Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Algebraic specification of a 3D-modeler based on hypermaps
CVGIP: Graphical Models and Image Processing
Formalizing mathematics in higher-order logic: a case study in geometric modelling
Theoretical Computer Science
CASL: A Guided Tour of Its Design
WADT '98 Selected papers from the 13th International Workshop on Recent Trends in Algebraic Development Techniques
Subsorted Partial Higher-Order Locig as an Extension of CASL
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Formal Specification and Theorem Proving Breakthroughs in Geometric Modeling
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
WADT '01 Selected papers from the 15th International Workshop on Recent Trends in Algebraic Development Techniques
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This paper presents an experiment that demonstrates the feasibility of successfully applying CASL to design 3D geometric modelling software. It presents an abstract specification of a 3D geometric model, its basic constructive primitives together with the definition of the rounding high-level operation. A novel methodology for abstractly specifying geometric operations is also highlighted. It allows one to faithfully specify the requirements of this specific area and reveals new mathematical definitions of geometric operations. The key point is to introduce an inclusion notion between geometric objects, in such a way that the result of an operation is defined as the smallest or largest object satisfying some pertinent criteria. This work has been made easier by using different useful CASL features, like first-order logic, free types or structured specifications. Some assets of this specification are to be abstract, readable by researchers in geometric modelling and to simplify the programming process.