Computer-aided design (CAD) relies on two foundations: (1), mathematical theory, especially discrete mathematics; (2), solid representation schemes. The prevalent researches on modern CAD systems have been the history?based modeling. There are two primary achievements in this area over past decade: one is parametric and feature-based modeling; the other one is constraint-based design. Both brought tremendous development to CAD/CAM applications, and facilitated designers to update geometric objects with different parameters. However, they are approaches that concerned only about the representation of a shape, totally ignored its structural description. Solid modeling is nowadays enjoying marvelous progress because of the accomplishments from the computer science field. CAD system providers offer unlimited freedom for designers to display their intents on the monitor. Obviously, the mathematic theory on intelligent geometry has been lagged behind the representation researches, and thus, resulted in the lack of formal depiction on geometric history. This research based upon the generative geometry, in which the evolution of geometric object was able to be described in manners of logic.