Enumerating the morphologies of non-degenerate Darboux cyclides

Mingyang Zhao (1, 2) , Xiaohong Jia (3, 2, 1) , Changhe Tu (4, 3) , Bernard Mourrain (5) , Wenping Wang (3)

1 KLMM - Key Laboratory of Mathematics Mechanization
2 NCMIS - National Center for Mathematics and Interdisciplinary Sciences [Beijing]
3 Computer Graphics Group [Hong Kong]
4 Shandong University
5 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

We provide an enumeration of all possible morphologies of non-degenerate Darboux cyclides. Based on the fact that every Darboux cyclide in R 3 is the stereographic projection of the intersection surface of a sphere and a quadric in 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 R 4 .

Mots clés: Darboux cyclides; stereographic projection; Segre characteristic; index sequences; morphologies

Domaines: Géométrie algébrique [math.AG]

Mingyang Zhao, Xiaohong Jia, Changhe Tu, Bernard Mourrain, Wenping Wang. Enumerating the morphologies of non-degenerate Darboux cyclides. Computer Aided Geometric Design, 2019, 75, pp.101776. ⟨10.1016/j.cagd.2019.101776⟩. ⟨hal-02400652⟩