Surface reconstruction using Delaunay triangulation for applications in life sciences

The Delaunay triangulation is an established method to define neighborhood relations in multi-particle systems. In particular, this method was employed for interacting multi-cellular systems in Biology. The extension of this method to a sub-cellular level that considers the membrane and the inner structure of cells is not straight forward and subject of this article. It is the objective to use a three-dimensional Delaunay-triangulation as a basis for the definition of a triangulation of a subset of particles that form a surface.An essential problem of this objective is the conservation of the number of particles belonging to the surface. This excludes established surface reconstruction algorithms. The presented algorithm allows the definition of a triangulation within a subset of particles attributed to a surface without the deletion of particles. A particular challenge is the deletion of connection that infer three-dimensional structures in the surface. The presented method is suitable for many configurations. Its performance and its limitations are analyzed and discussed.The developed algorithm for the reconstruction of connections in a surface is suitable to be used for simulations of biological cells because of the inherent conservation of the number of particles attributed to the membrane.