## Section: New Results

### Enumerating the morphologies of non-degenerate Darboux cyclides

Participant : Bernard Mourrain.

In [19] we provide an enumeration of all possible morphologies of non-degenerate Darboux cyclides. Based on the fact that every Darboux cyclide in ${\mathbb{R}}^{3}$ is the stereographic projection of the intersection surface of a sphere and a quadric in ${\mathbb{R}}^{4}$ , we transform the enumeration problem of morphologies of Darboux cyclides to the enumeration of the algebraic sequences that characterize the intersection of a sphere and a quadric in ${\mathbb{R}}^{4}$.

This is a joint work with Mingyang Zhao, Xiaohong Jia (KLMM - Key Laboratory of Mathematics Mechanization, Beijing, China), Changhe Tu (Shandong University, China), Wenping Wang (Computer Graphics Group, Department of Computer Science, Hong Kong, China).