Affiliation:
1. Classe di Scienze, Scuola Normale Superiore Pisa Italy
2. Department of Mathematical Sciences University of Bath Bath UK
Abstract
AbstractWe provide “growth schemes” for inductively generating uniform random ‐angulations of the sphere with faces, as well as uniform random simple triangulations of the sphere with faces. In the case of ‐angulations, we provide a way to insert a new face at a random location in a uniform ‐angulation with faces in such a way that the new map is precisely a uniform ‐angulation with faces. Similarly, given a uniform simple triangulation of the sphere with faces, we describe a way to insert two new adjacent triangles so as to obtain a uniform simple triangulation of the sphere with faces. The latter is based on a new bijective presentation of simple triangulations that relies on a construction by Poulalhon and Schaeffer.
Funder
Engineering and Physical Sciences Research Council
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software