Combining constructive and equational geometric constraint solving techniques

In the past few years, there has been a strong trend towards developing parametric, computer aided design systems based on geometric constraint solving. An efective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropiate techniques toachieve the expected functional capabilities. This work reports on a hybrid method which combines two geometric constraint solving techniques: Constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.Postprint (published version

Revisiting variable radius circles in constructive geometric constraint solving

Variable-radius circles are common constructs in planar constraint solving and are usually not handled fully by algebraic constraint solvers. We give a complete treatment of variable-radius circles when such a circle must be determined simultaneously with placing two groups of geometric entities. The problem arises for instance in solvers using triangle decomposition to reduce the complexity of the constraint problem.Postprint (published version

Geometric constraint problems and solution instances

Geometric constraint solving is a growing field devoted to solve geometric problems defined by relationships, called constraints, established between the geometric elements. In this work we show that what characterizes a geometric constraint problem is the set of geometric elements on which the problem is defined. If the problem is wellconstrained, a given solution instance to the geometric constraint problem admits different representations defined by measuring geometric relationships in the solution instance.Postprint (published version

Comment on the Possibility of a Geometric Constraint in the Schroedinger Quantum Mechanics

It is shown that the geometric constraint advocated in [R. S. Kaushal, Mod. Phys. Lett. A 15 (2000) 1391] is trivially satisfied. Therefore, such a constraint does not exist. We also point out another flaw in Kaushal's paper.Comment: to appear in Mod. Phys. Lett.

A constraint hierarchies approach to geometric constraints on sketches

International audienceWe propose an approach that uses preferences on the constraints in order to deal with over-constrained geometric constraint problems. This approach employs constraint hierarchies, a paradigm that has close relations with the traditional graph-based approaches used in geometric constraint solving. We also remark that any geometric constraint problem defined by imposing relations on a sketch becomes overconstrained as soon as the sketch is imposed as a weak constraint representing the designers intents. As a result our method appears very appropriate in CAD/CAM tools

On tree decomposability of Henneberg graphs

In this work we describe an algorithm that generates well constrained geometric constraint graphs which are solvable by the tree-decomposition constructive technique. The algorithm is based on Henneberg constructions and would be of help in transforming underconstrained problems into well constrained problems as well as in exploring alternative constructions over a given set of geometric elements.Postprint (published version