The popularity of 3D CAD systems is resulting in a large number of CAD models being generated. Availability of these CAD models is opening up new ways in which information can be archived, analyzed, and reused. 3D geometric information is one of the main components of CAD models. Therefore shape similarity assessment is a fundamental geometric reasoning problem that finds several different applications. In many design and manufacturing applications, the gross shape of the 3D parts does not play an important role in the similarity assessment. Instead certain attributes of part features play a dominant role in determining the similarity between two parts.

Different feature-based models are usually created using their own coordinate systems. Therefore, feature-based shape similarity assessment involves finding the optimal alignment transformations for two sets of feature vectors. The optimal alignment corresponds to the minimum value of a distance function that is computed between the two sets of feature vectors being aligned. In order to compute the distance function the closest neighbor to each feature vector needs to be identified. We have developed optimal feature alignment algorithms based on the partitioning of the transformation space into regions such that the closest neighbors are invariant within each region. These algorithms can work with customizable distance functions. We have shown that they have polynomial time complexity. For higher dimension transformation spaces it is harder to design algorithms based on the partitioning of transformation spaces because the data structures involved are very complex. In those cases, feature alignment algorithms based on iterative strategies have been developed. Iterative strategies make use of optimal feature alignment algorithms based on the partitioning of lower dimension transformation spaces. Extensive experiments have been carried out to provide empirical evidence that iterative strategies can find the optimal solution for feature alignment problems. A feature-based shape similarity analysis framework has been built based on the feature alignment algorithms. This framework has been demonstrated with the two following applications. A machining feature based alignment algorithm has been developed to automatically search databases for parts that are similar to a newly designed part in terms of machining features. We expect that the retrieved parts can be used as a basis to perform cost estimation of the newly designed part. A surface feature based alignment algorithm has been developed to automatically search databases for parts that are similar to a newly designed part in terms of surface features. We expect that the retrieved parts can be used as a basis to choose the most appropriate tool maker for the newly designed part.

We believe that the feature-based shape similarity assessment algorithms developed in this thesis will provide the foundations for designing new feature-based shape similarity algorithms that will enable designers to efficiently retrieve archived geometric information. We expect that these tools will facilitate information reuse and therefore decrease product development time and cost.