Foundation of a computable solid modeling
Abbas Edalat, André Lieutier · 1999
Correctness of algorithms in computational geometry are usually proved using the unrealistic Real RAM machine model of computation with the undes:uable result that correct algorithms, when implemented, turn into unreliable programs.In this paper, we use a domain-theoretic approach to recursive analysis to develop the basis of an effective and realistic framework for solid modeling.This framework is equipped with a well-defined and realistic notion of computability which reflects the observable properties of real solids.It is closed under the Boolean operations, admits non-regular sets and supports a design methodology for actual robust algorithms.Within this model, some unavoidable limitations of solid modeling computations are proved and a sound framework to design specifications for feasible modeling operators is provided.Some consequences in computation with the boundary representation paradigm are sketched that can incorporate existing methods into a general, mathematically well-founded theory.Moreover, the model is able to capture the uncertainties of input data in actual CAD situations.