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aka_ball.hh
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/**
* @file aka_ball.hh
*
* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
*
* @date creation: Fri Jan 04 2013
* @date last modification: Tue Jun 17 2014
*
* @brief bounding ball classes
*
* @section LICENSE
*
* Copyright (©) 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_BALL_HH__
#define __AKANTU_BALL_HH__
#include <iostream>
#include "aka_common.hh"
#include "aka_point.hh"
#include "aka_bounding_box.hh"
__BEGIN_AKANTU__
static Real epsilon = 10*std::numeric_limits<Real>::epsilon();
using std::cout;
using std::endl;
//! Ball class template
/*! This class template represents the abstraction of a d-dimensional sphere.
* \tparam d - Ball dimension
*/
template <int d>
class Ball : public Bounding_volume<d> {
public:
typedef Bounding_volume<d> base_type;
typedef typename base_type::point_type point_type;
typedef typename point_type::value_type value_type;
typedef BoundingBox<d> aabb_type;
//! Return ball dimension
constexpr static int dim()
{ return d; }
//! Parameter constructor takes the ball center point and its radius
Ball(const point_type& c = point_type(), value_type r = value_type()) : base_type(), c_(c), r_(r) {}
//! Combine two ball objects
virtual base_type* combine(const base_type& b) const {
const Ball* sp = dynamic_cast<const Ball*>(&b);
assert(sp != nullptr);
const Ball& s0 = *sp;
Ball r(s0);
r += *this;
return new Ball(r);
}
//! Standard output stream operator
virtual std::ostream& print(std::ostream& os) const;
aabb_type bounding_box() const {
point_type o = r_*point_type(1.);
return aabb_type(c_ - o, c_ + o);
}
//! Get ball center
point_type const& center() const
{ return c_; }
//! Get ball radius
value_type const& radius() const
{ return r_; }
//! Use in generic code as comparative measure of how big the sphere is
value_type measure() const;
//! Grow sphere if point lies outside of it
Ball& operator+=(const point_type& p) {
point_type diff = p - c_;
value_type sq_norm = diff.sq_norm();
if (sq_norm > r_*r_) {
value_type norm = sqrt(sq_norm);
value_type new_r = 0.5*(r_ + norm);
value_type scalar = (new_r - r_) / norm;
r_ = new_r;
c_ += scalar * diff;
}
return *this;
}
//! Determine the ball that encloses both spheres
Ball& operator+=(const Ball s) {
point_type diff = s.c_ - c_;
value_type sq_norm = diff.sq_norm();
// one ball is contained within the other
if (pow(s.r_ - r_, 2) >= sq_norm) {
if(s.r_ >= r_)
this->operator=(s);
// else do nothing, as the current ball is bigger
// and no further changes are required
}
// else balls partially overlapping or disjoint
else {
// compute new radius
value_type norm = sqrt(sq_norm);
value_type tmp = r_;
r_ = 0.5 * (norm + r_ + s.r_);
if (norm > epsilon)
c_ += ((r_ - tmp) / norm) * diff;
}
return *this;
}
//! Check for collision with a point
bool operator&(const point_type& p) const
{ return (p - c_).sq_norm() - r_*r_ < epsilon; }
//! Check for collision with another ball
bool operator&(const Ball& s) const
{ return (c_ - s.c_).sq_norm() - pow(r_ + s.r_,2.) < epsilon; }
//! Compute ball from intersection of bounding boxes of two balls
Ball operator&&(const Ball& b) const {
// get bounding boxes of spheres
aabb_type bb1 = bounding_box();
aabb_type bb2 = b.bounding_box();
// compute intersection
aabb_type bbint = bb1 && bb2;
// compute center and radius of the sphere
point_type c = 0.5*(bbint.min() + bbint.max());
value_type r = sqrt((bbint.min() - bbint.max()).sq_norm());
// construct sphere
return Ball(c,r);
}
private:
point_type c_; //!< Ball center
Real r_; //!< Ball radius
};
//! Interval type definition
typedef Ball<1> Interval;
//! Circle type definition
typedef Ball<2> Circle;
//! Sphere type definition
typedef Ball<3> Sphere;
//! Add two balls
template <int d>
Ball<d> operator+(const Ball<d>& s1, const Ball<d>& s2) {
Ball<d> r(s1);
return r += s2;
}
//! Extreme points algirhtm by Ritter
/*! J. Ritter, Graphics gems, Academic Press Professional, Inc., San Diego, CA, USA, 1990, Ch.
* An efficient bounding sphere, pp. 301–303. URL http://dl.acm.org/citation.cfm?id=90767.90836
*/
template <class point_container>
std::pair<size_t, size_t> extreme_points(const point_container& pts) {
typedef typename point_container::value_type point_type;
typedef typename point_type::value_type value_type;
size_t min[] = { 0, 0, 0 };
size_t max[] = { 0, 0, 0 };
// loop over container points to find extremal points
for (size_t i=1; i<pts.size(); ++i) {
const point_type& p = pts[i];
// loop over coordinates
for (int j=0; j<point_type::dim(); ++j) {
// check if new point is minimum
if (p[j] < pts[min[j]][j])
min[j] = i;
// check if new point is maximum
else if (p[j] > pts[max[j]][j])
max[j] = i;
}
}
// pick the pair of the longest distance
size_t m=0, M=0;
value_type sq_norm = value_type();
for (int i=0; i<point_type::dim(); ++i) {
point_type diff = pts[max[i]] - pts[min[i]];
value_type new_sq_norm = diff.sq_norm();
if (new_sq_norm > sq_norm) {
m = min[i];
M = max[i];
sq_norm = new_sq_norm;
}
}
return std::make_pair(m,M);
}
//! Create a bounding ball from a container of points
template <int d, class point_container>
Ball<d> bounding_ball(const point_container& pts) {
assert(!pts.empty());
typedef typename point_container::value_type point_type;
typedef typename point_type::value_type value_type;
// find extreme points on axis-aligned bounding box to construct
// first approximation of the sphere
std::pair<size_t, size_t> mM = extreme_points(pts);
// compute center and radius of the sphere
const point_type &m = pts[mM.first];
const point_type &M = pts[mM.second];
point_type c = 0.5*(m+M);
value_type r = sqrt((M-c).sq_norm());
// construct sphere
Ball<d> s(c,r);
// second pass: update the sphere so that all points lie inside
for (size_t i=0; i<pts.size(); ++i)
s += pts[i];
return s;
}
__END_AKANTU__
#endif /* __AKANTU_BALL_HH__ */

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