Geometric abstractions using medial axis transformation

Abstract: "The most important concerns in the design of a product are to ensure that the product serves the purpose it is intended for, and to maintain the producibility of the product at a reasonable cost. Ideally, in design environments, these two concerns should be taken into account. As a result, analyses should be performed from the viewpoint of these concerns. Some of these analyses are purely mathematical in nature, some are entirely heuristic, but quite often they require a treatment which is a mixture of both. In modern computer-aided design (CAD) environments, the products are usually represented by their indiscriminated geometry, such as faces, edges, vertices, primitive solids, etc. Such a mathematical representation is not convenient for heuristic analysis.Heuristic reasoning is expressed in terms of high level abstractions. One formalism to capture these abstractions is to view the products in terms of its features. Features are a way of representing patterns in form or in function. In essence, they are meant to facilitate the practice of design and reasoning about the designed object. Therefore, features emerge as the link to bridge the gap between the geometry and the heuristic analysis. However, to recognize features directly from geometry is rather difficult. But if an object can be expressed in terms of its skeletal model, then the recognition task might be easier. The features, then, would be viewed as patterns in the skeletal model. Recognizing features in this fashion may turn out to be a much simpler task.The medial axis transformation (MAT) provides one way of getting a skeletal form from the geometry. By incorporating MAT, one can expect the recognition of features from the designed object to become less cumbersome. This article describes a representation of form features using medial axis transformation. The MAT is defined, its properties are studied and its computation is investigated. Furthermore, the MAT data base is established and some examples of extracting features will be given."