Title :

Yvon-Villarceau Circle Equivalents on Dupin Cyclides

Author(s) :

De Comite, Francesco [Auteur]
Université de Lille, Sciences et Technologies
Methods and tools for gestural interactions [MINT]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Conference title :

Bridges 2015: Mathematics, Music, Art, Architecture, Culture

City :

Baltimore

Country :

Etats-Unis d'Amérique

Start date of the conference :

2015-07-29

Book title :

Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)

Publication date :

2015-07-30

HAL domain(s) :

Informatique [cs]/Traitement des images [eess.IV]
Informatique [cs]/Géométrie algorithmique [cs.CG]
Mathématiques [math]/Géométrie algébrique [math.AG]

English abstract : [en]

A torus contains four families of circles: parallels, meridians and two sets of Yvon-Villarceau circles. Craftworks and artworks based on Yvon-Villarceau circles can be very attractive. Dupin cyclides are images of tori ...
Show more >A torus contains four families of circles: parallels, meridians and two sets of Yvon-Villarceau circles. Craftworks and artworks based on Yvon-Villarceau circles can be very attractive. Dupin cyclides are images of tori under sphere inversion, so they contain the images of the torus circles families. I applied operations that are known to create effective artworks on tori to Dupin cyclides, and proved them to be feasible. The regularity and the hidden complexity of the objects I obtained make them very attractive. Reviving the 19th century's tradition of mathematical models making, I printed several models, which can help in understanding their geometry. The tools I developed can be generalized to explore transformations of other mathematical objects under sphere inversion. This exploration is just at its beginning, but has already produced interesting new objects.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL