/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* 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 *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program 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 General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.4 2004/05/04 02:37:58 ganovelli
Triangle3<T> replaced by TRIANGLE
Segment<T> replaced by EDGETYPE
Revision 1.3 2004/04/29 10:48:44 ganovelli
error in plane segment corrected
Revision 1.2 2004/04/26 12:34:50 ganovelli
plane line
plane segment
triangle triangle added
Revision 1.1 2004/04/21 14:22:27 cignoni
Initial Commit
****************************************************************************/
#ifndef __VCGLIB_INTERSECTION_3
#define __VCGLIB_INTERSECTION_3
#include <vcg/space/point3.h>
#include <vcg/space/line3.h>
#include <vcg/space/plane3.h>
#include <vcg/space/segment3.h>
#include <vcg/space/sphere3.h>
#include <vcg/space/triangle3.h>
#include <vcg/space/intersection/triangle_triangle3.h>
/** \addtogroup space */
/*@{*/
/**
Function computing the intersection between couple of geometric primitives in
3 dimension
*/
namespace vcg {
/// interseciton between sphere and line
template<class T>
inline bool Intersection( const Sphere3<T> & sp, const Line3<T> & li, Point3<T> & p0,Point3<T> & p1 ){
// Per prima cosa si sposta il sistema di riferimento
// fino a portare il centro della sfera nell'origine
Point3<T> neworig=li.Origin()-sp.Center();
// poi si risolve il sistema di secondo grado (con maple...)
T t1 = li.Direction().x()*li.Direction().x();
T t2 = li.Direction().y()*li.Direction().y();
T t3 = li.Direction().z()*li.Direction().z();
T t6 = neworig.y()*li.Direction().y();
T t7 = neworig.x()*li.Direction().x();
T t8 = neworig.z()*li.Direction().z();
T t15 = sp.Radius()*sp.Radius();
T t17 = neworig.z()*neworig.z();
T t19 = neworig.y()*neworig.y();
T t21 = neworig.x()*neworig.x();
T t28 = 2.0*t7*t6+2.0*t6*t8+2.0*t7*t8+t1*t15-t1*t17-t1*t19-t2*t21+t2*t15-t2*t17-t3*t21+t3*t15-t3*t19;
if(t28<0) return false;
T t29 = sqrt(t28);
T val0 = 1/(t1+t2+t3)*(-t6-t7-t8+t29);
T val1 = 1/(t1+t2+t3)*(-t6-t7-t8-t29);
p0=li.P(val0);
p1=li.P(val1);
return true;
}
/// intersection between line and plane
template<class T>
inline bool Intersection( const Plane3<T> & pl, const Line3<T> & li, Point3<T> & po){
const T epsilon = T(1e-8);
T k = pl.Direction() * li.Direction(); // Compute 'k' factor
if( (k > -epsilon) && (k < epsilon))
return false;
T r = (pl.Offset() - pl.Direction()*li.Origin())/k; // Compute ray distance
po = li.Origin() + li.Direction()*r;
return true;
}
/// intersection between segment and plane
template<typename SEGMENTTYPE>
inline bool Intersection( const Plane3<typename SEGMENTTYPE::ScalarType> & pl,
const SEGMENTTYPE & sg,
Point3<typename SEGMENTTYPE::ScalarType> & po){
typedef typename SEGMENTTYPE::ScalarType T;
const T epsilon = T(1e-8);
T k = pl.Direction() * (sg.P1()-sg.P0());
if( (k > -epsilon) && (k < epsilon))
return false;
T r = (pl.Offset() - pl.Direction()*sg.P0())/k; // Compute ray distance
if( (r<0) || (r > 1.0))
return false;
po = sg.P0()*(1-r)+sg.P1() * r;
return true;
}
/// intersection between plane and triangle
// not optimal: uses plane-segment intersection (and the fact the two or none edges can be intersected)
template<typename TRIANGLETYPE>
inline bool Intersection( const Plane3<typename TRIANGLETYPE::ScalarType> & pl,
const TRIANGLETYPE & tr,
Segment3<typename TRIANGLETYPE::ScalarType> & sg){
typedef typename TRIANGLETYPE::ScalarType T;
if(Intersection(pl,Segment3<T>(tr.P(0),tr.P(1)),sg.P0())){
if(Intersection(pl,Segment3<T>(tr.P(0),tr.P(2)),sg.P1()))
return true;
else
{
Intersection(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P1());
return true;
}
}else
{
if(Intersection(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P0()))
{
Intersection(pl,Segment3<T>(tr.P(0),tr.P(2)),sg.P1());
return true;
}
}
return false;
}
/// intersection between two triangles
template<typename TRIANGLETYPE>
inline bool Intersection( const TRIANGLETYPE & t0,const TRIANGLETYPE & t1){
return NoDivTriTriIsect(t0.P0(0),t0.P0(1),t0.P0(2),
t1.P0(0),t1.P0(1),t1.P0(2));
}
template<class T>
inline bool Intersection( Point3<T> V0,Point3<T> V1,Point3<T> V2,
Point3<T> U0,Point3<T> U1,Point3<T> U2){
return NoDivTriTriIsect(V0,V1,V2,U0,U1,U2);
}
template<class T>
inline bool Intersection( Point3<T> V0,Point3<T> V1,Point3<T> V2,
Point3<T> U0,Point3<T> U1,Point3<T> U2,int *coplanar,
Point3<T> &isectpt1,Point3<T> &isectpt2){
return tri_tri_intersect_with_isectline(V0,V1,V2,U0,U1,U2,
coplanar,isectpt1,isectpt2);
}
template<typename TRIANGLETYPE,typename SEGMENTTYPE >
inline bool Intersection( const TRIANGLETYPE & t0,const TRIANGLETYPE & t1,bool &coplanar,
SEGMENTTYPE & sg){
Point3<T> ip0,ip1;
return tri_tri_intersect_with_isectline(t0.P0(0),t0.P0(1),t0.P0(2),
t1.P0(0),t1.P0(1),t1.P0(2),
coplanar,sg.P0(),sg.P1()
);
}
} // end namespace
#endif