PROCEDURAL TEXTURE SYNTHESIS IN 3D RECONSTRUCTION

Abstract

The article explores the advantages of procedural texture synthesis in 3D reconstruction of historical objects and creating high-quality textures in virtual environments. The main focus is on methods for creating unique and realistic textures using fractal and space curves, such as the Cantor set, Gilbert and Gosper curves. The core contribution of the work lies in the systematic application of fractal geometry and space-filling curves to texture generation. The methodology rigorously examines three fundamental mathematical constructs: the Cantor set for creating discontinuous and dust-like patterns, the Gilbert curve for locality-preserving 2D space traversal, and the Gosper curve for generating hexagonal and snowflake-like tiling structures. By parameterizing these curves and integrating them with fractal noise functions, the authors propose a hybrid algorithmic pipeline that synthesizes textures at runtime, allowing for infinite variation and seamless detail across different levels of zoom (detail-invariant synthesis).