Constructing conformal maps of triangulated surfaces

Conformal Maps and Minimal Surfaces

Quasi-conformal Flat Representation of Triangulated Surfaces for Computerized Tomography

In this paper we present a simple method for flattening of triangulated surfaces for mapping and imaging. The method is based on classical results of F. Gehring and Y. Väisälä regarding the existence of quasi-conformal and quasi-isometric mappings between Riemannian manifolds. A random starting triangle version of the algorithm is presented. A curvature based version is also applicable. In addi...

Quasi-isometric and Quasi-conformal Development of Triangulated Surfaces for Computerized Tomography

In this paper we present a simple method for minimal distortion development of triangulated surfaces for mapping and imaging. The method is based on classical results of F. Gehring and Y. Väisälä regarding the existence of quasi-conformal and quasi-isometric mappings between Riemannian manifolds. A random starting triangle version of the algorithm is presented. A curvature based version is also...

Curvature Estimation for Segmentation of Triangulated Surfaces

An important aspect of reverse engineering is the production of digital representations of physical objects for CAD systems. The first stage involves taking 3D coordinate measurements for points on the surface of the object and producing in general an unstructured set of points, called a point cloud. A triangulated surface can be generated from such a point cloud, allowing copies of the origina...

Decomposition and Enumeration of Triangulated Surfaces

We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions and genus-surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most a fixed number of vertices. We specialize the theory for the case where the number of vertices is at most 11 and we get theoretical restrictions on genus-su...