Procedural Multiscale Geometry Modeling using Implicit Functions

Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is challenging but essential for computer graphics, engineering, and materials science. We present a framework inspired by hypertexture methods, using implicit functions and adaptive sphere tracing to synthesize multiscale structures on the fly without precomputation. This framework models volumetric materials with particulate, fibrous, porous, and laminar structures, allowing control over size, shape, density, distribution, and orientation. We enhance structural diversity by superimposing implicit periodic functions while improving computational efficiency. The framework also supports spatially varying particulate media, particle agglomeration, and piling on convex and concave structures, such as rock formations (mesoscale), without explicit simulation. We show its potential in the appearance modeling of volumetric materials and explore how spatially varying properties influence perceived macroscale appearance. Our framework enables seamless multiscale modeling, reconstructing procedural volumetric materials from image and signed distance field (SDF) synthetic exemplars using first-order and gradient-free optimization.