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Closed‐form Blending of Local Symmetries
Author(s) -
Ghosh Deboshmita,
Amenta Nina,
Kazhdan Michael
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2010.01777.x
Subject(s) - symmetrization , homogeneous space , symmetry (geometry) , deformation (meteorology) , point (geometry) , set (abstract data type) , rotational symmetry , transformation (genetics) , local symmetry , bending , complement (music) , computer science , mathematics , geometry , mathematical analysis , physics , biochemistry , chemistry , quantum mechanics , complementation , meteorology , phenotype , gene , programming language , thermodynamics
We present a closed‐form solution for the symmetrization problem, solving for the optimal deformation that reconciles a set of local bilateral symmetries. Given as input a set of point‐pairs which should be symmetric, we first compute for each local neighborhood a transformation which would produce an approximate bilateral symmetry. We then solve for a single global symmetry which includes all of these local symmetries, while minimizing the deformation within each local neighborhood. Our main motivation is the symmetrization of digitized fossils, which are often deformed by a combination of compression and bending. In addition, we use the technique to symmetrize articulated models.