We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.
|Original language||English (US)|
|Journal||ACM Transactions on Graphics|
|State||Published - Jul 29 2007|
- Shape analysis
- Shape optimization
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design