On Discrete Killing Vector Fields and Patterns on Surfaces

Mirela Ben-Chen, Adrian Butscher, Justin Solomon, Leonidas Guibas

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape's aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)1701-1711
Number of pages11
JournalComputer Graphics Forum
Issue number5
StatePublished - Sep 21 2010
Externally publishedYes


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