Systematic Derivation of a Standard Set of Declarative Constraints for Shape Definition in CAD

This paper describes the derivation of a consistent and comprehensive set of geometrical constraints for shape definition in Computer-Aided Design. These are needed to enable compatibility in parametric data exchange and to promote both standard capabilities and predictable solutions from constraint solving software kernels. The paper look at the mathematical basis for constraints present in the literature and elaborates about all types of constraints that can be described by the same mathematical basis. The approach considers all combinations of distance and angle constraints, on one point or all points of curves and surfaces, as well as transformations and mappings that are required in mechanical design.