A Micro-Ellipsoid Model for Wet Porous Materials Rendering

TL;DR

This work introduces a transmittable micro-ellipsoid model to render wet porous materials by extending the anisotropic radiative transfer equation to account for porosity $P$ and saturation $S$. It defines a micro-ellipsoid particle representation and derives attenuation coefficients and a phase function for aggregated particles, enabling volume rendering that captures both reflection and transmission. To address practical rendering, the authors propose WetSpongeCake, a position-free BSDF that integrates single and multiple scattering, delta transmission, and air-liquid interfaces within a layered framework, with phase-function and parameter-mapping networks facilitating efficient multiple-scattering handling. The approach is validated across diverse scenes (sand, cloth, sculptures), showing close agreement with real photographs and outperforming empirical or less physically grounded methods, while offering physically meaningful control and applicability to a range of wet-porous appearances.

Abstract

Wet porous materials, like wet ground, moist walls, or wet cloth, are common in the real world. These materials consist of transmittable particles surrounded by liquid, where the individual particle is invisible in the macroscopic view. While modeling wet porous materials is critical for various applications, a physically based model for wet porous materials is still absent. In this paper, we model these appearances in the media domain by extending the anisotropic radiative transfer equation to model porosity and saturation. Then, we introduce a novel particle model -- micro-ellipsoid -- by treating each particle as a transmittable ellipsoid, analogous to a micro-flake, to statistically characterize the overall optical behavior of the medium. This way, the foundational theory for media with porosity and saturation is established. Building upon this new medium, we further propose a practical bidirectional scattering distribution function (BSDF) model within the position-free framework--WetSpongeCake. As a result, our WetSpongeCake model is able to represent various appearances of wet porous materials using physical parameters (e.g., porosity and saturation), allowing both reflection and transmission. We validated our model through several examples: a piece of wet cloth, sand saturated with different liquids, or damp sculptures, demonstrating its ability to match real-world appearances closely.

Figures (14)

• Figure 1: Wet porous material is made of discrete particles, air, and liquid. After a light ray enters this material, it can be either reflected or refracted by the particle surface and travels in the air or the liquid. The ray is bounced within this material until it leaves the surface.
• Figure 2: Several examples of parameters defined on particles and medium.
• Figure 3: Left: Comparison of several transmittance functions w.r.t. the traveling distance. Our saturation is set as 0. Right: our transmittance function as a function of the distance across several parameters.
• Figure 4: (a) Each particle is modeled as an ellipsoid, defined by eigenvectors ($\omega_1$, $\omega_2$ and $\omega_3$) and eigenvalues, where $\omega_3$ is aligned with the ellipsoid normal. (b) the particle phase function is defined as the possibility of all paths originating from the projected area of $\omega_i$, traveling in direction $\omega_i$, bouncing within the ellipsoid, and finally exiting in direction $\omega_o$.
• Figure 5: Visualization of the phase function for particles surrounded by air and water, respectively, with the mean cosine value provided in the bottom-right corner. The remaining parameters are set to $\eta_p = 1.8$, $\sigma = 1$, and $\sigma_p = 1$. Additional results are provided in the supplementary material.