510 lines
15 KiB
C++
510 lines
15 KiB
C++
/****************************************************************************
|
|
* 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 1.16 2005/09/28 19:40:55 m_di_benedetto
|
|
Added intersection for ray-triangle (with Ray3 type).
|
|
|
|
Revision 1.15 2005/06/29 15:28:31 callieri
|
|
changed intersection names to more specific to avoid ambiguity
|
|
|
|
Revision 1.14 2005/03/15 11:22:39 ganovelli
|
|
added intersection between tow planes (porting from old vcg lib)
|
|
|
|
Revision 1.13 2005/01/26 10:03:08 spinelli
|
|
aggiunta intersect ray-box
|
|
|
|
Revision 1.12 2004/10/13 12:45:51 cignoni
|
|
Better Doxygen documentation
|
|
|
|
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/ray3.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 IntersectionLineSphere( 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 IntersectionLinePlane( 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 = T(1.0) / det;
|
|
dist *= inv_det;
|
|
a *= inv_det;
|
|
b *= inv_det;
|
|
|
|
return true;
|
|
}
|
|
|
|
// ray-triangle, gives barycentric coords of intersection and distance along ray.
|
|
// Ray3 type used.
|
|
template<class T>
|
|
bool Intersection( const Ray3<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 = T(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;
|
|
}
|
|
|
|
|
|
// ray-box
|
|
template<class T>
|
|
bool Intersection( const Box3<T> & box, const Line3<T> & r, Point3<T> & coord )
|
|
{
|
|
const int NUMDIM = 3;
|
|
const int RIGHT = 0;
|
|
const int LEFT = 1;
|
|
const int MIDDLE = 2;
|
|
|
|
int inside = 1;
|
|
char quadrant[NUMDIM];
|
|
int i;
|
|
int whichPlane;
|
|
Point3<T> maxT,candidatePlane;
|
|
|
|
// Find candidate planes; this loop can be avoided if
|
|
// rays cast all from the eye(assume perpsective view)
|
|
for (i=0; i<NUMDIM; i++)
|
|
{
|
|
if(r.Origin()[i] < box.min[i])
|
|
{
|
|
quadrant[i] = LEFT;
|
|
candidatePlane[i] = box.min[i];
|
|
inside = 0;
|
|
}
|
|
else if (r.Origin()[i] > box.max[i])
|
|
{
|
|
quadrant[i] = RIGHT;
|
|
candidatePlane[i] = box.max[i];
|
|
inside = 0;
|
|
}
|
|
else
|
|
{
|
|
quadrant[i] = MIDDLE;
|
|
}
|
|
}
|
|
|
|
// Ray origin inside bounding box
|
|
if(inside){
|
|
coord = r.Origin();
|
|
return true;
|
|
}
|
|
|
|
// Calculate T distances to candidate planes
|
|
for (i = 0; i < NUMDIM; i++)
|
|
{
|
|
if (quadrant[i] != MIDDLE && r.Direction()[i] !=0.)
|
|
maxT[i] = (candidatePlane[i]-r.Origin()[i]) / r.Direction()[i];
|
|
else
|
|
maxT[i] = -1.;
|
|
}
|
|
|
|
// Get largest of the maxT's for final choice of intersection
|
|
whichPlane = 0;
|
|
for (i = 1; i < NUMDIM; i++)
|
|
if (maxT[whichPlane] < maxT[i])
|
|
whichPlane = i;
|
|
|
|
// Check final candidate actually inside box
|
|
if (maxT[whichPlane] < 0.) return false;
|
|
for (i = 0; i < NUMDIM; i++)
|
|
if (whichPlane != i)
|
|
{
|
|
coord[i] = r.Origin()[i] + maxT[whichPlane] *r.Direction()[i];
|
|
if (coord[i] < box.min[i] || coord[i] > box.max[i])
|
|
return false;
|
|
}
|
|
else
|
|
{
|
|
coord[i] = candidatePlane[i];
|
|
}
|
|
return true; // ray hits box
|
|
}
|
|
|
|
template<class T>
|
|
bool Intersection (const Plane3<T> & plane0, const Plane3<T> & plane1,
|
|
Line3<T> & line)
|
|
{
|
|
// If Cross(N0,N1) is zero, then either planes are parallel and separated
|
|
// or the same plane. In both cases, 'false' is returned. Otherwise,
|
|
// the intersection line is
|
|
//
|
|
// L(t) = t*Cross(N0,N1) + c0*N0 + c1*N1
|
|
//
|
|
// for some coefficients c0 and c1 and for t any real number (the line
|
|
// parameter). Taking dot products with the normals,
|
|
//
|
|
// d0 = Dot(N0,L) = c0*Dot(N0,N0) + c1*Dot(N0,N1)
|
|
// d1 = Dot(N1,L) = c0*Dot(N0,N1) + c1*Dot(N1,N1)
|
|
//
|
|
// which are two equations in two unknowns. The solution is
|
|
//
|
|
// c0 = (Dot(N1,N1)*d0 - Dot(N0,N1)*d1)/det
|
|
// c1 = (Dot(N0,N0)*d1 - Dot(N0,N1)*d0)/det
|
|
//
|
|
// where det = Dot(N0,N0)*Dot(N1,N1)-Dot(N0,N1)^2.
|
|
|
|
T n00 = plane0.Direction()*plane0.Direction();
|
|
T n01 = plane0.Direction()*plane1.Direction();
|
|
T n11 = plane1.Direction()*plane1.Direction();
|
|
T det = n00*n11-n01*n01;
|
|
|
|
const T tolerance = (T)(1e-06f);
|
|
if ( math::Abs(det) < tolerance )
|
|
return false;
|
|
|
|
T invDet = 1.0f/det;
|
|
T c0 = (n11*plane0.Offset() - n01*plane1.Offset())*invDet;
|
|
T c1 = (n00*plane1.Offset() - n01*plane0.Offset())*invDet;
|
|
|
|
line.SetDirection(plane0.Direction()^plane1.Direction());
|
|
line.SetOrigin(plane0.Direction()*c0+ plane1.Direction()*c1);
|
|
|
|
return true;
|
|
}
|
|
|
|
|
|
// Ray-Triangle Functor
|
|
template <bool BACKFACETEST = true>
|
|
class RayTriangleIntersectionFunctor {
|
|
public:
|
|
template <class TRIANGLETYPE, class SCALARTYPE>
|
|
inline bool operator () (const TRIANGLETYPE & f, const Ray3<SCALARTYPE> & ray, SCALARTYPE & t) {
|
|
typedef SCALARTYPE ScalarType;
|
|
ScalarType a;
|
|
ScalarType b;
|
|
|
|
bool bret = Intersection(ray, Point3<SCALARTYPE>::Construct(f.P(0)), Point3<SCALARTYPE>::Construct(f.P(1)), Point3<SCALARTYPE>::Construct(f.P(2)), a, b, t);
|
|
if (BACKFACETEST) {
|
|
if (!bret) {
|
|
bret = Intersection(ray, Point3<SCALARTYPE>::Construct(f.P(0)), Point3<SCALARTYPE>::Construct(f.P(2)), Point3<SCALARTYPE>::Construct(f.P(1)), a, b, t);
|
|
}
|
|
}
|
|
return (bret);
|
|
}
|
|
};
|
|
|
|
|
|
/*@}*/
|
|
|
|
} // end namespace
|
|
#endif
|