Function representation in geometric modeling: concepts, implementation and applications

Abstract

Concepts of functionally based geometric modeling including sets of objects, operations, and relations are discussed. Transformations of a defining real function are described for set-theoretic operations, blending, offsetting, bijective mapping, projection, cartesian products, and metamorphosis. Inclusion, point membership, and intersection relations are also described. We use a high-level geometric language that can extend the interactive modeling 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.

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Pasko, A., Adzhiev, V., Sourin, A. et al. Function representation in geometric modeling: concepts, implementation and applications. The Visual Computer 11, 429–446 (1995). https://doi.org/10.1007/BF02464333

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Key words

  • Geometric modeling
  • Solid modeling
  • Real functions
  • Implicit surfaces
  • R functions