Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems

Simon Thierry (1) , Pascal Schreck (1) , Dominique Michelucci (2) , Christoph Fünfzig (2) , Jean-David Génevaux (1)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection
2 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems. Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number of solutions to a finite number. An algorithm to efficiently identify all maximal well-constrained parts of a geometric constraint system is described. This allows us to design a powerful algorithm of decomposition, called W-decomposition, which is able to identify all well-constrained subsystems: it manages to decompose systems which were not decomposable by classic combinatorial methods.

Mots clés: Geometric constraints solving; Witness configuration; W-decomposition

Domaines: Modélisation et simulation

Simon Thierry, Pascal Schreck, Dominique Michelucci, Christoph Fünfzig, Jean-David Génevaux. Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems. Computer-Aided Design, 2011, 43 (10), pp.1234-1249. ⟨10.1016/j.cad.2011.06.018⟩. ⟨hal-00691690⟩