis[0].Dot(diff);
if (w < wMin)
{
wMin = w;
}
else if (w > wMax)
{
wMax = w;
}
}
Real radius = ((Real)0.5)*(wMax - wMin);
Real rSqr = radius*radius;
box.Center += (((Real)0.5)*(wMax + wMin))*box.Axis[0];
Real aMin = Math<Real>::MAX_REAL;
Real aMax = -aMin;
Real bMin = Math<Real>::MAX_REAL;
Real bMax = -bMin;
Real discr, radical, u, v, test;
for (i = 0; i < numPoints; ++i)
{
diff = points[i] - box.Center;
u = box.Axis[2].Dot(diff);
v = box.Axis[1].Dot(diff);
w = box.Axis[0].Dot(diff);
discr = rSqr - w*w;
radical = Math<Real>::Sqrt(Math<Real>::FAbs(discr));
test = u + radical;
if (test < aMin)
{
aMin = test;
}
test = u - radical;
if (test > aMax)
{
aMax = test;
}
test = v + radical;
if (test < bMin)
{
bMin = test;
}
test = v - radical;
if (test > bMax)
{
bMax = test;
}
}
// The enclosing region might be a capsule or a sphere.
if (aMin >= aMax)
{
test = ((Real)0.5)*(aMin + aMax);
aMin = test;
aMax = test;
}
if (bMin >= bMax)
{
test = ((Real)0.5)*(bMin + bMax);
bMin = test;
bMax = test;
}
// Make correction for points inside mitered corner but outside quarter
// sphere.
for (i = 0; i < numPoints; ++i)
{
diff = points[i] - box.Center;
u = box.Axis[2].Dot(diff);
v = box.Axis[1].Dot(diff);
Real* aExtreme = 0;
Real* bExtreme = 0;
if (u > aMax)
{
if (v > bMax)
{
aExtreme = &aMax;
bExtreme = &bMax;
}
else if (v < bMin)
{
aExtreme = &aMax;
bExtreme = &bMin;
}
}
else if (u < aMin)
{
if (v > bMax)
{
aExtreme = &aMin;
bExtreme = &bMax;
}
else if (v < bMin)
{
aExtreme = &aMin;
bExtreme = &bMin;
}
}
if (aExtreme)
{
Real deltaU = u - *aExtreme;
Real deltaV = v - *bExtreme;
Real deltaSumSqr = deltaU*deltaU + deltaV*deltaV;
w = box.Axis[0].Dot(diff);
Real wSqr = w*w;
test = deltaSumSqr + wSqr;
if (test > rSqr)
{
discr = (rSqr - wSqr)/deltaSumSqr;
Real t = -Math<Real>::Sqrt(Math<Real>::FAbs(discr));
*aExtreme = u + t*deltaU;
*bExtreme = v + t*deltaV;
}
}
}
Lozenge3<Real> lozenge;
lozenge.Radius = radius;
lozenge.Rectangle.Axis[0] = box.Axis[2];
lozenge.Rectangle.Axis[1] = box.Axis[1];
if (aMin < aMax)
{
if (bMin < bMax)
{
// Container is a lozenge.
lozenge.Rectangle.Center = box.Center + aMin*box.Axis[2] +
bMin*box.Axis[1];
lozenge.Rectangle.Extent[0] = ((Real)0.5)*(aMax - aMin);
lozenge.Rectangle.Extent[1] = ((Real)0.5)*(bMax - bMin);
}
else
{
// Container is a capsule.
lozenge.Rectangle.Center = box.Center + aMin*box.Axis[2] +
(((Real)0.5)*(bMin + bMax))*box.Axis[1];
lozenge.Rectangle.Extent[0] = ((Real)0.5)*(aMax - aMin);
lozenge.Rectangle.Extent[1] = (Real)0;
}
}
else
{
if (bMin < bMax)
{
// Container is a capsule.
lozenge.Rectangle.Center = box.Center + bMin*box.Axis[1] +
(((Real)0.5)*(aMin + aMax))*box.Axis[2];
lozenge.Rectangle.Extent[0] = (Real)0;
lozenge.Rectangle.Extent[1] = ((Real)0.5)*(bMax - bMin);
}
else
{
// Container is a sphere.
lozenge.Rectangle.Center = box.Center +
(((Real)0.5)*(aMin + aMax))*box.Axis[2] +
(((Real)0.5)*(bMin + bMax))*box.Axis[1];
lozenge.Rectangle.Extent[0] = (Real)0;
lozenge.Rectangle.Extent[1] = (Real)0;
}
}
return lozenge;
}
//----------------------------------------------------------------------------
template <typename Real>
bool InLozenge (const Vector3<Real>& point, const Lozenge3<Real>& lozenge)
{
Real dist = DistPoint3Rectangle3<Real>(point, lozenge.Rectangle).Get();
return dist <= lozenge.Radius;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
Lozenge3<float> ContLozenge<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
bool InLozenge<float> (const Vector3<float>&, const Lozenge3<float>&);
template WM5_MATHEMATICS_ITEM
Lozenge3<double> ContLozenge<double> (int, const Vector3<double>*);
template WM5_MATHEMATICS_ITEM
bool InLozenge<double> (const Vector3<double>&, const Lozenge3<double>&);
//----------------------------------------------------------------------------
}
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