Theoretical bases of mathematical apparatus of parallel computing realization in computer-aided design systems

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Abstract

The purpose of the work is the development of mathematical apparatus and computational algorithms for the implementation of parallel computing in geometric modeling and computer-aided design systems. The analysis of existing approaches to the implementation of parallel computing in CAD systems has been carried out. As a result, it was found that for most information modeling and computer-aided design systems, there is no support for parallel computing at the level of the geometric kernel. A concept for the development of a CAD geometric kernel based on the invariants of parallel projection of geometric objects onto the axes of the global coordinate system is proposed, which combines the potential of constructive methods of geometric modeling capable of providing parallelization of geometric constructions by tasks (message passing) and the mathematical apparatus of “Point Calculus”, capable of implementing parallelization by data through coordinate-by-coordinate calculation (data parallel). The use of coordinate-by-coordinate calculation of point equations not only allows you to parallelize calculations along coordinate axes, but also ensures the consistency of computational operations along streams, which significantly reduces the idle time of calculations and optimizes the processor’s work to achieve the maximum effect from the use of parallel computing.

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About the authors

E. Konopatskiy

Nizhny Novgorod State University of Architecture and Civil Engineering

Author for correspondence.
Email: e.v.konopatskiy@mail.ru
Russian Federation, Nizhny Novgorod

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Supplementary files

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2. Fig. 1. Geometric interpretation of coordinate-by-coordinate calculation for a straight line segment in 3-dimensional space.

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3. Fig. 2. Geometric scheme for constructing a 2nd order curve.

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4. Fig. 3. Geometrical scheme of modeling a bypass arc based on the Desargues configuration.

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5. Fig. 4. Geometrical scheme of modeling a 9-point surface section.

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6. Fig. 5. Geometric scheme for defining a solid model of a parallelepiped.

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