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Vol. 3 No. 11 (2026)
Engineering & Education

Articles

FAZOVIY GEOMETRIK OBYEKTLARNI PARAMETRIK MODELLASHTIRISH VA PROYEKSIYALARNI HOSIL QILISH USULLARINING QIYOSIY TAHLILI

DOI 10.63294/isja/vol3iss11/300 Google Scholar Google Scholar Pages 27-38

Published 2026-09-29

Authors
Haqberdiyev B.R a , Abdukarimova G.D b
Affiliations
a p.f.f.d., dots Alfraganus universiteti, Umumkasbiy fanlar kafedrasi mudiri
b TIQXMMI Milliy tadqiqot universiteti tayanch doktoranti
Alfraganus — Vol. 3, Issue 11 (2026)
PDF (Uzbek)

Abstract

Designing a system for the automatic generation of graphic tasks requires resolving how a spatial object is to be represented and how its orthographic projections are to be produced. This paper comparatively analyses the principal solid representation schemes — constructive solid geometry (CSG), boundary representation (B-rep), procedural-grammatical models and polygonal meshes — against five criteria. The analysis shows that a hybrid use of CSG and B-rep is optimal for the task-generation problem: CSG provides parametric control and regularised Boolean operations, while B-rep supplies the topological information required for constructing projections. The central computational problem in projection construction is hidden-line determination, with classical algorithms exhibiting worst-case complexity of order O(n2). It is substantiated that the Euler–Poincaré relation serves as a necessary condition for verifying the consistency between a solid and its projections, but cannot serve as a sufficient one. It is further shown that the non-uniqueness of solid reconstruction from three orthographic views has direct methodological consequences for the generated tasks. The results enable a justified choice of architecture for the generative module.

Keywords

parametric modelling, constructive solid geometry, boundary representation, orthographic projection, hidden-line removal, geometric constraint system, Euler–Poincaré formula, solid reconstruction, CAD

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