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

Abstract

Geometric constraints are at the heart of parametric and featurebased CAD systems. Changing values of geometric constraint parameters is one of the most common operations in such systems. However, because allowable parameter values are not known to the user beforehand, this is often a trial-and-error process. We present a solution for automatically determining the allowable range for parameters of geometric constraints. Considered are systems of distance and angle constraints on points in 3D that can be decomposed into triangular and tetrahedral subproblems, by which most practical situations in parametric and feature-based CAD systems can be represented. Our method uses the decomposition to find critical parameter values for which subproblems degenerate. By solving one problem instance for each interval between two subsequent critical values, the exact parameter ranges are determined for which a solution exists.

Fab forms

“…Although these tools are able to constrain the design according to parametric and geometric constraints set by the designer, parameter manipulation of such models is reserved for experts, who can detect and correct design problems, which range from unsatisfiable constraints to complex functional failures. Simply determining ranges of parameters where constraints are satisfiable is a known hard problem, and has only been addressed analytically for a number of severely limited scenarios [Hoffmann and Kim 2001;Van der Meiden and Bronsvoort 2006;Hidalgo and Joan-Arinyo 2012]. In addition to low-level constraints, some previous work allows setting high-level topological constraints on the realized design [van der Meiden and Bronsvoort 2007], or defining and maintaining semantic feature information during parameter manipulation [Bidarra and Bronsvoort 2000], albeit that these methods heavily rely on their chosen sets of constraints.…”

h-graphs: A new representation for tree decompositions of graphs

“…[5,6,23]. In these fields, knowing beforehand which is the set of values for λ such that the geometric construction can actually be built plays a central role.…”

“…A direct method to compute the set of values of λ for which the construction plan solution to a constraint problem is feasible was described for the first time in [22,23]. The method was formalized in [5,6] where a correctness proof along with specific implementation details were given.…”

“…For the first time, van Der Meiden and Bronsvoort [23] described a method to directly figure out the allowable range for a single parameter in the problem, called variant parameter, such that an actual solution exists for any value in the range. The method was formalized by Hidalgo and Joan-Arinyo in [5,6] where a correctness proof along with specific implementation details were given.…”

The Increasing Role of Semantics in Object Modeling

“…To help users instantiate family members, we have developed methods to compute parameter ranges, i.e. the range of allowable values for any parameter [8]. Also, we have developed methods to determine the critical parameter values, i.e.…”