I have a set of vertices $V\subset\mathbb R^3$ and a set of edges $S=\{(a,b)|a,b \in V\}$. I want to know whether an edge in the set $S$ is Delaunay against the vertices in $V$. My assumed definition of a Delaunay edge is: An edge is Delaunay, iff there exists a circumsphere of its endpoints not containing any other vertex inside it.I would like to know practical approaches/algorithms for such Delaunay-edge test.UPDATE: Answer to a question here models Delaunay-edge criteria as a linear programming feasibility problem. Concisely, it searches for a vector, scalar tuple $(v,c)$ such that for a set of vertices $P$(formed by transforming original points $(x,y,z)$ in 3D space to $(x,y,z,x^2+y^2+z^2)$ in 4D space) and endpoints of a  Delaunay edge candidate $(p_i,p_j)\in P$,$v.p_a \geq c$$v.p_b=c$where $p_a\in P-\{p_i,p_j\}$ and $p_b\in\{p_i,p_j\}$and it recommends using ellipsoid method, but Wiki section on this method describes it as numerically unstable beyond 2 dimensions. Is there any other practical yet numerically stable(in three dimensions) linear programming approach for performing Delaunay edge test?P.S.: I have already asked this question on ComputerScience SE but did not recieve any relevant response.
Practical algorithm for testing whether an edge is Delaunay
ds.algorithms;cg.comp geom;linear programming