/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
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* All rights reserved. *
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* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
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* (at your option) any later version. *
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* This program is distributed in the hope that it will be useful, *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.8 2005/02/22 14:18:15 ponchio
assert addded.
Revision 1.7 2005/02/21 17:03:03 ponchio
Added Tight creation.
Revision 1.6 2004/12/01 16:06:59 ponchio
Distance
Revision 1.5 2004/09/29 13:55:33 ponchio
Added Distance shpere - point.
Revision 1.4 2004/04/02 09:49:01 ponchio
Ehm... a couople of small errors.
Revision 1.3 2004/04/02 09:44:13 ponchio
Sphere ->Sphere3
Revision 1.2 2004/03/25 17:25:46 ponchio
#include sbagliato.
Revision 1.1 2004/03/21 17:51:57 ponchio
First version.
****************************************************************************/
#ifndef VCG_SPHERE_H
#define VCG_SPHERE_H
#include <assert.h>
#include <vcg/space/point3.h>
namespace vcg {
/** \addtogroup space */
/*@{*/
/**
Templated class for 3D sphere.
This is the class for definition of a sphere in 3D space. It is stored just as a Point3 and a radius
@param T (template parameter) Specifies the type of scalar used to represent coords.
Various policy could be added to improve efficience (keeping square of radius for instance).
*/
template <class T> class Sphere3 {
protected:
Point3<T> _center;
T _radius;
public:
typedef T ScalarType;
Sphere3(): _radius(-1) {}
Sphere3(const Point3<T> ¢er, T radius): _center(center), _radius(radius) {}
T &Radius() { return _radius; }
const T &Radius() const { return _radius; }
Point3<T> &Center() { return _center; }
const Point3<T> &Center() const { return _center; }
bool IsEmpty() const { return _radius < 0; }
///return true if @param p - Center() <= Radius()
bool IsIn(const Point3<T> &p) const;
void Add(const Point3<T> &p);
void Add(const Sphere3 &sphere);
void Intersect(const Sphere3 &sphere);
//makes 36 iterations over the data... but get good results.
int CreateTight(int n, const Point3<T> *points,
T threshold = 1.01, T speed = 0.6);
};
template <class T> T Distance(const Sphere3<T> &sphere,
const Point3<T> &point) {
T dist = Distance(point, sphere.Center()) - sphere.Radius();
if(dist < 0) dist = 0;
return dist;
}
template <class T> T Distance(const Sphere3<T> &sphere,
const Sphere3<T> &s) {
T dist = Distance(s.Center(), sphere.Center())
- sphere.Radius() - s.Radius();
if(dist < 0) dist = 0;
return dist;
}
typedef Sphere3<float> Sphere3f;
typedef Sphere3<double> Sphere3d;
template <class T> void Sphere3<T>::Add(const Sphere3<T> &sphere) {
if(IsEmpty()) {
*this = sphere;
return;
}
Point3<T> dist = sphere.Center() - _center;
float distance = dist.Norm();
float fartest = distance + sphere.Radius();
if(fartest <= _radius)
return;
if(distance == 0)
_radius = sphere.Radius();
else {
_center += dist * ((fartest - _radius) / (dist.Norm() * 2));
_radius = (_radius + fartest)/2;
}
}
template <class T> void Sphere3<T>::Add(const Point3<T> &p) {
if(IsEmpty()) {
_center = p;
_radius = 0;
}
Point3<T> dist = p - _center;
float fartest = dist.Norm();
if(fartest <= _radius) return;
_center += dist * ((fartest - _radius) / (fartest*2));
_radius = (_radius + fartest)/2;
}
template <class T> bool Sphere3<T>::IsIn(const Point3<T> &p) const {
if(IsEmpty()) return false;
Point3<T> dist = p - _center;
return dist.SquaredNorm() <= _radius*_radius;
}
template <class T> void Sphere3<T>::Intersect(const Sphere3<T> &s) {
float dist = Distance(_center, s.Center());
float r = 0.5 * (_radius + s.Radius() - dist);
if(r < 0) {
_radius = -1;
return;
}
_center = (s.Center()*(_radius - r) + _center*(s.Radius() - r))/dist;
_radius = r;
}
template <class T> int Sphere3<T>::CreateTight(int n, const Point3<T> *points,
T threshold, T speed) {
//This is quantized gradient descent... really ugly. But simple :P
//TODO step should adapt to terrain...
for(int i = 0; i < n; i++)
Add(points[i]);
Radius() *= 1.0001;
Point3<T> center;
T radius;
//Test with 6 directions
Point3f pert[6];
T step = Radius()/8;
int count = 0;
while(1) {
count++;
T radius = Radius();
pert[0] = Point3f(step, 0, 0);
pert[1] = -pert[0];
pert[2] = Point3f(0, step, 0);
pert[3] = -pert[2];
pert[4] = Point3f(0, 0, step);
pert[5] = -pert[4];
unsigned int best = 6;
T best_radius = Radius()/threshold;
for(unsigned int k = 0; k < 6; k++) {
center = Center() + pert[k];
radius = 0;
for(unsigned int i = 0; i < n; i++) {
float r = Distance(center, points[i]);
if(r > radius)
radius = r;
}
if(radius < best_radius) {
best = k;
best_radius = radius;
}
}
if(best != 6) {
Center() = Center() + pert[best];
Radius() = best_radius;
}
step *= speed;
if(step < Radius() * (threshold - 1))
break;
}
Radius() *= 1.01;
//Test we did it correctly.
for(int i = 0; i < n; i++)
assert(IsIn(points[i]));
return count;
}
} //namespace
#endif