HYBRID REPRESENTATION OF SOLIDS USING IMPLICIT AND PARAMETRIC FUNCTIONS
DOI:
https://doi.org/10.15588/1607-3274-2017-3-7Keywords:
Solid, implicit function, R-function, parametric function, discrete model, distance function, parity test, computer-aided design.Abstract
Context. The present article deals with the problem of representation of solids in computer-aided design. The object of the study is a process of representation of solids in computer-aided design.
Objective. The objective of the study is the development of a hybrid representation scheme which uses implicit functions, Roperations and parametric functions.
Method. In the article, a hybrid representation scheme has been suggested to model solids. An abstract notion “solid” denotes bounded and closed subsets of Euclidean space, which model physical bodies. A representation scheme is a syntactically and semantically correct relation between a set of formal models and a set of solids. It is supposed that boundary represented regions are defined by parametric functions. On the other hand, functionally represented regions are defined by implicit functions. The hybrid representation scheme is based on an idea of combining the boundary representation scheme with the functional representation scheme. The hybrid representation scheme uses a signed distance function to transform regions with parametric boundaries into implicitly defined regions. Adaptive discrete models are used to evaluate a signed distance from some point to a boundary of a region which boundaries are defined by parametric functions. A distance from a point to the closest discrete element approximates a distance from a point to a boundary of a region. The parity test has been used to define a sign of a distance.
Results. The developed hybrid representation scheme has been implemented in software and investigated for solving the problems of solid modeling.
Conclusions. Carried out numerical experiments have confirmed the proposed software operability. The prospects for further research may include the development of parallel methods for calculation of a signed distance functionReferences
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