Voronoi diagrams of algebraic distance fields

Voronoi diagrams of algebraic distance fields

We design and implement an efficient and certified algorithm for the computation of Voronöı Diagrams (VD’s) constrained to a given domain. Our framework is general and applicable to any VD-type where the distance field is given explicitly or implicitly by a polynomial, notably the anisotropic VD or VD’s of non-punctual sites. We use the Bernstein form of polynomials and DeCasteljau’s algorithm ...

Voronöı Diagrams of Algebraic Distance Fields

We design and implement an efficient and certified algorithm for the computation of Voronöı Diagrams (VD’s) constrained to a given domain. Our framework is general and applicable to any VD-type where the distance field is given explicitly or implicitly by a polynomial, notably the anisotropic VD or VD’s of non-punctual sites. We use the Bernstein form of polynomials and DeCasteljau’s algorithm ...

Voronoi Diagrams from Distance Graphs ∗

We present a new type of Voronoi diagram in R that respects the anisotropy exerted on the plane by a given distance graph. It is based on a metric obtained by smoothly and injectively embedding R into R, and a scalar-valued function for re-scaling the distances. A spline representation of the embedding surface is constructed with the Gauß-Newton algorithm, which approximates the given distance ...

Voronoi diagrams of semi-algebraic sets

Voronoi diagrams of semi-algebraic sets