2 research outputs found
Pre-Symmetry Sets of 3D shapes
The investigation of 3D euclidean symmetry sets (SS) and medial axis is an
important area, due in particular to their various important applications.
The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in
2D) is the set of pairs of points which contribute to the symmetry set, that
is, the closure of the set of pairs of distinct points p and q in M, for which
there exists a sphere (resp. a circle) tangent to M at p and at q. The aim of
this paper is to address problems related to the smoothness and the
singularities of the pre-symmetry sets of 3D shapes.
We show that the pre-symmetry set of a smooth surface in 3-space has locally
the structure of the graph of a function from R^2 to R^2, in many cases of
interest.Comment: ACM-class: I.2; I.5; I.4; J.2. Latex, 3 grouped figures. The final
version will appear in the proceedings of the First International Workshop on
Deep Structure, Singularities and Computer Vision, Maastricht June 200