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/****************************************************************************
**
** Copyright (C) 2014 Klaralvdalens Datakonsult AB (KDAB).
** Contact: http://www.qt-project.org/legal
**
** This file is part of the Qt3D module of the Qt Toolkit.
**
** $QT_BEGIN_LICENSE:LGPL3$
** Commercial License Usage
** Licensees holding valid commercial Qt licenses may use this file in
** accordance with the commercial license agreement provided with the
** Software or, alternatively, in accordance with the terms contained in
** a written agreement between you and The Qt Company. For licensing terms
** and conditions see http://www.qt.io/terms-conditions. For further
** information use the contact form at http://www.qt.io/contact-us.
**
** GNU Lesser General Public License Usage
** Alternatively, this file may be used under the terms of the GNU Lesser
** General Public License version 3 as published by the Free Software
** Foundation and appearing in the file LICENSE.LGPLv3 included in the
** packaging of this file. Please review the following information to
** ensure the GNU Lesser General Public License version 3 requirements
** will be met: https://www.gnu.org/licenses/lgpl.html.
**
** GNU General Public License Usage
** Alternatively, this file may be used under the terms of the GNU
** General Public License version 2.0 or later as published by the Free
** Software Foundation and appearing in the file LICENSE.GPL included in
** the packaging of this file. Please review the following information to
** ensure the GNU General Public License version 2.0 requirements will be
** met: http://www.gnu.org/licenses/gpl-2.0.html.
**
** $QT_END_LICENSE$
**
****************************************************************************/
#include "sphere.h"
#include <QPair>
#include <math.h>
QT_BEGIN_NAMESPACE
namespace {
inline QPair<int, int> findExtremePoints(const QVector<QVector3D> &points)
{
// Find indices of extreme points along x, y, and z axes
int xMin = 0, xMax = 0, yMin = 0, yMax = 0, zMin = 0, zMax = 0;
for (int i = 1; i < points.size(); ++i) {
const QVector3D &p = points.at(i);
if (p.x() < points[xMin].x())
xMin = i;
if (p.x() > points[xMax].x())
xMax = i;
if (p.y() < points[yMin].y())
yMin = i;
if (p.y() > points[yMax].y())
yMax = i;
if (p.z() < points[zMin].z())
zMin = i;
if (p.z() > points[zMax].z())
zMax = i;
}
// Calculate squared distance for the pairs of points
const float xDist2 = (points.at(xMax) - points.at(xMin)).lengthSquared();
const float yDist2 = (points.at(yMax) - points.at(yMin)).lengthSquared();
const float zDist2 = (points.at(zMax) - points.at(zMin)).lengthSquared();
// Select most distant pair
QPair<int, int> extremeIndices(xMin, xMax);
if (yDist2 > xDist2 && yDist2 > zDist2)
extremeIndices = qMakePair(yMin, yMax);
if (zDist2 > xDist2 && zDist2 > yDist2)
extremeIndices = qMakePair(zMin, zMax);
return extremeIndices;
}
inline void sphereFromExtremePoints(Qt3D::Sphere &s, const QVector<QVector3D> &points)
{
// Find two most separated points on any of the basis vectors
QPair<int, int> extremeIndices = findExtremePoints(points);
// Construct sphere to contain these two points
const QVector3D &p = points.at(extremeIndices.first);
const QVector3D &q = points.at(extremeIndices.second);
const QVector3D c = 0.5f * (p + q);
s.setCenter(c);
s.setRadius((q - c).length());
}
inline void constructRitterSphere(Qt3D::Sphere &s, const QVector<QVector3D> &points)
{
// Calculate the sphere encompassing two axially extreme points
sphereFromExtremePoints(s, points);
// Now make sure the sphere bounds all points by growing if needed
s.expandToContain(points);
}
} // anonymous namespace
namespace Qt3D {
const float Sphere::ms_epsilon = 1.0e-7f;
Sphere Sphere::fromPoints(const QVector<QVector3D> &points)
{
Sphere s;
s.initializeFromPoints(points);
return s;
}
void Sphere::initializeFromPoints(const QVector<QVector3D> &points)
{
constructRitterSphere(*this, points);
}
void Sphere::expandToContain(const QVector3D &p)
{
const QVector3D d = p - m_center;
const float dist2 = d.lengthSquared();
if (dist2 > m_radius * m_radius) {
// Expand radius so sphere also contains p
const float dist = sqrt(dist2);
const float newRadius = 0.5f * (m_radius + dist);
const float k = (newRadius - m_radius) / dist;
m_radius = newRadius;
m_center += k * d;
}
}
void Sphere::expandToContain(const Sphere &sphere)
{
const QVector3D d(sphere.m_center - m_center);
const float dist2 = d.lengthSquared();
const float dr = sphere.m_radius - m_radius;
if (dr * dr >= dist2) {
// Larger sphere encloses the smaller. Set our size to the larger
if (m_radius > sphere.m_radius)
return;
else
*this = sphere;
} else {
// The spheres are overlapping or disjoint
const float dist = sqrt(dist2);
const float newRadius = 0.5f * (dist + m_radius + sphere.m_radius);
if (dist > ms_epsilon)
m_center += d * (newRadius - m_radius) / dist;
}
}
Sphere Sphere::transformed(const QMatrix4x4 &mat)
{
// Transform extremities in x, y, and z directions to find extremities
// of the resulting ellipsoid
QVector3D x = mat.mapVector(m_center + QVector3D(m_radius, 0.0f, 0.0f));
QVector3D y = mat.mapVector(m_center + QVector3D(0.0f, m_radius, 0.0f));
QVector3D z = mat.mapVector(m_center + QVector3D(0.0f, 0.0f, m_radius));
// Transform center and find maximum radius of ellipsoid
QVector3D c = mat.mapVector(m_center);
float rSquared = qMax(qMax((x - c).lengthSquared(), (y - c).lengthSquared()), (z - c).lengthSquared());
return Sphere(c, sqrt(rSquared));
}
}
QT_END_NAMESPACE
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