Voronoi diagrams on piecewise flat surfaces and an application to biological growth

Authors:
C. Indermitte;Th. Liebling;M. Troyanov;H. Clémençon
Affiliations:
Ecole Polytechnique, Lausanne, Switzerland;Ecole Polytechnique, Lausanne, Switzerland;Ecole Polytechnique, Lausanne, Switzerland;Univ. de Lausanne, Switzerland
Venue:
Theoretical Computer Science
Year:
2001

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Abstract

This 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.