Hilderick A. van der Meiden

Specification of freeform features

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, prototype-driven 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.

AN EFFICIENT METHOD TO DETERMINE THE INTENDED SOLUTION FOR A SYSTEM OF GEOMETRIC CONSTRAINTS

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 prototype-based 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.

Solving topological constraints for declarative families of objects

Parametric and feature-based CAD models can be considered to represent families of similar objects. In current modelling systems, however, the semantics of such families are unclear and ambiguous. We present the Declarative Family of Objects Model (DFOM), which enables us to adequately specify and maintain family semantics. In this model, not only geometry, but also topology is specified declaratively, by means of constraints. A family of objects is modelled by a DFOM with multiple realizations. A member of the family is modelled by adding constraints, e.g. to set dimension variables, until a single realization remains. The declarative approach guarantees that the realization of a family member is also a realization of the family. The realization of a family member is found by solving first the geometric constraints, and then the topological constraints. From the geometric solution, a cellular model is constructed. Topological constraints indirectly specify which combinations of cellular model entities are allowed in the realization. The system of topological constraints is mapped to a Boolean constraint satisfaction problem. The realization is found by solving this problem using a SAT solver.

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

We present a new constructive solving approach for systems of 3D geometric constraints. The solver is based on the cluster rewriting approach, which can efficiently solve large systems of constraints on points, and incrementally handle changes to a system, but can so far solve only a limited class of problems. The new solving approach extends the class of problems that can be solved, while retaining the advantages of the cluster rewriting approach. Whereas previous cluster rewriting solvers only determined rigid clusters, we also determine two types of non-rigid clusters, i.e. clusters with particular degrees of freedom. This allows us to solve many additional problems that cannot be decomposed into rigid clusters, without resorting to expensive algebraic solving methods. In addition to the basic ideas of the approach, an incremental solving algorithm, two methods for solution selection, and a method for mapping constraints on 3D primitives to constraints on points are presented.

Tracking topological changes in parametric models

In current parametric CAD systems, the relation between the values of the parameters of a model and the topology of the model is often not clear to the user. To give the user better control over the topology of the model, this relation should be made explicit. A method is presented here that determines the parameter values for which the topology of a model changes, i.e. the critical values of a given variant parameter. The considered model consists of a system of geometric constraints, which relates parameters and feature geometries, and a cellular model, which partitions space into volumetric cells determined by the intersections of the feature geometries and represented by topological entities. Our method creates a new system of geometric constraints to relate the parameters of the model to the topological entities. For each entity that is dependent on the variant parameter, degenerate cases are enforced by specific geometric constraints. Solving the resulting constraint systems yields the critical parameter values. Critical values can be used to compute parameter ranges corresponding to families of objects, i.e. all parameter values which correspond to models that satisfy a given set of geometric and topological constraints.

Tracking topological changes in feature models

Current feature models do not explicitly represent the relation between the parameters and the topology of the model. For theoretical and practical purposes, it is important to make this relation more explicit. A method is presented here that determines parameter values for which the topology of a feature model changes, i.e. the critical values of a given variant parameter. The considered feature model consists of a system of geometric constraints, relating parameters to feature geometry, and a cellular model. The cellular model partitions Euclidean space into quasi-disjoint cells, determined by the intersections of the feature geometry. Our method creates a new system of geometric constraints to relate the parameters of the model to topological entities in the cellular model. For each entity that is dependent on the variant parameter, degenerate cases are enforced by specific geometric constraints. Solving this system of constraints yields the critical parameter values. Critical values can be used to compute parameter ranges corresponding to families of objects, e.g. all parameter values which correspond to models that satisfy given topological constraints.

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

Geometric constraints are at the heart of parametric and feature-based 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.

Solving systems of 3D geometric constraints with non-rigid clusters

We present a new constructive solving algorithm for systems of 3D geometric constraints. The solver is based on the cluster rewriting approach, which can efficiently solve large constraint systems, and incrementally handle changes to a system, but can so far solve only a limited class of problems. The new solving algorithm extends the class of problems that can be solved, while retaining the advantages of the cluster rewriting approach. It rewrites a system of constraints to clusters with various internal degrees of freedom. Whereas previous constructive solvers only determined rigid clusters, we also determine two types of non-rigid clusters. This allows us to solve many additional problems that cannot be decomposed into rigid clusters, without resorting to expensive algebraic solving methods.