Procedural Multiscale Geometry Modeling using Implicit Functions

TL;DR

This work tackles the challenge of modeling geometric structures across mesoscopic to microscopic scales to predict macroscale appearance. It introduces a procedural framework based on implicit surfaces and adaptive sphere tracing that synthesizes multiscale microstructures on demand without precomputation, covering suspended particulate, agglomerated, and piling geometries as well as implicit periodic patterns. Key contributions include a dual-grid particulate modeling approach with spatial variation, particle agglomeration and piling mechanisms, implicit periodic function synthesis, adaptive sphere-tracing optimization, and reconstruction from image and SDF exemplars via both parametric and gradient-free optimization. The results demonstrate realistic appearance variation due to anisotropy and spatial correlations, with practical implications for graphics, materials science, and potentially fabrication and dynamic simulations.

Abstract

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.

Figures (13)

• Figure 1: To consider the particles that may overlap an arbitrary query point $\bm{p}$, we check that the bounding sphere radius of a particle is at most half a grid cell width. Once we identify the cell in the stippled dual grid to which $\bm{p}$ belongs, the particles that could potentially overlap must be found in the $2^D$ grid cells that intersect with the stippled dual-grid cell (where $D$ represents the number of dimensions).
• Figure 2: Left: Red blood cell (RBC) particle cloud modeled using our method and an implicit function available for the shape of these cells in kuchel2021surface. Right: A rendering of sparkling water with spatially varying air bubble particle sizes. The bubbles are smaller and sparser at the bottom, gradually becoming larger and denser towards the top of the liquid.
• Figure 3: Inspired by a photo of air bubbles in ice (right), we used our multi-phase particle cloud approach to model a similar material (left). Our model has ice as the host medium and contains air particles that vary in size and shape with the spatial location in the medium, transitioning from spherical to non-spherical.
• Figure 4: Particle agglomeration structures generated using Bézier curves as polynomial functions on grid cell $\bm{q}$ in the 27-neighbourhood of the point $\bm{p}$. The shape of each agglomerate is different from the others. It is spatially varying throughout a large section of microgeometry. The particle arrangement mimics a snapshot of a gelation process.
• Figure 5: Left: Fibrous microstructure with diameter 1mm generated using particle agglomeration method, right: same microstructure as left but smooth it using the smooth min operator. We generate the snapshot of the processes of particle agglomeration (the clustering of particles) and crystal growth using polynomial functions on the regular lattice of particle clouds.