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Commit 3288e972 authored by Pierre Kraemer's avatar Pierre Kraemer
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ridge lines computation

parent 9567ab6e
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Showing with 385 additions and 294 deletions
include/Algo/Geometry/feature.h
View file @ 3288e972
......@@ -36,64 +36,141 @@ namespace Algo
namespace Geometry
{
#define EMPTY 0
#define SEGMENT 1
#define BARY 2
enum
{
EMPTY,
SEGMENT,
BARY
};
//#define EMPTY 0
//#define SEGMENT 1
//#define BARY 2
typedef struct { Dart d ; float w ; } e0point ;
typedef struct { e0point p1 ; e0point p2 ; int valid ; } e0segment ;
typedef struct { e0point p1 ; e0point p2 ; unsigned char type ; } e0segment ;
typedef NoMathIONameAttribute<e0segment> ridgeSegment ;
template <typename PFP>
void featureEdgeDetection(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& featureEdge) ;
template <typename PFP>
void computeArea(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TREAL& area, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
void computeFaceGradient(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TVEC3& face_gradient, const typename PFP::TVEC3& face_normal, const typename PFP::TREAL& kmax, const typename PFP::TREAL& area, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
void computeGradient(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TVEC3& gradient, typename PFP::TVEC3& face_gradient, const typename PFP::TREAL& area, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
void computeTriangleType(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& regularMarker, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
void computeRidgeLines(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& regularMarker, const typename PFP::TVEC3& faceGradient, const typename PFP::TREAL& area, typename PFP::TVEC3& k, AttributeHandler<ridgeSegment>& ridge_segments, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
void initRidgeSegments(typename PFP::MAP& map, const typename PFP::TVEC3& position, AttributeHandler<ridgeSegment>& ridge_segments, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
void computeSingularTriangle(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& regularMarker, typename PFP::TVEC3& k, AttributeHandler<ridgeSegment>& ridge_segments, const FunctorSelect& select = allDarts, unsigned int thread = 0) ;
template <typename PFP>
std::vector<typename PFP::VEC3> occludingContoursDetection(typename PFP::MAP& map, const typename PFP::VEC3& cameraPosition, const typename PFP::TVEC3& position, const typename PFP::TVEC3& normal) ;
template <typename PFP>
typename PFP::TREAL faceArea(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position) ;
template <typename PFP>
typename PFP::VEC3 faceGradient(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position, const typename PFP::TVEC3& face_normal, const typename PFP::TREAL& kmax, const typename PFP::TREAL& area) ;
template <typename PFP>
bool triangleType(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position) ;
template <typename PFP>
bool isInSameOctant(const typename PFP::VEC3& pos1, const typename PFP::VEC3& pos2) ;
template <typename PFP>
void ridgeLines(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position, CellMarker& regularMarker, typename PFP::TVEC3& k, const typename PFP::TVEC3& faceGradient, const typename PFP::TREAL& area, AttributeHandler<ridgeSegment>& ridge_segments) ;
template <typename PFP>
typename PFP::REAL extremality(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position, typename PFP::TVEC3& k, const typename PFP::TVEC3& faceGradient, const typename PFP::TREAL& area) ;
template <typename PFP>
typename PFP::TVEC3 vertexGradient(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position, const typename PFP::TVEC3& face_gradient, const typename PFP::TREAL& area) ;
template <typename PFP>
void singularTriangle(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position, CellMarker& regularMarker, AttributeHandler<ridgeSegment>& ridge_segments) ;
void featureEdgeDetection(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
CellMarker& featureEdge) ;
template <typename PFP>
void computeFaceGradient(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
typename PFP::TVEC3& face_gradient,
const typename PFP::TVEC3& face_normal,
const typename PFP::TREAL& kmax,
const typename PFP::TREAL& area,
const FunctorSelect& select = allDarts,
unsigned int thread = 0) ;
//template <typename PFP>
//void computeVertexGradient(
// typename PFP::MAP& map,
// const typename PFP::TVEC3& position,
// typename PFP::TVEC3& gradient,
// typename PFP::TVEC3& face_gradient,
// const typename PFP::TREAL& area,
// const FunctorSelect& select = allDarts,
// unsigned int thread = 0) ;
template <typename PFP>
void computeTriangleType(
typename PFP::MAP& map,
const typename PFP::TVEC3& Kmax,
CellMarker& regularMarker,
const FunctorSelect& select = allDarts,
unsigned int thread = 0) ;
template <typename PFP>
void computeRidgeLines(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
CellMarker& regularMarker,
const typename PFP::TVEC3& faceGradient,
const typename PFP::TREAL& area,
const typename PFP::TVEC3& K,
AttributeHandler<ridgeSegment>& ridge_segments,
const FunctorSelect& select = allDarts,
unsigned int thread = 0) ;
template <typename PFP>
void initRidgeSegments(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
AttributeHandler<ridgeSegment>& ridge_segments,
const FunctorSelect& select = allDarts,
unsigned int thread = 0) ;
template <typename PFP>
void computeSingularTriangle(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
CellMarker& regularMarker,
typename PFP::TVEC3& k,
AttributeHandler<ridgeSegment>& ridge_segments,
const FunctorSelect& select = allDarts,
unsigned int thread = 0) ;
template <typename PFP>
std::vector<typename PFP::VEC3> occludingContoursDetection(
typename PFP::MAP& map,
const typename PFP::VEC3& cameraPosition,
const typename PFP::TVEC3& position,
const typename PFP::TVEC3& normal) ;
template <typename PFP>
typename PFP::VEC3 faceGradient(
typename PFP::MAP& map,
Dart d,
const typename PFP::TVEC3& position,
const typename PFP::TVEC3& face_normal,
const typename PFP::TREAL& kmax,
const typename PFP::TREAL& area) ;
template <typename PFP>
bool isTriangleRegular(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& Kmax) ;
//template <typename PFP>
//bool isInSameOctant(const typename PFP::VEC3& pos1, const typename PFP::VEC3& pos2) ;
template <typename PFP>
void ridgeLines(
typename PFP::MAP& map,
Dart d,
const typename PFP::TVEC3& position,
const typename PFP::TVEC3& K,
const typename PFP::TVEC3& faceGradient,
const typename PFP::TREAL& area,
AttributeHandler<ridgeSegment>& ridge_segments) ;
template <typename PFP>
typename PFP::REAL extremality(
typename PFP::MAP& map,
Dart d,
const typename PFP::VEC3& K,
const typename PFP::TVEC3& faceGradient,
const typename PFP::TREAL& area) ;
//template <typename PFP>
//typename PFP::TVEC3 vertexGradient(
// typename PFP::MAP& map,
// Dart d,
// const typename PFP::TVEC3& position,
// const typename PFP::TVEC3& face_gradient,
// const typename PFP::TREAL& area) ;
template <typename PFP>
void singularTriangle(
typename PFP::MAP& map,
Dart d,
const typename PFP::TVEC3& position,
CellMarker& regularMarker,
AttributeHandler<ridgeSegment>& ridge_segments) ;
template <typename PFP>
bool isEdgeInTriangle(typename PFP::MAP& map, Dart edge, Dart triangle) ;
......
include/Algo/Geometry/feature.hpp
View file @ 3288e972
......@@ -36,7 +36,10 @@ namespace Geometry
{
template <typename PFP>
void featureEdgeDetection(typename PFP::MAP& map, typename PFP::TVEC3& position, CellMarker& featureEdge)
void featureEdgeDetection(
typename PFP::MAP& map,
typename PFP::TVEC3& position,
CellMarker& featureEdge)
{
typedef typename PFP::VEC3 VEC3 ;
typedef typename PFP::REAL REAL ;
......@@ -59,76 +62,106 @@ void featureEdgeDetection(typename PFP::MAP& map, typename PFP::TVEC3& position,
}
template <typename PFP>
void computeArea(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TREAL& area, const FunctorSelect& select = allDarts, unsigned int thread = 0)
{
TraversorF<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
area[d] = faceArea<PFP>(map, d, position)[1] ;
}
template <typename PFP>
void computeFaceGradient(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TVEC3& face_gradient, const typename PFP::TVEC3& face_normal, const typename PFP::TREAL& kmax, const typename PFP::TREAL& area, const FunctorSelect& select = allDarts, unsigned int thread = 0)
void computeFaceGradient(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
typename PFP::TVEC3& face_gradient,
const typename PFP::TVEC3& face_normal,
const typename PFP::TREAL& kmax,
const typename PFP::TREAL& area,
const FunctorSelect& select,
unsigned int thread)
{
TraversorF<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
face_gradient[d] = faceGradient<PFP>(map, d, position, face_normal, kmax, area) ;
}
template <typename PFP>
void computeGradient(typename PFP::MAP& map, const typename PFP::TVEC3& position, typename PFP::TVEC3& gradient, typename PFP::TVEC3& face_gradient, const typename PFP::TREAL& area, const FunctorSelect& select = allDarts, unsigned int thread = 0)
{
TraversorV<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
gradient[d] = vertexGradient<PFP>(map, d, position, face_gradient, area) ;
}
//template <typename PFP>
//void computeVertexGradient(
// typename PFP::MAP& map,
// const typename PFP::TVEC3& position,
// typename PFP::TVEC3& gradient,
// typename PFP::TVEC3& face_gradient,
// const typename PFP::TREAL& area,
// const FunctorSelect& select,
// unsigned int thread)
//{
// TraversorV<typename PFP::MAP> trav(map, select, thread);
// for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
// gradient[d] = vertexGradient<PFP>(map, d, position, face_gradient, area) ;
//}
template <typename PFP>
void computeTriangleType(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& regularMarker, const FunctorSelect& select = allDarts, unsigned int thread = 0)
void computeTriangleType(
typename PFP::MAP& map,
const typename PFP::TVEC3& Kmax,
CellMarker& regularMarker,
const FunctorSelect& select,
unsigned int thread)
{
TraversorF<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
if(triangleType<PFP>(map, d, position))
if(isTriangleRegular<PFP>(map, d, Kmax))
regularMarker.mark(d) ;
}
template <typename PFP>
void computeRidgeLines(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& regularMarker, const typename PFP::TVEC3& faceGradient, const typename PFP::TREAL& area, typename PFP::TVEC3& k, AttributeHandler<ridgeSegment>& ridge_segments, const FunctorSelect& select = allDarts, unsigned int thread = 0)
void computeRidgeLines(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
CellMarker& regularMarker,
const typename PFP::TVEC3& faceGradient,
const typename PFP::TREAL& area,
const typename PFP::TVEC3& K,
AttributeHandler<ridgeSegment>& ridge_segments,
const FunctorSelect& select,
unsigned int thread)
{
TraversorF<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
{
if (regularMarker.isMarked(d))
{
ridgeLines<PFP>(map, d, position, regularMarker, k, faceGradient, area, ridge_segments) ;
}
ridgeLines<PFP>(map, d, position, K, faceGradient, area, ridge_segments) ;
}
}
template <typename PFP>
void initRidgeSegments(typename PFP::MAP& map, const typename PFP::TVEC3& position, AttributeHandler<ridgeSegment>& ridge_segments, const FunctorSelect& select = allDarts, unsigned int thread = 0)
void initRidgeSegments(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
AttributeHandler<ridgeSegment>& ridge_segments,
const FunctorSelect& select,
unsigned int thread)
{
TraversorF<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
{
ridge_segments[d].valid = EMPTY ;
}
ridge_segments[d].type = EMPTY ;
}
template <typename PFP>
void computeSingularTriangle(typename PFP::MAP& map, const typename PFP::TVEC3& position, CellMarker& regularMarker, AttributeHandler<ridgeSegment>& ridge_segments, const FunctorSelect& select = allDarts, unsigned int thread = 0)
void computeSingularTriangle(
typename PFP::MAP& map,
const typename PFP::TVEC3& position,
CellMarker& regularMarker,
AttributeHandler<ridgeSegment>& ridge_segments,
const FunctorSelect& select = allDarts,
unsigned int thread = 0)
{
TraversorF<typename PFP::MAP> trav(map, select, thread);
for (Dart d = trav.begin(); d != trav.end(); d = trav.next())
{
if (! regularMarker.isMarked(d))
{
singularTriangle<PFP>(map, d, position, regularMarker, ridge_segments) ;
}
}
}
template <typename PFP>
std::vector<typename PFP::VEC3> occludingContoursDetection(typename PFP::MAP& map, const typename PFP::VEC3& cameraPosition, const typename PFP::TVEC3& position, const typename PFP::TVEC3& normal)
std::vector<typename PFP::VEC3> occludingContoursDetection(
typename PFP::MAP& map,
const typename PFP::VEC3& cameraPosition,
const typename PFP::TVEC3& position,
const typename PFP::TVEC3& normal)
{
typedef typename PFP::VEC3 VEC3 ;
typedef typename PFP::REAL REAL ;
......@@ -182,250 +215,223 @@ std::vector<typename PFP::VEC3> occludingContoursDetection(typename PFP::MAP& ma
}
template <typename PFP>
float faceArea(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position)
typename PFP::VEC3 faceGradient(
typename PFP::MAP& map,
Dart d,
const typename PFP::TVEC3& position,
const typename PFP::TVEC3& face_normal,
const typename PFP::TREAL& kmax,
const typename PFP::TREAL& area)
{
typedef typename PFP::REAL REAL ;
typedef typename PFP::VEC3 VEC3 ;
float A [1] ;
VEC3 pos1(0) ;
VEC3 pos2(0) ;
VEC3 pos3(0) ;
Traversor2FV<typename PFP::MAP> t(map, d) ;
Dart it = t.begin() ;
pos1 += position[it] ;
it = t.next ;
pos2 += position[it] ;
it = t.next ;
pos3 += position[it] ;
A = 1/2 * abs(
( (pos2.x - pos1.x) * (pos3.y - pos1.y) )
-
( (pos3.x - pos1.x) * (pos2.y - pos1.y) )
) ;
return A ;
}
template <typename PFP>
typename PFP::VEC3 faceGradient(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position, const typename PFP::TVEC3& face_normal, const typename PFP::TREAL& kmax, const typename PFP::TREAL& area)
{
typedef typename PFP::REAL REAL ;
typedef typename PFP::VEC3 VEC3 ;
VEC3 G(0) ;
VEC3 pos1(0) ;
VEC3 pos2(0) ;
VEC3 pos3(0) ;
VEC3 n = face_normal[d] ;
REAL k1 ;
REAL k2 ;
REAL k3 ;
REAL a = area[d] ;
Traversor2FV<typename PFP::MAP> t(map, d) ;
Dart it = t.begin() ;
VEC3 pos1 = position[it] ;
REAL k1 = kmax[it] ;
pos1 += position[it] ;
k1 = kmax[it] ;
it = t.next() ;
pos2 += position[it] ;
k2 = kmax[it] ;
VEC3 pos2 = position[it] ;
REAL k2 = kmax[it] ;
it = t.next() ;
pos3 += position[it] ;
k3 = kmax[it] ;
VEC3 pos3 = position[it] ;
REAL k3 = kmax[it] ;
G += k1 * ( ( n ^ ( pos3 - pos2 ) ) / ( 2 * a ) ) +
k2 * ( ( n ^ ( pos1 - pos3 ) ) / ( 2 * a ) ) +
k3 * ( ( n ^ ( pos2 - pos1 ) ) / ( 2 * a ) ) ;
VEC3 n = face_normal[d] ;
REAL a = area[d] ;
VEC3 G = k1 * ( ( n ^ ( pos3 - pos2 ) ) / ( 2 * a ) ) +
k2 * ( ( n ^ ( pos1 - pos3 ) ) / ( 2 * a ) ) +
k3 * ( ( n ^ ( pos2 - pos1 ) ) / ( 2 * a ) ) ;
G.normalize() ;
return G ;
}
template <typename PFP>
bool triangleType(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& position)
bool mutuallyPositive(typename PFP::VEC3& v1, typename PFP::VEC3& v2, typename PFP::VEC3& v3)
{
typedef typename PFP::REAL REAL ;
typedef typename PFP::VEC3 VEC3 ;
VEC3 pos1(0) ;
VEC3 pos2(0) ;
VEC3 pos3(0) ;
Traversor2FV<typename PFP::MAP> t(map, d) ;
Dart it = t.begin() ;
pos1 += position[it] ;
it = t.next() ;
pos2 += position[it] ;
it = t.next() ;
pos3 += position[it] ;
if ( isInSameOctant<PFP>(pos1,pos2) && isInSameOctant<PFP>(pos1,pos3) )
{
//regular triangle
typename PFP::REAL v1v2 = v1 * v2 ;
typename PFP::REAL v1v3 = v1 * v3 ;
typename PFP::REAL v2v3 = v2 * v3 ;
if(v1v2 > 0 && v1v3 > 0 && v2v3 > 0)
return true ;
}
else
{
//singular triangle
return false ;
}
return false ;
}
template <typename PFP>
bool isInSameOctant(const typename PFP::VEC3& pos1, const typename PFP::VEC3& pos2)
bool isTriangleRegular(typename PFP::MAP& map, Dart d, const typename PFP::TVEC3& Kmax)
{
return ( ( pos1[0] > 0 && pos1[1] > 0 && pos1[2] > 0 && //one of the eight octant
( ( pos2[0] > 0 && pos2[1] > 0 && pos2[2] > 0 ) or //one choice of sign
( pos2[0] < 0 && pos2[1] < 0 && pos2[2] < 0 ) ) ) or //the other choice
( pos1[0] > 0 && pos1[1] > 0 && pos1[2] < 0 &&
( ( pos2[0] > 0 && pos2[1] > 0 && pos2[2] < 0 ) or
( pos2[0] < 0 && pos2[1] < 0 && pos2[2] > 0 ) ) ) or
( pos1[0] > 0 && pos1[1] < 0 && pos1[2] > 0 &&
( ( pos2[0] > 0 && pos2[1] < 0 && pos2[2] > 0 ) or
( pos2[0] < 0 && pos2[1] > 0 && pos2[2] < 0 ) ) ) or
typedef typename PFP::REAL REAL ;
typedef typename PFP::VEC3 VEC3 ;
( pos1[0] > 0 && pos1[1] < 0 && pos1[2] < 0 &&
( ( pos2[0] > 0 && pos2[1] < 0 && pos2[2] < 0 ) or
( pos2[0] < 0 && pos2[1] > 0 && pos2[2] > 0 ) ) ) or
Dart v1 = d ;
Dart v2 = map.phi1(v1) ;
Dart v3 = map.phi1(v2) ;
( pos1[0] < 0 && pos1[1] > 0 && pos1[2] > 0 &&
( ( pos2[0] < 0 && pos2[1] > 0 && pos2[2] > 0 ) or
( pos2[0] > 0 && pos2[1] < 0 && pos2[2] < 0 ) ) ) or
VEC3 K1 = Kmax[v1] ;
VEC3 K2 = Kmax[v2] ;
VEC3 K3 = Kmax[v3] ;
( pos1[0] < 0 && pos1[1] > 0 && pos1[2] < 0 &&
( ( pos2[0] < 0 && pos2[1] > 0 && pos2[2] < 0 ) or
( pos2[0] > 0 && pos2[1] < 0 && pos2[2] > 0 ) ) ) or
// VEC3 K1n = typename VEC3::DATA_TYPE(-1) * K1 ;
VEC3 K2n = typename VEC3::DATA_TYPE(-1) * K2 ;
VEC3 K3n = typename VEC3::DATA_TYPE(-1) * K3 ;
( pos1[0] < 0 && pos1[1] < 0 && pos1[2] > 0 &&
( ( pos2[0] < 0 && pos2[1] < 0 && pos2[2] > 0 ) or
( pos2[0] > 0 && pos2[1] > 0 && pos2[2] < 0 ) ) ) or
if(mutuallyPositive<PFP>(K1, K2, K3))
return true ;
if(mutuallyPositive<PFP>(K1, K2, K3n))
return true ;
if(mutuallyPositive<PFP>(K1, K2n, K3))
return true ;
if(mutuallyPositive<PFP>(K1, K2n, K3n))
return true ;
( pos1[0] < 0 && pos1[1] < 0 && pos1[2] < 0 &&
( ( pos2[0] < 0 && pos2[1] < 0 && pos2[2] < 0 ) or
( pos2[0] > 0 && pos2[1] > 0 && pos2[2] > 0 ) ) ) ) ;
// if(mutuallyPositive<PFP>(K1n, K2, K3))
// return true ;
// if(mutuallyPositive<PFP>(K1n, K2, K3n))
// return true ;
// if(mutuallyPositive<PFP>(K1n, K2n, K3))
// return true ;
// if(mutuallyPositive<PFP>(K1n, K2n, K3n))
// return true ;
return false ;
// if ( isInSameOctant<PFP>(K1, K2) && isInSameOctant<PFP>(K1, K3) )
// {
// //regular triangle
// return true ;
// }
// else
// {
// //singular triangle
// return false ;
// }
}
//template <typename PFP>
//bool isInSameOctant(const typename PFP::VEC3& pos1, const typename PFP::VEC3& pos2)
//{
// return ( ( pos1[0] > 0 && pos1[1] > 0 && pos1[2] > 0 && //one of the eight octant
// ( ( pos2[0] > 0 && pos2[1] > 0 && pos2[2] > 0 ) or //one choice of sign
// ( pos2[0] < 0 && pos2[1] < 0 && pos2[2] < 0 ) ) ) or //the other choice
//
// ( pos1[0] > 0 && pos1[1] > 0 && pos1[2] < 0 &&
// ( ( pos2[0] > 0 && pos2[1] > 0 && pos2[2] < 0 ) or
// ( pos2[0] < 0 && pos2[1] < 0 && pos2[2] > 0 ) ) ) or
//
// ( pos1[0] > 0 && pos1[1] < 0 && pos1[2] > 0 &&
// ( ( pos2[0] > 0 && pos2[1] < 0 && pos2[2] > 0 ) or
// ( pos2[0] < 0 && pos2[1] > 0 && pos2[2] < 0 ) ) ) or
//
// ( pos1[0] > 0 && pos1[1] < 0 && pos1[2] < 0 &&
// ( ( pos2[0] > 0 && pos2[1] < 0 && pos2[2] < 0 ) or
// ( pos2[0] < 0 && pos2[1] > 0 && pos2[2] > 0 ) ) ) or
//