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Hi,
 
I'm using Delaunay_triangulation_3 to triangulate points on the surface of a unit sphere. Everything is working as it should, however when I feed this class vectors of unit length (that is, points on the surface) without "perturbing" them slightly (making them randomly slightly longer/shorter), I get CGAL precondition errors.
 
Apparently, it's this one:
 
template < class Gt, class Tds >
Oriented_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_oriented_sphere(const Point &p0, const Point &p1, const Point &p2,
const Point &p3, const Point &p, bool perturb) const
{
CGAL_triangulation_precondition( orientation(p0, p1, p2, p3) == POSITIVE );
 
[...]
}
 
I've looked in the documentation, and I found this:
 
"returns POSITIVE, if s lies on the positive side of the oriented plane h defined by p, q, and r, returns NEGATIVE if s lies on the negative side of h, and returns COPLANAR if s lies on h."
 
I don't know why exactly this is used however. Can some on explain this to me?
 
I guess I'm getting this error because my input is degenerate? Is there any way to fix this?
 
I'm using the following data structures:
 
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Filtered_kernel.h>
typedef CGAL::Filtered_kernel<CGAL::Simple_cartesian<float>> KernelFloat;
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel KernelDouble;
typedef KernelFloat KernelActive;
 
#include <CGAL/Delaunay_triangulation_3.h>
#include <CGAL/Triangulation_hierarchy_3.h>
typedef CGAL::Triangulation_vertex_base_3<KernelActive> TVB;
typedef CGAL::Triangulation_hierarchy_vertex_base_3<TVB> THVB;
typedef CGAL::Triangulation_data_structure_3<THVB> TDS;
typedef CGAL::Delaunay_triangulation_3<KernelActive, TDS> DT;
typedef CGAL::Triangulation_hierarchy_3<DT> CGAL_Triangulation;
typedef CGAL_Triangulation::Point CGAL_Point;
typedef CGAL_Triangulation::Vertex_handle CGAL_VertexHandle;
typedef CGAL_Triangulation::Finite_vertices_iterator CGAL_FiniteVerticesIter;
typedef CGAL_Triangulation::Cell_handle CGAL_CellHandle;
 
And my triangulation code:
 
std::vector<CGAL_Point> pointsOnSphere;
Vector3 pointOnUnitSphere;
for(int n = 1; n < 61; ++n)
{
    pointOnUnitSphere = MathUtil::getPositionOnUnitSphere_Halton(n) /*hack: * Math::RangeRandom(1, 1.0001)*/;
    CGAL_Point newPoint(pointOnUnitSphere.x, pointOnUnitSphere.y, pointOnUnitSphere.z);
    pointsOnSphere.push_back(newPoint);
}
 
triangulation.insert(pointsOnSphere.begin(), pointsOnSphere.end());
 
 
Thank you,
 
Peter.

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