MATHEMATICAL FOUNDATIONS OF AI-ASSISTED AUTOMATED TEXTURING OF 3D OBJECTS
Abstract The article explores the mathematical foundations and architectural solutions for developing an automated texturing system for three-dimensional objects using artificial intelligence. It analyzes the limitations of classical UV mapping and justifies the use of a projection mapping method combined with the developed "Smart Stencil" algorithm to eliminate visual artifacts and texture stretching. Particular attention is given to the integration of latent diffusion models and the ControlNet architecture, which utilizes normalized depth maps to accurately control the spatial structure of textures. The proposed approach enables efficient generation of high-quality seamless textures on consumer-grade hardware in alignment with the actual geometric shape of 3D models.