Dynamic Shape Typing

Automatic processing of shape information requires the selection of a representation form of shape. Shape modeling is based on a choice of shape type, which is the joint specification of representation form and a set of operations. In shape applications, such as shape design and shape optimization, it is not sufficient to maintain a static shape type. Depending on the specific needs during the application, i.e. depending on the modeling context, the appropriate shape type might be continuously varying. Programmed systems can handle static shape types relatively well. However, to support dynamic shape typing a number of fundamental problems need to be understood and solved. An approach to dynamic typing of freeform shapes is presented. Theoretical issues will be described and some concrete examples and initial experimental results will be presented. INTRODUCTION Shape modeling is any method that provides a controllable representation of geometric objects. In engineering, shape modeling thus supports part design, part shape analysis, shape optimization and shape information processing for manufacturing, assembly planning, simulation etc. From the application’s point of view, the computer representation of the shape model is only a secondary issue. However, during the creation, usage and modification of shape data, it turns out that any particular representation form is not adequate to support the full spectrum of computation needs. This shortcoming is the source of a number of current problems, including • Failing interoperability in collaborative engineering applications (Vergeest 2001) • The necessity to perform work arounds by the users of shape modeling systems • Forcing shape modeling users to operate on low-level geometry • Lack of direct, precise and intuitive control of shape in engineering applications • Inhibiting effective operations such as the reuse of precedent shapes (Vergeest 2001a). There are some recent approaches to achieve effective and high-level modeling in the freeform surface domain (Fontana 1999, Wyvill 2001) and in the solid domain (van den Berg 2002). In this paper we address the interplay of two fundamental interpretations of shape, its computational type and its appreciated type. The computational type defines the geometric representation form and the variables (if any) on which shape instances depend. The computational type can be understood as what is commonly known in computer science as an object class. The appreciated type is the set of shape parameters that