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

Manual construction of parametric geometric objects requires repeatedrecalculation of coordinates, curves, and topological relations whenever designparameters change; existing approaches do not sufficiently coordinate process accuracywith computational performance. The aim is to develop an algorithm for automaticallygenerating 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 andnonlinear programming optimization, system design, software testing, and performancemeasurement. Geometric coordinate, parameter, and topological errors were combined ina unified loss function, while the evaluation protocol used identical input conditions; theRMS coordinate error of B-spline and NURBS curves and surfaces was examinedseparately. Results – the benchmark indicator expressed by the number 64 enabled thecomputational and geometric components of automatic generation to be compared withinone testing procedure; when parameters changed in complex topologies, the algorithmconsistently reconstructed coordinates and connections. Conclusion – the unified lossfunction supports parametric model generation with controllable accuracy,reproducibility, and resource adaptability.