/****************************************************************************
* 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 1.11 2004/09/09 14:41:32 ponchio
forgotten typename SEGMENTTYPE::...
Revision 1.10 2004/08/09 09:48:43 pietroni
correcter .dir to .Direction and .ori in .Origin()
Revision 1.9 2004/08/04 20:55:02 pietroni
added rey triangle intersections funtions
Revision 1.8 2004/07/11 22:08:04 cignoni
Added a cast to remove a warning
Revision 1.7 2004/05/14 03:14:29 ponchio
Fixed some minor bugs
Revision 1.6 2004/05/13 23:43:54 ponchio
minor bug
Revision 1.5 2004/05/05 08:21:55 cignoni
syntax errors in inersection plane line.
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>
namespace vcg {
/** \addtogroup space */
/*@{*/
/**
Function computing the intersection between couple of geometric primitives in
3 dimension
*/
/// 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 = T(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<typename SEGMENTTYPE::PointType> 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()
);
}
// ray-triangle, gives barycentric coords of intersection and distance along ray
template<class T>
bool Intersection( const Line3<T> & ray, const Point3<T> & vert0,
const Point3<T> & vert1, const Point3<T> & vert2,
T & a ,T & b, T & dist)
{
// small (hum) borders around triangle
const T EPSILON2= T(1e-8);
const T EPSILON = T(1e-8);
Point3<T> edge1 = vert1 - vert0;
Point3<T> edge2 = vert2 - vert0;
// determinant
Point3<T> pvec = ray.Direction() ^ edge2;
T det = edge1*pvec;
// if determinant is near zero, ray lies in plane of triangle
if (fabs(det) < EPSILON) return false;
// calculate distance from vert0 to ray origin
Point3<T> tvec = ray.Origin()- vert0;
// calculate A parameter and test bounds
a = tvec * pvec;
if (a < -EPSILON2*det || a > det+det*EPSILON2) return false;
// prepare to test V parameter
Point3<T> qvec = tvec ^ edge1;
// calculate B parameter and test bounds
b = ray.Direction() * qvec ;
if (b < -EPSILON2*det || b + a > det+det*EPSILON2) return false;
// calculate t, scale parameters, ray intersects triangle
dist = edge2 * qvec;
if (dist<0) return false;
T inv_det = 1.0 / det;
dist *= inv_det;
a *= inv_det;
b *= inv_det;
return true;
}
// ray-triangle, gives intersection 3d point and distance along ray
template<class T>
bool Intersection( const Line3<T> & ray, const Point3<T> & vert0,
const Point3<T> & vert1, const Point3<T> & vert2,
Point3<T> & inte)
{
// small (hum) borders around triangle
const T EPSILON2= T(1e-8);
const T EPSILON = T(1e-8);
Point3<T> edge1 = vert1 - vert0;
Point3<T> edge2 = vert2 - vert0;
// determinant
Point3<T> pvec = ray.Direction() ^ edge2;
T det = edge1*pvec;
// if determinant is near zero, ray lies in plane of triangle
if (fabs(det) < EPSILON) return false;
// calculate distance from vert0 to ray origin
Point3<T> tvec = ray.Origin() - vert0;
// calculate A parameter and test bounds
T a = tvec * pvec;
if (a < -EPSILON2*det || a > det+det*EPSILON2) return false;
// prepare to test V parameter
Point3<T> qvec = tvec ^ edge1;
// calculate B parameter and test bounds
T b = ray.Direction() * qvec ;
if (b < -EPSILON2*det || b + a > det+det*EPSILON2) return false;
// calculate t, scale parameters, ray intersects triangle
double dist = edge2 * qvec;
//if (dist<0) return false;
T inv_det = 1.0 / det;
dist *= inv_det;
a *= inv_det;
b *= inv_det;
inte = vert0 + edge1*a + edge2*b;
return true;
}
/*@}*/
} // end namespace
#endif