Differential geometry on discrete surfaces

David Cohen-Steiner, Jean Marie Morvan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Point clouds and meshes are ubiquitous in computational geometry and its applications. These subsets of Euclidean space represent in general smooth objects with or without singularities. It is then natural to study their geometry by mimicking the differential geometry techniques adapted for smooth surfaces. The aim of the following pages is to list some geometric quantities (length, area, curvatures) classically defined on smooth curves or surfaces, and to define their analog for discrete objects, justifying our definition by a continuity property: if a sequence of discrete objects tends (in a certain sense) to a smooth object, do the corresponding geometric quantities tend to the ones of the smooth object?

Original languageEnglish (US)
Title of host publicationEffective Computational Geometry for Curves and Surfaces
PublisherSpringer Berlin Heidelberg
Pages157-179
Number of pages23
ISBN (Print)9783540332589
DOIs
StatePublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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