Abstract: A method, useful in computer-aided design, of identifying possible solutions to an over-constrained system having a collection of entities and constraints. The method represents the entities in terms of degrees of freedom and incrementally assembles the system by adding entities, satisfying constraints and reducing the degrees of freedom of the entities. For an over-constrained system, the method constructs a dependency graph of the system and identifies the set of constraints which over-constrains the system. The over-constraining set includes the constraint which initiated the over-constraint and those constraints back traced in the dependency graph from the initiating constraint. Removal of one or more constraints from the over-constraining set results in a solvable fully or under-constrained system. Intelligent selection of the removed constraint may increase computational efficiency or system stability.

Abstract: A method, useful in computer-aided design, for finding possible configurations of a system having a collection of geometric entities and constraints. The method represents the geometric entities in terms of degrees of freedom and systematically satisfies the constraints reducing the degrees of freedom of the geometric entities. The method uses a number of specialized routines, called plan fragments, which satisfy a particular constraint relating to a particular geometric entity. Each plan fragment changes the configuration of a geometric entity in space--i.e. the location and orientation--satisfying a constraint and reducing a degree of freedom. The series of plan fragments which reduce the degrees of freedom and satisfy the constraints comprise an assembly plan for possible configurations of the system. The method identifies overconstrained, fully constrained, and underconstrained systems to the user and assists in finding possible configurations if the constraints are changed, added, or deleted.

Abstract: A method, useful in computer-aided design, for finding configurations of collections of geometric elements representing shapes of physical objects that satisfy a set of geometric constraints, when these constraints relate to topological properties of the geometric elements. In particular, the invention relates to a method that classifies the geometric elements in terms of degrees of freedom, categorizes topological properties in terms of biases, and synthesizes a solution by progressively reducing the total degrees of freedom in the system.