TOPOLOGICAL STRUCTURES OF VIRTUAL REALITY

Abstract

This paper addresses an urgent scientific and practical problem of enhancing the computational rendering efficiency and ensuring the stability of dynamic deformation of 3D surfaces in real-time virtual reality (VR) systems. Modern 3D scanning, medical image segmentation, and generative artificial intelligence (AI) technologies generate high-poly unstructured meshes with excessive density (up to 107 polygons) and numerous topological defects. Direct rendering of such objects on standalone VR headsets causes a critical frame rate drop below the standard 90 FPS, triggering cybersickness. Traditional geometry simplification methods chaotically destroy the structure of edge loops, leading to visual artifacts and mesh collapsing during animation.

To overcome these limitations, an adaptive retopology algorithm has been developed based on the decomposition of geometric data into two independent levels: a computationally lightweight regular quad-mesh and a high-frequency detail map for hardware-accelerated lighting calculation. The mathematical framework of the algorithm combines initial simplification via the quadric error metric (QEM) with Euler characteristic control to preserve the topological genus of the surface, alongside the generation of a tangential orientation cross-field. This enables the automatic alignment of polygon edges along the lines of principal curvatures and the relocation of topological singularities into static zones of the object that remain immobile during animation.

Experimental validation of the developed algorithm was performed within the Unreal Engine 5.5 environment on a standalone Meta Quest 3 VR headset and a stationary PCVR system. Three types of models were utilized for testing: a high-precision human head scan, an anatomical heart model, and an industrial mechanical joint. The simulation results demonstrate that the proposed method reduces the average geometric Hausdorff distance by 4.5 times compared to traditional decimation. Furthermore, the single-frame rendering time on Meta Quest 3 was reduced to 8.3–10.8 ms, enabling a stable frame rate of 92–120 FPS.

Keywords: topological structures, modeling, neural networks, virtual reality, avatar facial expressions.