delaunaySubdivision -- the Delaunay subdivision of a point set

The Delaunay subdivision of a finite point set $P \subset \mathbb{R}^d$ is the polyhedral subdivision of the convex hull of $P$ characterized by the empty-sphere property: a $d$-simplex with vertices in $P$ is a maximal cell iff the open ball circumscribed about it contains no point of $P$ in its interior. Equivalently, it is the projection of the lower faces of the lifted paraboloid -- the convex hull of the points $(v_i, \|v_i\|^2) \in \mathbb{R}^{d+1}$. When the points are in general position (no $d{+}2$ of them cospherical), the Delaunay subdivision is a triangulation; otherwise some cells may be non-simplicial. It is dual to the Voronoi diagram of $P$ and is widely used in computational geometry, mesh generation, and interpolation.

This function realises the lifted-paraboloid construction by calling regularSubdivision with the squared norms produced by delaunayWeights: lifting heights to $\|v_i\|^2$, taking the lower envelope, and projecting back.

Like delaunayWeights, this function is meaningful only for point configurations, not vector configurations.