The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. B-rep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable B-rep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n^3.5 log^4 n), and a justification is given that on common engineering objects it takes about O(n^2 log^4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.

This thesis is concerned not with geometric features on a single component but rather with those that arise from the spatial adjacency of two, or more, components in an assembly. From a review of the literature on the nature and use of assembly features, it is concluded that the majority of assembly features involve sets of spatially adjacent faces. Three principle types of adjacency relationships proposed in CHAPTER 3.1 are identified and an algorithm is presented for identifying assembly features which arise from "external spatial", "internal spatial" and "contact" face adjacency relationships (known as esadjacency , is-adjacency and c-adjacency respectively).

Abstract. Engineering geometric models are often designed to have symmetries and other regularities. In knowledge based reuse, creative design and design for mass customization, to have the information of such symmetries and other regularities from a geometric model is very useful. And this can make us understand more about the geometric model. In reverse engineering, B-rep models are created by fitting surfaces from point sets obtained by scanning an object using a 3D laser scanner. Each fitted surface is determined independently. The reverse engineered object can be improved by imposing these symmetries and other regularities on. This paper discusses the particular problem of finding partial approximate symmetries present in geometric model. A practical algorithm for finding partial approximate symmetries within a 3D B-rep model defined with planes, spheres, cylinders, cones and tori is presented. The experiment results show that the algorithm detects the symmetries expected and can do so reasonably.