Pre-symmetry sets of 3d shapes

Authors:
André Diatta;Peter Giblin
Affiliations:
Department of Mathematical Sciences, University of Liverpool, Liverpool, England;Department of Mathematical Sciences, University of Liverpool, Liverpool, England
Venue:
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Year:
2005

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Abstract

We show that the pre-symmetry set of a smooth surface in 3-space has the structure of the graph of a function from ℝ2 to ℝ2 in many cases of interest, generalising known results for the pre-symmetry set of a curve in the plane. We explain how this function is obtained, and illustrate with examples both on and off the diagonal. There are other cases where the pre-symmetry set is singular; we mention some of these cases but leave their investigation to another occasion.