Theoretical Basis of Mathematical Apparatus for Parallel Computing Implementation in Computer-Aided Design Systems

The purpose of this work is to develop a mathematical apparatus and computational algorithms for implementation of parallel computing in geometric modeling and computer-aided design (CAD) systems. The analysis of existing approaches to parallel computing implementation in CAD systems is carried out. As a result, it is found that most information modeling and CAD systems do not support 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. It combines the potential of constructive methods for geometric modeling, capable of parallelizing geometric constructions by tasks (message passing), and the mathematical apparatus of point calculus, capable of parallelization by data through coordinate-by-coordinate calculation (data parallel). The use of the coordinate-by-coordinate calculation for point equations not only makes it possible to parallelize computations along coordinate axes, but also ensures the consistency of computational operations with respect to threads, which significantly reduces the idle time and optimizes the CPU operation to achieve the maximum effect from the use of parallel computing.