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 language||English (US)|
|Number of pages||11|
|Journal||Computer Graphics Forum|
|State||Published - Sep 21 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank Peter Wonka and Yuan Li for their help with the vase model, and gratefully acknowledge the support of the following grants: The Fulbright fellowship, the Weizmann Institute's “Women in Science” award, NSF grants 0808515 and 0808515, NIH grant GM-072970, a grant from the King Abdullah University of Science and Technology, and a gift from Google, Inc.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.