/****************************************************************************
* 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. *
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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 *
* 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 1.33 2007/06/07 15:16:39 fiorin
Added IntersectionSphereTriangle
Revision 1.32 2007/05/29 14:33:29 fiorin
Added IntersectionSegmentSphere
Revision 1.31 2007/04/16 09:08:15 cignoni
commented out non compiling intersectionSpherePlane
Revision 1.30 2007/04/10 22:26:47 pietroni
IntersectionPlanePlane first parameter is a const
Revision 1.29 2007/04/04 23:19:40 pietroni
- Changed name of intersection function between plane and triangle from Intersection to IntersectionPlaneTriangle.
- Added Intersection_Plane_Sphere function.
Revision 1.28 2007/02/21 02:40:52 m_di_benedetto
Added const qualifier to bbox parameter in Intersection_Triangle_Box().
Revision 1.27 2006/10/25 16:04:32 pietroni
added intersection control between bounding boxes for intersection between segment and triangle function
Revision 1.26 2006/09/14 08:39:07 ganovelli
Intersection_sphere_sphere added
Revision 1.25 2006/06/06 14:35:31 zifnab1974
Changes for compilation on linux AMD64. Some remarks: Linux filenames are case-sensitive. _fileno and _filelength do not exist on linux
Revision 1.24 2006/06/01 08:38:02 pietroni
Added functions:
- Intersection_Segment_Triangle
- Intersection_Plane_Box
- Intersection_Triangle_Box
Revision 1.23 2006/03/29 07:53:36 cignoni
Missing ';' (thx Maarten)
Revision 1.22 2006/03/20 14:42:49 pietroni
IntersectionSegmentPlane and Intersection_Segment_Box functions Added
Revision 1.21 2006/01/20 16:35:51 pietroni
added Intersection_Segment_Box function
Revision 1.20 2005/10/03 16:07:50 ponchio
Changed order of functions intersection_line_box and
intersectuion_ray_box
Revision 1.19 2005/09/30 13:11:39 pietroni
corrected 1 compiling error on Ray_Box_Intersection function
Revision 1.18 2005/09/29 15:30:10 pietroni
Added function RayBoxIntersection, renamed intersection line box from "Intersection" to "Intersection_Line_Box"
Revision 1.17 2005/09/29 11:48:00 m_di_benedetto
Added functor RayTriangleIntersectionFunctor.
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/math/base.h>
#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;
}
/*
* Function computing the intersection between a sphere and a segment.
* @param[in] sphere the sphere
* @param[in] segment the segment
* @param[out] intersection the intersection point, meaningful only if the segment intersects the sphere
* \return (0, 1 or 2) the number of intersections between the segment and the sphere.
* t1 is a valid intersection only if the returned value is at least 1;
* similarly t2 is valid iff the returned value is 2.
*/
template < class SCALAR_TYPE >
inline int IntersectionSegmentSphere(const Sphere3<SCALAR_TYPE>& sphere, const Segment3<SCALAR_TYPE>& segment, Point3<SCALAR_TYPE> & t0, Point3<SCALAR_TYPE> & t1)
{
typedef SCALAR_TYPE ScalarType;
typedef typename vcg::Point3< ScalarType > Point3t;
Point3t s = segment.P0() - sphere.Center();
Point3t r = segment.P1() - segment.P0();
ScalarType rho2 = sphere.Radius()*sphere.Radius();
ScalarType sr = s*r;
ScalarType r_squared_norm = r.SquaredNorm();
ScalarType s_squared_norm = s.SquaredNorm();
ScalarType sigma = sr*sr - r_squared_norm*(s_squared_norm-rho2);
if (sigma<ScalarType(0.0)) // the line containing the edge doesn't intersect the sphere
return 0;
ScalarType sqrt_sigma = ScalarType(sqrt( ScalarType(sigma) ));
ScalarType lambda1 = (-sr - sqrt_sigma)/r_squared_norm;
ScalarType lambda2 = (-sr + sqrt_sigma)/r_squared_norm;
int solution_count = 0;
if (ScalarType(0.0)<=lambda1 && lambda1<=ScalarType(1.0))
{
ScalarType t_enter = vcg::math::Max< ScalarType >(lambda1, ScalarType(0.0));
t0 = segment.P0() + r*t_enter;
solution_count++;
}
if (ScalarType(0.0)<=lambda2 && lambda2<=ScalarType(1.0))
{
Point3t *pt = (solution_count>0) ? &t1 : &t0;
ScalarType t_exit = vcg::math::Min< ScalarType >(lambda2, ScalarType(1.0));
*pt = segment.P0() + r*t_exit;
solution_count++;
}
return solution_count;
}; // end of IntersectionSegmentSphere
/*!
* Compute the intersection between a sphere and a triangle.
* \param[in] sphere the input sphere
* \param[in] triangle the input triangle
* \param[out] witness it is the point on the triangle nearest to the center of the sphere (even when there isn't intersection)
* \param[out] res if not null, in the first item is stored the minimum distance between the triangle and the sphere,
* while in the second item is stored the penetration depth
* \return true iff there is an intersection between the sphere and the triangle
*/
template < class SCALAR_TYPE, class TRIANGLETYPE >
bool IntersectionSphereTriangle(const vcg::Sphere3 < SCALAR_TYPE > & sphere ,
TRIANGLETYPE triangle,
vcg::Point3 < SCALAR_TYPE > & witness ,
std::pair< SCALAR_TYPE, SCALAR_TYPE > * res=NULL)
{
typedef SCALAR_TYPE ScalarType;
typedef typename vcg::Point3< ScalarType > Point3t;
typedef TRIANGLETYPE Triangle3t;
bool penetration_detected = false;
ScalarType radius = sphere.Radius();
Point3t center = sphere.Center();
Point3t p0 = triangle.P(0)-center;
Point3t p1 = triangle.P(1)-center;
Point3t p2 = triangle.P(2)-center;
Point3t p10 = p1-p0;
Point3t p21 = p2-p1;
Point3t p20 = p2-p0;
ScalarType delta0_p01 = p10*p1;
ScalarType delta1_p01 = -p10*p0;
ScalarType delta0_p02 = p20*p2;
ScalarType delta2_p02 = -p20*p0;
ScalarType delta1_p12 = p21*p2;
ScalarType delta2_p12 = -p21*p1;
// the closest point can be one of the vertices of the triangle
if (delta1_p01<=ScalarType(0.0) && delta2_p02<=ScalarType(0.0)) { witness = p0; }
else if (delta0_p01<=ScalarType(0.0) && delta2_p12<=ScalarType(0.0)) { witness = p1; }
else if (delta0_p02<=ScalarType(0.0) && delta1_p12<=ScalarType(0.0)) { witness = p2; }
else
{
ScalarType temp = p10*p2;
ScalarType delta0_p012 = delta0_p01*delta1_p12 + delta2_p12*temp;
ScalarType delta1_p012 = delta1_p01*delta0_p02 - delta2_p02*temp;
ScalarType delta2_p012 = delta2_p02*delta0_p01 - delta1_p01*(p20*p1);
// otherwise, can be a point lying on same edge of the triangle
if (delta0_p012<=ScalarType(0.0))
{
ScalarType denominator = delta1_p12+delta2_p12;
ScalarType mu1 = delta1_p12/denominator;
ScalarType mu2 = delta2_p12/denominator;
witness = (p1*mu1 + p2*mu2);
}
else if (delta1_p012<=ScalarType(0.0))
{
ScalarType denominator = delta0_p02+delta2_p02;
ScalarType mu0 = delta0_p02/denominator;
ScalarType mu2 = delta2_p02/denominator;
witness = (p0*mu0 + p2*mu2);
}
else if (delta2_p012<=ScalarType(0.0))
{
ScalarType denominator = delta0_p01+delta1_p01;
ScalarType mu0 = delta0_p01/denominator;
ScalarType mu1 = delta1_p01/denominator;
witness = (p0*mu0 + p1*mu1);
}
else
{
// or else can be an point internal to the triangle
ScalarType denominator = delta0_p012 + delta1_p012 + delta2_p012;
ScalarType lambda0 = delta0_p012/denominator;
ScalarType lambda1 = delta1_p012/denominator;
ScalarType lambda2 = delta2_p012/denominator;
witness = p0*lambda0 + p1*lambda1 + p2*lambda2;
}
}
if (res!=NULL)
{
ScalarType witness_norm = witness.Norm();
res->first = vcg::math::Max< ScalarType >( witness_norm-radius, ScalarType(0.0) );
res->second = vcg::math::Max< ScalarType >( radius-witness_norm, ScalarType(0.0) );
}
penetration_detected = (witness.SquaredNorm() <= (radius*radius));
witness += center;
return penetration_detected;
}; //end of IntersectionSphereTriangle
/// 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<class T>
inline bool IntersectionSegmentPlane( const Plane3<T> & pl, const Segment3<T> & s, Point3<T> & po){
vcg::Line3<T> l;
l.Set(s.P0(),s.P1()-s.P0());
l.Normalize();
if (IntersectionLinePlane(pl,l,po))
return((po-s.P0()).Norm()<=(s.P0()-s.P1()).Norm());
return false;
}
/// 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 IntersectionPlaneTriangle( 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;
}
// line-box
template<class T>
bool Intersection_Line_Box( 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
}
// ray-box
template<class T>
bool Intersection_Ray_Box( const Box3<T> & box, const Ray3<T> & r, Point3<T> & coord )
{
Line3<T> l;
l.SetOrigin(r.Origin());
l.SetDirection(r.Direction());
return(Intersection_Line_Box<T>(box,l,coord));
}
// segment-box return fist intersection found from p0 to p1
template<class ScalarType>
bool Intersection_Segment_Box( const Box3<ScalarType> & box,
const Segment3<ScalarType> & s,
Point3<ScalarType> & coord )
{
//as first perform box-box intersection
Box3<ScalarType> test;
test.Add(s.P0());
test.Add(s.P1());
if (!test.Collide(box))
return false;
else
{
Line3<ScalarType> l;
Point3<ScalarType> dir=s.P1()-s.P0();
dir.Normalize();
l.SetOrigin(s.P0());
l.SetDirection(dir);
if(Intersection_Line_Box<ScalarType>(box,l,coord))
return (test.IsIn(coord));
return false;
}
}
// segment-box intersection , return number of intersections and intersection points
template<class ScalarType>
int Intersection_Segment_Box( const Box3<ScalarType> & box,
const Segment3<ScalarType> & s,
Point3<ScalarType> & coord0,
Point3<ScalarType> & coord1 )
{
int num=0;
Segment3<ScalarType> test= s;
if (Intersection_Segment_Box(box,test,coord0 ))
{
num++;
Point3<ScalarType> swap=test.P0();
test.P0()=test.P1();
test.P1()=swap;
if (Intersection_Segment_Box(box,test,coord1 ))
num++;
}
return num;
}
// segment-triangle intersection
template<class ScalarType>
bool Intersection_Segment_Triangle( const vcg::Segment3<ScalarType> & seg,
const Point3<ScalarType> & vert0,
const Point3<ScalarType> & vert1, const
Point3<ScalarType> & vert2,
ScalarType & a ,ScalarType & b, ScalarType & dist)
{
//control intersection of bounding boxes
vcg::Box3<ScalarType> bb0,bb1;
bb0.Add(seg.P0());
bb0.Add(seg.P1());
bb1.Add(vert0);
bb1.Add(vert1);
bb1.Add(vert2);
Point3<ScalarType> inter;
if (!bb0.Collide(bb1))
return false;
if (!vcg::Intersection_Segment_Box(bb1,seg,inter))
return false;
//first set both directions of ray
vcg::Ray3<ScalarType> ray;
vcg::Point3<ScalarType> dir;
dir=(seg.P1()-seg.P0());
dir.Normalize();
ray.Set(seg.P0(),dir);
//then control for each direction the intersection with triangle
if ((Intersection<ScalarType>(ray,vert0,vert1,vert2,a,b,dist))
||(Intersection<ScalarType>(ray,vert1,vert0,vert2,b,a,dist)))
return (dist<(seg.P1()-seg.P0()).Norm());
else
return(false);
}
template <class ScalarType>
bool Intersection_Plane_Box(const vcg::Plane3<ScalarType> &pl,
vcg::Box3<ScalarType> &bbox)
{
typedef typename vcg::Segment3<ScalarType> SegmentType;
typedef typename vcg::Point3<ScalarType> CoordType;
SegmentType diag[4];
CoordType intersection;
//find the 4 diagonals
diag[0]=SegmentType(bbox.P(0),bbox.P(7));
diag[1]=SegmentType(bbox.P(1),bbox.P(6));
diag[2]=SegmentType(bbox.P(2),bbox.P(5));
diag[3]=SegmentType(bbox.P(3),bbox.P(4));
ScalarType a,b,dist;
for (int i=0;i<3;i++)
//call intersection of segment and plane
if (vcg::Intersection<SegmentType>(pl,diag[i],intersection))
return true;
return false;
}
///if exists return the center and ardius of circle
///that is the intersectionk between the sphere and
//the plane
template <class ScalarType>
bool Intersection_Plane_Sphere(const Plane3<ScalarType> &pl,
const Sphere3<ScalarType> &sphere,
Point3<ScalarType> ¢er,
ScalarType &radius)
{
/* ///set the origin on the center of the sphere
vcg::Plane3<ScalarType> pl1;
vcg::Point3<ScalarType> p_plane=pl.Direction()*pl.Offset();
vcg::Point3<ScalarType> p_plane=p_plane-sphere.Center();
///set again the plane
pl1.Set(p_plane,pl.Direction());
///test d must be positive
d=pl1.Offset();
vcg::Point3<ScalarType> n=pl1.Direction();
///invert d if is <0
if (d<0)
{
n=-n;
d=-d;
}
///no intersection occour
if (d>r)
return false;
else
{
///calculate center and translate in back
center=n*d;
center+=sphere.Center();
radius=math::Sqrt((r*r)-(d*d));
}
*/
assert(0);
return true;
}
template<class ScalarType>
bool Intersection_Triangle_Box(const vcg::Box3<ScalarType> &bbox,
const vcg::Point3<ScalarType> &p0,
const vcg::Point3<ScalarType> &p1,
const vcg::Point3<ScalarType> &p2)
{
typedef typename vcg::Point3<ScalarType> CoordType;
CoordType intersection;
/// control bounding box collision
vcg::Box3<ScalarType> test;
test.SetNull();
test.Add(p0);
test.Add(p1);
test.Add(p2);
if (!test.Collide(bbox))
return false;
/// control if each point is inside the bouding box
if ((bbox.IsIn(p0))||(bbox.IsIn(p1))||(bbox.IsIn(p2)))
return true;
/////control plane of the triangle with bbox
//vcg::Plane3<ScalarType> plTri=vcg::Plane3<ScalarType>();
//plTri.Init(p0,p1,p2);
//if (!Intersection_Plane_Box<ScalarType>(plTri,bbox))
// return false;
///then control intersection of segments with box
if (Intersection_Segment_Box<ScalarType>(bbox,vcg::Segment3<ScalarType>(p0,p1),intersection)||
Intersection_Segment_Box<ScalarType>(bbox,vcg::Segment3<ScalarType>(p1,p2),intersection)||
Intersection_Segment_Box<ScalarType>(bbox,vcg::Segment3<ScalarType>(p2,p0),intersection))
return true;
///control intersection of diagonal of the cube with triangle
Segment3<ScalarType> diag[4];
diag[0]=Segment3<ScalarType>(bbox.P(0),bbox.P(7));
diag[1]=Segment3<ScalarType>(bbox.P(1),bbox.P(6));
diag[2]=Segment3<ScalarType>(bbox.P(2),bbox.P(5));
diag[3]=Segment3<ScalarType>(bbox.P(3),bbox.P(4));
ScalarType a,b,dist;
for (int i=0;i<3;i++)
if (Intersection_Segment_Triangle<ScalarType>(diag[i],p0,p1,p2,a,b,dist))
return true;
return false;
}
template <class SphereType>
bool Intersection_Sphere_Sphere( const SphereType & s0,const SphereType & s1){
return (s0.Center()-s1.Center()).SquaredNorm() < (s0.Radius()+s1.Radius())*(s0.Radius()+s1.Radius());
}
template<class T>
bool IntersectionPlanePlane (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