Shape Instance Generation From Domain Distributed Vague Models

Representing the possible shapes of a cluster of objects by a variation domain, vague discrete modeling is a powerful method for describing non-nominal shapes. A vague discrete model (VDM) is vague in the sense that multiple objects are represented by one domain model, and that multiple shape instances can be generated based on certain instantiation rules. The vaguely defined particles contained in a VDM provide a discrete representation that supports multi-resolution manipulation of shapes. This paper presents the latest results related to deriving instance shapes from a given VDM. The problem here is that a VDM may contain multiple regions, which have to be instantiated individually and the generated parts have to be unified in order to get an instance of a complex shape. First the paper gives a concise overview of vague discrete modeling. It introduces the concept as well as the process of rule-based instantiation of shapes from a VDM. It proposes simple, compound and constrained instantiation techniques for treating the various cases. To map the application field-dependent instantiation rules to explicit mathematical terms, the concept of effect function is applied. The discontinuous set of particle clouds received after instantiation are geometrically connected by fuzzy transition functions. The first experiences show that the vague discrete modeling extended with rule-based instantiation has a great potential to support intuitive shape conceptualization, especially in collaborative virtual design environments.