Décomposition et paramétrisation de systèmes de contraintes géométriques sous-contraints
Abstract
Solving geometric constraint systems (GCS) aims at yielding figures which respect geometric requirements given by the user under the form of a technical sketch. The GCS given by the user can be well-constrained (it describes a non-zero finite number of figures), under-constrained (an infinity of figures) or over-constrained (no solutions at all). Classically, under-constrained systems are considered as errors to be corrected by the user. Our work proposes another approach, i.e. try to homogeneously solve all non-over-constrained systems. For that, we propose parameterization algorithms: they indicate which elements of the system need to be anchored for there to be a finite number of solutions~; and decomposition algorithms, which allow to identify well-constrained subsystems. These tools open the way to constraint-based modelers which are accessible to non-expert users: they give intuitive visual feedback about the constrainedness level of the system. Since our algorithms are all incremental, they allow a trial and error approach: the user corrects the sketch as the resolution goes.
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