Algebras and formal specifications in geometric modelling

We revisit the theoretical foundations of geometric modelling from the algebraic and functional points of view. We present algebras as a powerful tool to describe old and recent geometric models and their operations of construction, manipulation and retrieval. They can be systematically and algebraically specified by a first-order equational logic. This contributes to accurately defining adequateness, ambiguity, correctness, uniqueness and implementation classes. It gives a firm guide to programming geometric modelling systems. We show that generic, unevaluated, geometric objects and histories of constructions can be systematically built and handled in functional specifications by an extended j-calculus based on the algebraic specifications.

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