Publication

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

Thomas Liebling, Marc Troyanov
2001
Journal Articles

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.

Official source

https://infoscience.epfl.ch/entities/publication/58e0b103-8842-43b9-a6b8-b0856d646681

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Thomas Liebling, Marc Troyanov
2001
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/58e0b103-8842-43b9-a6b8-b0856d646681

About this result

Related concepts (31)

Voronoi diagram

In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation.

Delaunay triangulation

In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934.

Membrane

A membrane is a selective barrier; it allows some things to pass through but stops others. Such things may be molecules, ions, or other small particles. Membranes can be generally classified into synthetic membranes and biological membranes. Biological membranes include cell membranes (outer coverings of cells or organelles that allow passage of certain constituents); nuclear membranes, which cover a cell nucleus; and tissue membranes, such as mucosae and serosae.

Related publications (11)

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

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