Development of an algorithm for the automatic generation of parametric geometric models and its implementation in a computer graphics environment
Keywords:
algorithmic analysis, B-spline and NURBS, geometric coordinate, parametric model, topological consistency, unified loss functionAbstract
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. The scientific contribution is an algorithmic protocol that integrates coordinate, parameter, and topological errors and organizes automatic reconstruction within a computer graphics environment. The proposed design also establishes a common basis for evaluating geometry-preserving transformations, parameter updates, and topology-sensitive reconstruction. Its implementation creates a practical route for reducing manual recalculation during iterative modelling and for maintaining consistent geometric relations when a model undergoes structural modification. The protocol can therefore serve as a reusable foundation for further testing of computationally efficient modelling procedures.
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