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.

Freeform feature modeling is an extension to feature modeling in which, in addition to regular-shaped features, also freeform features are possible. Due to the large variety of freeform features, a generic approach to specify such features is required. This paper describes such an approach. A freeform feature class is specified by using a prototype and constraints. The latter are used to define intuitive parameters and validity conditions for the class. A new, prototypedriven constraint solving method is used to unambiguously determine a freeform feature during the specification both of a class and of an instance to be added to a model. The specification of freeform features and the prototype-driven constraint solving method are discussed. Several examples are given.

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.

Object modeling for applications like CAD/CAM, simulation and computer games, has traditionally been limited to the shape of objects. Currently, a trend can be observed to add several types of semantics to object models. This observation is discussed in some detail for three modeling approaches worked on in our research group: feature modeling, including recent advances for freeform features, modeling families of objects, and modeling virtual worlds. The use of semantics in some other modeling approaches is briefly discussed. Adding semantics can ease specification and modification of an object model, help to guarantee its validity, and be useful for applications which use the model, such as process planning for manufacturing or gameplay. Much work remains to be done to determine the types of semantics most useful in practice. 439descriptions it is possible to synthesize gear boxes, with various configurations of gears, such that the complete system has a given input-output speed ratio.So, besides in the modeling approaches discussed in Sections 3 to 5, specific types of semantics are being exploited in several other modeling approaches too, always to improve the modeling process in one way or another.

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