Locally Resolvable B-reps

A typical B-rep describes a solid in its full detail. Operations that locally analyze the B-rep usually process the entire B-rep due to the lack of spatial ordering of its topological entities. For very complex objects, this global processing is time consuming and yet unnecessary. One approach in avoiding the global processing is to use several B-reps of different levels of detail. However, this does not always help. For instance, when objects in close proximity need to be analyzed for contact, the need for a local increase in resolution forces a global increase in detail. Our motivation is to unify the different levels of detail and provide the means to locally control them. We introduce a locally resolvable b-rep (LRB-rep) as a non-manifold B-rep data structure for representing objects. The LRB-rep locally hides the solid's details with several layers of faces. A subset of the faces provides a global approximation of this solid, which we call the wrapper. The wrapper starts with the faces of the LRB-rep's outer layer and controlled by some application, may change its shape. Local face refinement reveals more detail and eventually resolves the wrapper to the original object with the highest level of detail. The LRB-rep is motivated by the need to avoid checking all the faces while detecting collisions between two complex objects in close proximity. Instead of checking the complex boundaries of both solids, the wrapper of one solid can be checked against the other solid. The wrapper faces that interpenetrate are refined and recursively checked. Faces that do not interpenetrate are discarded from further checking and refinement. In this paper we introduce the LRB-rep, the wrapper and its operations, and suggest their use in a collision detection application. I This work has been support by ONR Grant N00014--94--I--0576. 2 http://www.cs.purdue.edu/people/gonzalez, [email protected] 3 http://www.cs.purdue.edu/people/Vanecek, vanecek@cs,purdue.edu Locally Resolvable B-reps 11/14/94