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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. *
* *
****************************************************************************/
#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 = std::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 = std::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.dot(p1);
ScalarType delta1_p01 = -p10.dot(p0);
ScalarType delta0_p02 = p20.dot(p2);
ScalarType delta2_p02 = -p20.dot(p0);
ScalarType delta1_p12 = p21.dot(p2);
ScalarType delta2_p12 = -p21.dot(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.dot(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.dot(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 = std::max< ScalarType >( witness_norm-radius, ScalarType(0.0) );
res->second = std::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().dot(li.Direction()); // Compute 'k' factor
if( (k > -epsilon) && (k < epsilon))
return false;
T r = (pl.Offset() - pl.Direction().dot(li.Origin()))/k; // Compute ray distance
po = li.Origin() + li.Direction()*r;
return true;
}
/// intersection between segment and plane
template<class T>
inline bool IntersectionPlaneSegment( const Plane3<T> & pl, const Segment3<T> & s, Point3<T> & p0){
T p1_proj = s.P1()*pl.Direction()-pl.Offset();
T p0_proj = s.P0()*pl.Direction()-pl.Offset();
if ( (p1_proj>0)-(p0_proj<0)) return false;
if(p0_proj == p1_proj) return false;
// check that we perform the computation in a way that is independent with v0 v1 swaps
if(p0_proj < p1_proj)
p0 = s.P0() + (s.P1()-s.P0()) * fabs(p0_proj/(p1_proj-p0_proj));
if(p0_proj > p1_proj)
p0 = s.P1() + (s.P0()-s.P1()) * fabs(p1_proj/(p0_proj-p1_proj));
return true;
}
/// intersection between segment and plane
template<class ScalarType>
inline bool IntersectionPlaneSegmentEpsilon(const Plane3<ScalarType> & pl,
const Segment3<ScalarType> & sg,
Point3<ScalarType> & po,
const ScalarType epsilon = ScalarType(1e-8)){
typedef ScalarType T;
T k = pl.Direction().dot((sg.P1()-sg.P0()));
if( (k > -epsilon) && (k < epsilon))
return false;
T r = (pl.Offset() - pl.Direction().dot(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(IntersectionPlaneSegment(pl,Segment3<T>(tr.P(0),tr.P(1)),sg.P0())){
if(IntersectionPlaneSegment(pl,Segment3<T>(tr.P(0),tr.P(2)),sg.P1()))
return true;
else
{
IntersectionPlaneSegment(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P1());
return true;
}
}
else
{
if(IntersectionPlaneSegment(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P0()))
{
IntersectionPlaneSegment(pl,Segment3<T>(tr.P(0),tr.P(2)),sg.P1());
return true;
}
}
return false;
}
/// intersection between two triangles
template<typename TRIANGLETYPE>
inline bool IntersectionTriangleTriangle(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 IntersectionTriangleTriangle(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);
}
#if 0
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()
);
}
#endif
/*
* Function computing the intersection between a line and a triangle.
* from:
* Tomas Moller and Ben Trumbore,
* ``Fast, Minimum Storage Ray-Triangle Intersection'',
* journal of graphics tools, vol. 2, no. 1, pp. 21-28, 1997
* @param[in] line
* @param[in] triangle vertices
* @param[out]=(t,u,v) the intersection point, meaningful only if the line intersects the triangle
* t is the line parameter and
* (u,v) are the baricentric coords of the intersection point
*
* Line.Orig + t * Line.Dir = (1-u-v) * Vert0 + u * Vert1 +v * Vert2
*
*/
template<class T>
bool IntersectionLineTriangle( const Line3<T> & line, const Point3<T> & vert0,
const Point3<T> & vert1, const Point3<T> & vert2,
T & t ,T & u, T & v)
{
#define EPSIL 0.000001
vcg::Point3<T> edge1, edge2, tvec, pvec, qvec;
T det,inv_det;
/* find vectors for two edges sharing vert0 */
edge1 = vert1 - vert0;
edge2 = vert2 - vert0;
/* begin calculating determinant - also used to calculate U parameter */
pvec = line.Direction() ^ edge2;
/* if determinant is near zero, line lies in plane of triangle */
det = edge1 * pvec;
/* calculate distance from vert0 to line origin */
tvec = line.Origin() - vert0;
inv_det = 1.0 / det;
qvec = tvec ^ edge1;
if (det > EPSIL)
{
u = tvec * pvec ;
if ( u < 0.0 || u > det)
return 0;
/* calculate V parameter and test bounds */
v = line.Direction() * qvec;
if ( v < 0.0 || u + v > det)
return 0;
}
else if(det < -EPSIL)
{
/* calculate U parameter and test bounds */
u = tvec * pvec ;
if ( u > 0.0 || u < det)
return 0;
/* calculate V parameter and test bounds */
v = line.Direction() * qvec ;
if ( v > 0.0 || u + v < det)
return 0;
}
else return 0; /* line is parallell to the plane of the triangle */
t = edge2 * qvec * inv_det;
( u) *= inv_det;
( v) *= inv_det;
return 1;
}
template<class T>
bool IntersectionRayTriangle( const Ray3<T> & ray, const Point3<T> & vert0,
const Point3<T> & vert1, const Point3<T> & vert2,
T & t ,T & u, T & v)
{
Line3<T> line(ray.Origin(), ray.Direction());
if (IntersectionLineTriangle(line, vert0, vert1, vert2, t, u, v))
{
if (t < 0) return 0;
else return 1;
}else return 0;
}
// line-box
template<class T>
bool IntersectionLineBox( 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 IntersectionRayBox( const Box3<T> & box, const Ray3<T> & r, Point3<T> & coord )
{
Line3<T> l;
l.SetOrigin(r.Origin());
l.SetDirection(r.Direction());
return(IntersectionLineBox<T>(box,l,coord));
}
// segment-box return fist intersection found from p0 to p1
template<class ScalarType>
bool IntersectionSegmentBox( 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(IntersectionLineBox<ScalarType>(box,l,coord))
return (test.IsIn(coord));
return false;
}
}
// segment-box intersection , return number of intersections and intersection points
template<class ScalarType>
int IntersectionSegmentBox( const Box3<ScalarType> & box,
const Segment3<ScalarType> & s,
Point3<ScalarType> & coord0,
Point3<ScalarType> & coord1 )
{
int num=0;
Segment3<ScalarType> test= s;
if (IntersectionSegmentBox(box,test,coord0 ))
{
num++;
Point3<ScalarType> swap=test.P0();
test.P0()=test.P1();
test.P1()=swap;
if (IntersectionSegmentBox(box,test,coord1 ))
num++;
}
return num;
}
/**
* Compute the intersection between a segment and a triangle.
* It relies on the lineTriangle Intersection
* @param[in] segment
* @param[in] triangle vertices
* @param[out]=(t,u,v) the intersection point, meaningful only if the line of segment intersects the triangle
* t is the baricentric coord of the point on the segment
* (u,v) are the baricentric coords of the intersection point in the segment
*
*/
template<class ScalarType>
bool IntersectionSegmentTriangle( const vcg::Segment3<ScalarType> & seg,
const Point3<ScalarType> & vert0,
const Point3<ScalarType> & vert1, const
Point3<ScalarType> & vert2,
ScalarType & a ,ScalarType & b)
{
//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::IntersectionSegmentBox(bb1,seg,inter))
return false;
//first set both directions of ray
vcg::Line3<ScalarType> line;
vcg::Point3<ScalarType> dir;
ScalarType lenght=seg.Length();
dir=(seg.P1()-seg.P0());
dir.Normalize();
line.Set(seg.P0(),dir);
ScalarType orig_dist;
if(IntersectionLineTriangle<ScalarType>(line,vert0,vert1,vert2,orig_dist,a,b))
return (orig_dist<=lenght);
return false;
}
/**
* Compute the intersection between a segment and a triangle.
* Wrapper of the above function
*/
template<class TriangleType>
bool IntersectionSegmentTriangle( const vcg::Segment3<typename TriangleType::ScalarType> & seg,
const TriangleType &t,
typename TriangleType::ScalarType & a ,typename TriangleType::ScalarType & b)
{
return IntersectionSegmentTriangle(seg,t.P(0),t.P(1),t.P(2),a,b);
}
template<class ScalarType>
bool IntersectionPlaneBox(const vcg::Plane3<ScalarType> &pl,
vcg::Box3<ScalarType> &bbox)
{
ScalarType dist,dist1;
if(bbox.IsNull()) return false; // intersection with a null bbox is empty
dist = Distance(pl,bbox.P(0)) ;
for (int i=1;i<8;i++) if( Distance(pl,bbox.P(i))*dist<0) return true;
return true;
}
template<class ScalarType>
bool IntersectionTriangleBox(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 (!IntersectionPlaneBox<ScalarType>(plTri,bbox))
// return false;
///then control intersection of segments with box
if (IntersectionSegmentBox<ScalarType>(bbox,vcg::Segment3<ScalarType>(p0,p1),intersection)||
IntersectionSegmentBox<ScalarType>(bbox,vcg::Segment3<ScalarType>(p1,p2),intersection)||
IntersectionSegmentBox<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 (IntersectionSegmentTriangle<ScalarType>(diag[i],p0,p1,p2,a,b,dist))
return true;
return false;
}
template <class SphereType>
bool IntersectionSphereSphere( 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 u;
ScalarType v;
bool bret = IntersectionRayTriangle(ray, Point3<SCALARTYPE>::Construct(f.P(0)), Point3<SCALARTYPE>::Construct(f.P(1)), Point3<SCALARTYPE>::Construct(f.P(2)), t, u, v);
if (BACKFACETEST) {
if (!bret) {
bret = IntersectionRayTriangle(ray, Point3<SCALARTYPE>::Construct(f.P(0)), Point3<SCALARTYPE>::Construct(f.P(2)), Point3<SCALARTYPE>::Construct(f.P(1)), t, u, v);
}
}
return (bret);
}
};
/*@}*/
} // end namespace
#endif
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