bool interLineSeg(const VEC3& A, const VEC3& AB, typename VEC3::DATA_TYPE AB2,
const VEC3& P, const VEC3& Q, VEC3& inter)
{
#define EPSILON (1.0e-5)
typedef typename VEC3::DATA_TYPE T ;
T dist = Geom::distancePoint2TrianglePlane(AB-A,A,P,Q);
// std::cout << "dist "<< dist << std::endl;
if (dist>EPSILON)
return false;
VEC3 AP = P - A ;
VEC3 PQ = Q - P ;
T X = AB * PQ ;
T beta = ( AB2 * (AP*PQ) - X * (AP*AB) ) / ( X*X - AB2 * PQ.norm2() ) ;
// std::cout << "beta "<< beta << std::endl;
if ((beta<0.0) || (beta>1.0))
return false;
inter = beta*Q +(1.0-beta)*P;
return true;
#undef EPSILON
}
Intersection intersectionLineTriangle(const VEC3& P, const VEC3& Dir, const VEC3& Ta, const VEC3& Tb, const VEC3& Tc, VEC3& Inter)
{
typedef typename VEC3::DATA_TYPE T ;
VEC3 u = Tb - Ta ;
VEC3 v = Tc - Ta ;
VEC3 n = u ^ v ;
VEC3 w0 = P - Ta ;
T a = -(n * w0) ;
T b = (n * Dir) ;
#define PRECISION 1e-20
if(fabs(b) < PRECISION) //ray parallel to triangle
return NO_INTERSECTION ;
#undef PRECISION
T r = a / b ;
Inter = P + r * Dir ; // intersect point of ray and plane
// is I inside T?
T uu = u.norm2() ;
T uv = u * v ;
T vv = v.norm2() ;
VEC3 w = Inter - Ta ;
T wu = w * u ;
T wv = w * v ;
T D = (uv * uv) - (uu * vv) ;
// get and test parametric coords
T s = ((uv * wv) - (vv * wu)) / D ;
if(s < T(0) || s > T(1))
return NO_INTERSECTION ;
T t = ((uv * wu) - (uu * wv)) / D ;
if(t < T(0) || (s + t) > T(1))
return NO_INTERSECTION ;
if((s == T(0) || s == T(1)))
if(t == T(0) || t == T(1))
return VERTEX_INTERSECTION ;
else
return EDGE_INTERSECTION ;
else if(t == T(0) || t == T(1))
return EDGE_INTERSECTION ;
return FACE_INTERSECTION ;
}
bool intersectionSphereEdge(typename PFP::MAP& map, const typename PFP::VEC3& center, typename PFP::REAL radius, Edge e, const VertexAttribute<typename PFP::VEC3, typename PFP::MAP>& position, typename PFP::REAL& alpha)
{
typedef typename PFP::VEC3 VEC3 ;
typedef typename PFP::REAL REAL ;
const VEC3& p1 = position[e.dart];
const VEC3& p2 = position[map.phi1(e.dart)];
if(Geom::isPointInSphere(p1, center, radius) && !Geom::isPointInSphere(p2, center, radius))
{
VEC3 p = p1 - center;
VEC3 qminusp = p2 - center - p;
REAL s = p * qminusp;
REAL n2 = qminusp.norm2();
alpha = (- s + sqrt(s*s + n2 * (radius*radius - p.norm2()))) / n2;
return true ;
}
return false ;
}
Intersection intersectionSegmentTriangle(const VEC3& PA, const VEC3& PB, const VEC3& Ta, const VEC3& Tb, const VEC3& Tc, VEC3& Inter)
{
typedef typename VEC3::DATA_TYPE T ;
const T precision = 0.0001;//std::numeric_limits<T>::min();
VEC3 u = Tb - Ta ;
VEC3 v = Tc - Ta ;
VEC3 Dir = PB - PA ;
VEC3 n = u ^ v ;
VEC3 w0 = PA - Ta ;
float a = -(n * w0) ;
float b = (n * Dir) ;
if(fabs(b) < precision) //ray parallel to triangle
return NO_INTERSECTION ;
//compute intersection
T r = a / b ;
if((r < -precision) || (r > (T(1) + precision)))
return NO_INTERSECTION;
Inter = PA + r * Dir; // intersect point of ray and plane
// is I inside T?
T uu = u.norm2() ;
T uv = u * v ;
T vv = v.norm2() ;
VEC3 w = Inter - Ta ;
T wu = w * u ;
T wv = w * v ;
T D = (uv * uv) - (uu * vv) ;
// get and test parametric coords
T s = ((uv * wv) - (vv * wu)) / D ;
if(s <= precision)
s = 0.0f;
if(s < T(0) || s > T(1))
return NO_INTERSECTION ;
T t = ((uv * wu) - (uu * wv)) / D ;
if(t <= precision)
t = 0.0f;
if(t < T(0) || (s + t) > T(1))
return NO_INTERSECTION ;
if((s == T(0) || s == T(1)))
if(t == T(0) || t == T(1))
return VERTEX_INTERSECTION ;
else
return EDGE_INTERSECTION ;
else if(t == T(0) || t == T(1))
return EDGE_INTERSECTION ;
return FACE_INTERSECTION ;
}