An Efficient Method to Determine the Intended Solution for a System of Geometric Constraints

Abstract

The number of solutions of a geometric constraint problem is generally exponential to the number of geometric elements in the problem. Finding a single intended solution, satisfying additional criteria, typically results in an NP-complete problem. A prototypebased selection scheme is presented here that avoids this problem. First, a resemblance relation between configurations is formally defined. This relation should be satisfied between the intended solution and a prototype configuration. The resemblance relation is in our approach satisfied by applying selection rules to subproblems in a bottom-up solving approach. The resulting solving algorithm is polynomial, because the selection rules are not used as search heuristic, but to unambiguously select a single solution such that no backtracking search is needed. For many applications, in particular CAD, this solution is both meaningful and intuitive.

Developments in Feature Modelling

“…• more powerful constraint solving techniques [25] • families of objects with well-defined semantics [26] • deformation techniques for freeform features [27] • exchange of feature models between different systems, without losing semantic information [28] • exploitation of the feature concept in other applications, e.g. advanced manufacturing [29].…”

A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints

“…Therefore, various solution selection schemes have been proposed, e.g., interactive approaches [5,18], genetic algorithms [19] and sketchbased methods [20]. Our solver supports two solution selection schemes, namely declarative solution selection [21] and prototype-based solution selection [22].…”

“…We use a prototype-based solution selection mechanism that always determines at most one solution, the so-called intended solution, described in [22]. The intended solution satisfies the following properties:…”

“…In [22], it is shown, for a somewhat simpler constraint solver, which only recognises triangular and tetrahedral rigid subproblems, that the intended solution can be found using selection constraints. Basically, we formally define the properties that the resemblance relation must satisfy, in order to find the intended solution.…”

A constructive approach to calculate parameter ranges for systems of geometric constraints

“…The constraint solver used in our implementation is a simple bottom-up solver, similar to the solvers presented in [Bouma et al 1995;Hoffmann and Vermeer 1995], with a prototype-based solution selection scheme [van der Meiden and Bronsvoort 2004]. Constraint systems are solved as follows:…”