No 5 (2024)

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.

A new method for estimating the complexity of geometric shapes (spots) is proposed, taking into account the internal structure of the spots, and not only their external contour. The task of calculating the degree of complexity of objects is divided into components: segmentation of spots and estimation of the complexity of isolated spots. The new method has a relatively low computational complexity compared to the alternative methods considered in the work. Using the new method, an algorithm based on parallel computing of the CUDA programming language for graphics accelerators (video cards) was created, which further increases the performance of our method. A qualitative and quantitative analysis of existing (alternative) methods has been carried out, their advantages and disadvantages in comparison with our method and with each other have been revealed. The algorithm implemented on the basis of the new method has been tested on both artificial and real digital images.

Currently, digital technologies for modeling buildings and infrastructure are successfully used in international and national practice in the implementation of complex construction projects and large-scale programmes. At the same time, the transition to machine-readable standards being implemented in many countries in order to improve the quality of design documentation and to automate its verification faces serious methodological and technical problems. First of all, they are associated with the complexity of the digital models, as well as with the variety of requirements formulated in natural languages and imposed on models at the state, regional, departmental and corporate levels. Attempts to create catalogues of requirements and software tools for their maintenance and use, usually have specialized nature and do not provide the necessary completeness, normalization, consistency, linked set, unambiguity, traceability and validatability of requirement descriptions. In this regard, it seems constructive to use formal methods for specification and verification of requirements that have proven themselves in system and software engineering. The paper provides a comparative analysis of software tools for automated verification of regulatory requirements in the construction domain. There is an increased popularity of tools focused on the international standards IFC (Industry Foundation Classes), IDS (Information Delivery Specification) and providing control of the completeness of the object and attribute composition of models, as well as clarification of acceptable ranges of values. At the same time, the IDS standard is not formalized and does not provide for specifying the requirements expressed by arbitrary algebraic conditions. The use of the object-oriented data modeling language EXPRESS, in which the IFC information schema is also specified, looks promising for the formal specification and verification of requirements for digital models in construction. As a justification, it is shown that IDS specifications can be represented by logical expressions and EXPRESS functions, as well as arbitrary algebraic conditions can be specified as EXPRESS declarative rules. Examples of the formalization of some requirements from national construction standards and set of rules on the safety of buildings, structures and processes are provided in the paper as illustrations of the proposed approach. The possibilities of harmonizing the proposed formal approach with the IDS standard as a result of defining new facets for representing EXPRESS local, unique and global rules are also discussed.