Indermitte, ClaudeLiebling, Th. M.Troyanov, M.Clémençon, H.2008-03-182008-03-182008-03-18200110.1016/S0304-3975(00)00248-6https://infoscience.epfl.ch/handle/20.500.14299/20149WOS:000170245800025This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise flat, triangulated surface. Based on properties of such structures, a generalized flip algorithm to construct the Delaunay triangulation and Voronoi diagram is presented. An application to biological membrane growth modeling is then given. A Voronoi partition of the membrane into cells is maintained during the growth process, which is driven by the creation of new cells and by restitutive forces of the elastic membrane.TriangulationVoronoi diagramDelaunay triangulationFlip algorithmtext::journal::journal article::research article