PARAMETRIK GEOMETRIK MODELLARNI AVTOMATIK SHAKLLANTIRISH ALGORITMINI ISHLAB CHIQISH VA UNI KOMPYUTER GRAFIKASI MUHITIDA AMALGA OSHIRISH

Abstract

Manual construction of parametric geometric objects requires repeated
recalculation of coordinates, curves, and topological relations whenever design
parameters change; existing approaches do not sufficiently coordinate process accuracy
with computational performance. The aim is to develop an algorithm for automatically
generating parametric geometric models, deploy it in a computer graphics environment,
and compare it with established geometric algorithms through a benchmark. Methods –
axiomatic-deductive analysis, multivariable ordinary least-squares regression, linear and
nonlinear programming optimization, system design, software testing, and performance
measurement. Geometric coordinate, parameter, and topological errors were combined in
a unified loss function, while the evaluation protocol used identical input conditions; the
RMS coordinate error of B-spline and NURBS curves and surfaces was examined
separately. Results – the benchmark indicator expressed by the number 64 enabled the
computational and geometric components of automatic generation to be compared within
one testing procedure; when parameters changed in complex topologies, the algorithm
consistently reconstructed coordinates and connections. Conclusion – the unified loss
function supports parametric model generation with controllable accuracy,
reproducibility, and resource adaptability.