"A Data Type for Solid Modeling and Computational Geometry "
ABSTRACT:
Solid modelling and computational geometry are based on classical topology
and geometry in which the basic predicates and operations, such as
membership, subset inclusion, union and intersection, are not continuous
and therefore not computable. But a sound computational framework for
solids and geometry can only be built in a framework with computable
predicates and operations. In practice, correctness of algorithms in
computational geometry is usually proved using the unrealistic Real RAM
machine model of computation, which allows comparison of real numbers,
with the undesirable result that correct algorithms, when implemented,
turn into unreliable programs.
Here, we use a domain-theoretic approach to recursive analysis to develop
the basis of an effective and realistic framework for solid modelling.
This framework is equipped with a well-defined and realistic notion of
computability which reflects the observable properties of real solids. The
basic predicates and operations on solids are computable in this model
which admits regular and non-regular sets and supports a design
methodology for actual robust algorithms. Moreover, the model is able to
capture the uncertainties of input data in actual CAD situations.
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