Hybrid Approaches to 3D Avatar Modeling in Virtual Learning Environments: An Analysis of Spline, Polygonal, and R-Function Methods

This paper presents a comparative analysis of spline, polygon, and R-function-based approaches to modeling 3D avatars for virtual university platforms, focusing specifically on the modeling stage rather than later interaction or task execution. Each method is examined for its inherent strengths: spline models enable smooth and continuous surface generation, polygonal models ensure broad compatibility across virtual learning platforms, and R-function-based models provide mathematically precise boundary representation. This methodological relevance is particularly significant for distributed virtual learning systems and networked educational environments. As a result, the study demonstrates that hybrid modeling enhances geometric realism, optimizes computational performance, and strengthens the applicability of 3D avatars within virtual university systems.

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