Algebraic method for manipulation of dimensional relationships in geometric models

Abstract The paper describes a new algebraic method for the manipulation of dimensional relationships defined in geometric models, and for the generation of their dimensional variants. Consistent and sufficient geometric constraints are automatically generated by the interpretation of the executed modeling operations that are implemented as manipulations on a nonmanifold geometric model. These constraints are internally represented as polynomials, and the relationships and dependencies between these constrainsts are managed and updated by algebraic methods based on a polynomial ideal theory when the manipulation of dimensional relationships such as canceling, adding etc. are executed.