Suspended Particulate Media: The framework procedurally generates spatially varying, multiscale particulate media without precomputation or tiling, illustrated by an icy Stanford bunny whose air bubbles smoothly transition from large and sparse at the top to small and dense at the bottom, as shown in close-up insets. Using multiple noise scales combined via implicit surfaces and a multiscale sphere tracing algorithm, it efficiently renders macro-, meso-, and micro-scale details, where individual particles become visible when large enough or viewed up close. Particle Agglomeration: Particles from a suspended cloud are selected using polynomial functions and grow in size to form agglomerates. Particle Piling: On-the-fly granular media can also be piled without inter-penetrations like rock pile generation, using deformations of the implicit surfaces, as can be seen in the zoomed-in contact point between grains. Notice that grains can have both convex and concave shapes.

News

• August, 2025: Paper accepted in CGF (PG 2025).
• August, 2025: Website launched.

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 surfaces and 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 demonstrate its potential in the appearance modeling of volumetric materials and investigate how spatially varying properties affect the perceived macroscale appearance. As a proof of concept, we show that microstructures created by our framework can be reconstructed from image and distance values defined by implicit surfaces, using both first-order and gradient-free optimization methods.

Approach

We can create complex, multiscale spatially varying geometries like particles, fibers, pores, and layers using random but controlled space-filling implicit primitive distributions, and then apply spatially varying transformations. We apply various operations to particles to achieve different properties, such as anisotropy, correlation, piling, and agglomeration. Some regular, repeating patterns, such as gyroid (implicit periodic surface), can generate various geometries and are often faster to compute. Dual grid: To consider the particles that may overlap an arbitrary query point 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 point p belongs, the particles that could potentially overlap must be found in the $2^n$ n grid cells that intersect with the stippled dual-grid cell (where $\mathrm{n}$ represents the number of dimensions).

Results Gallery

Supplemental video showcasing how our framework creates diverse materials, revealing details from the macroscale down to the microscale.

We used our multi-phase particle cloud approach to model an ice material with air bubbles (left) matching the appearance of real ice (right). 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.

Inspire by A Radiative Transfer Framework for Spatially-Correlated Materials paper, our framework compares how particle orientation and spatial correlation affect material appearance. The top row shows isotropic versus anisotropic particle alignments (along x and z), influencing light transport while keeping particle density constant. The bottom row illustrates how random, clustered, and regular particle distributions (with the same density) lead to different macroscopic visual effects.

Particle agglomeration resembles a snapshot of a gelation process. Particle agglomeration structures generated using spatially varying Bezier curves as polynomial functions on grid cell q in the 27-neighbourhood of the point p. Each agglomerate has a distinct shape.

We generate a multiscale rockpile (left) without physically-based simulation, where smaller grains settle at the bottom and larger grains remain at the top, with well-defined arrangements across different scales without interprenetations. In the same cloud, we can also control grain morphology, ranging from convex to concave shapes (right).

Downloads

Code

The code and data provided are property of the Technical University of Denmark and Universidad de Zaragoza - free for non-commercial purposes.

Bibtex

Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956585 (PRIME). We would like to thank Adolfo Muñoz, Adrian Jarabo, Jeppe Frisvad and Andreas Bærentzen for their support and insightful discussions about the project; Nestor Monzon for proofreading; and Mark Bo Jensen and Jeppe Frisvad for creating the Figure 12.