"HyperJazz" project: development of geometric modelling systems with inherent symbolic interactivity

The paper presents a project called 'HyperJazz' devoted to development and implementation of the 'empirical' approach to solid modelling, which stresses the importance of interactive experiments of the user with the model. The approach is based on two foundations: geometric modelling based on the function representation and definitive programming environment. We propose a technology of user's interactive work with the modeller and a technology of creating interactive geometric modelling systems that can be adapted to different application domains and can be customized for needs of particular users. The basic set of API-procedures and the Kernel Geometric Interactive Environment are introduced. Their charasteristic feature called "inherent symbolic interactivity" is based on a high-level definitive language of point-sets. The technology of building a particular CSG system as well as an example of behaviour modelling are presented. Introduction It was recently pointed out once more in [..

Function representation in geometric modeling: concepts, implementation and applications

Geometric modelling using continuous real functions of several variables is discussed. Modelling concepts include sets of objects, operations and relations. An object is a closed point set of n-dimensional Euclidean space with a defining inequality f x x xn (,,..., ) 1 2 0 °Ÿ¸. Transformations of a defining function are described for the set-theoretic operations, blending, offsetting, bijective mapping, projection, Cartesian product and metamorphosis. Inclusion, point membership and intersection relations are described. In the implemented interactive modelling system, we use highlevel geometric language that provides extendibility of the modelling system by input symbolic descriptions of primitives, operations and predicates. This approach supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxel-based objects, deformable and other animated objects. Application examples of aesthetic design, collisions simulation, NC machining, range data processing, and 3D texture generation are given