Meshing genus-1 point clouds using discrete one-forms

Authors:
Geetika Tewari;Craig Gotsman;Steven J. Gortler
Affiliations:
Computer Science Department, Harvard University, Cambridge, MA 02138, USA;Computer Science Department, Harvard University, Cambridge, MA 02138, USA;Computer Science Department, Harvard University, Cambridge, MA 02138, USA
Venue:
Computers and Graphics
Year:
2006

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Abstract

We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1. The method relies on a doubly periodic global parameterization of the point cloud to the plane, so no segmentation of the point cloud is required. Based on some recent techniques for parameterizing higher genus meshes, when some mild conditions on the sampling density are satisfied, the algorithm generates a closed toroidal manifold which interpolates the input and is geometrically similar to the sampled surface.