Pre-symmetry Sets of 3D Shapes

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.

• Type: Conference
• Year: 2005
• Where: DSSCV
• Authors: André Diatta, Peter J. Giblin
• Keywords: 3-space, Computer Vision, DSSCV 2005, Pre-symmetry Set, Smooth Surface