vcglib/vcg/space/intersection3.h

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/****************************************************************************
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* 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. *
* *
****************************************************************************/
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/****************************************************************************
History
$Log: not supported by cvs2svn $
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
2005-01-26 11:03:08 +01:00
Revision 1.12 2004/10/13 12:45:51 cignoni
Better Doxygen documentation
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Revision 1.11 2004/09/09 14:41:32 ponchio
forgotten typename SEGMENTTYPE::...
2004-09-09 16:41:32 +02:00
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
2004-07-12 00:08:04 +02:00
Revision 1.7 2004/05/14 03:14:29 ponchio
Fixed some minor bugs
2004-05-14 05:14:29 +02:00
Revision 1.6 2004/05/13 23:43:54 ponchio
minor bug
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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
2004-04-29 12:48:44 +02:00
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
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****************************************************************************/
#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>
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namespace vcg {
/** \addtogroup space */
/*@{*/
/**
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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 ){
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// 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...)
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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();
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T t15 = sp.Radius()*sp.Radius();
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T t17 = neworig.Z()*neworig.Z();
T t19 = neworig.Y()*neworig.Y();
T t21 = neworig.X()*neworig.X();
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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);
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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){
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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;
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else
{
Intersection(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P1());
return true;
}
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}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);
}
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template<typename TRIANGLETYPE,typename SEGMENTTYPE >
inline bool Intersection(const TRIANGLETYPE & t0,const TRIANGLETYPE & t1,bool &coplanar,
SEGMENTTYPE & sg){
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Point3<typename SEGMENTTYPE::PointType> ip0,ip1;
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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()
);
}
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// 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;
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inte = vert0 + edge1*a + edge2*b;
return true;
}
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// 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;
}
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/*@}*/
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} // end namespace
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#endif