Discrete Complex Structure on Surfel Surfaces

Christian Mercat (1, 2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier

This paper defines a theory of conformal parametrization of digital surfaces made of surfels equipped with a normal vector. The main idea is to locally project each surfel to the tangent plane, therefore deforming its aspect-ratio. It is a generalization of the theory known for polyhedral surfaces. The main difference is that the conformal ratios that appear are no longer real in general. It yields a generalization of the standard Laplacian on weighted graphs.

Mots clés: discrete Riemann surfaces; digital geometry; discrete differential geometry

Domaines: Géométrie algorithmique [cs.CG]; Variables complexes [math.CV]; Synthèse d'image et réalité virtuelle [cs.GR]

Christian Mercat. Discrete Complex Structure on Surfel Surfaces. 14th IAPR International Conference on Discrete Geometry for Computer Imagery, Apr 2008, Lyon, France. pp.153-164, ⟨10.1007/978-3-540-79126-3⟩. ⟨hal-00250975⟩