Discrete-Euclidean operations

Gaëlle Largeteau-Skapin (1) , Eric Andres (1)

1 SIC

In this paper we study the relationship between the Euclidean and the discrete space. We study discrete operations based on Euclidean functions: the discrete smooth scaling and the discrete-continuous rotation. Conversely, we study Euclidean oper- ations based on discrete functions: the discrete based simplification, the Euclidean- discrete union and the Euclidean-discrete co-refinement. These operations operate partly in the discrete and partly in the continuous space. Especially for the discrete smooth scaling operation, we provide error bounds when different such operations are chained.

Mots clés: discrete geometry; operations; multi-representation modeler

Domaines: Mathématique discrète [cs.DM]; Modélisation et simulation

Gaëlle Largeteau-Skapin, Eric Andres. Discrete-Euclidean operations. Discrete Applied Mathematics, 2009, 157 (3), pp.510--523. ⟨10.1016/j.dam.2008.05.034⟩. ⟨hal-00346007⟩