Published in ACM Transactions on Graphics, Volume 27, Issue 1

Modeling and Rendering Heterogeneous Translucent Materials using Diffusion Equation

fabrication resutls

Synthesis of a bunny with marble material. (a) Physical sample. (b) Bunny rendered with the acquired material model. (c) After interactive editing to add patterns. (d) After placing a pattern at a different depth.


In this paper, we propose techniques for modeling and rendering of heterogeneous translucent materials that enable acquisition from measured samples, interactive editing of material attributes, and real-time rendering. The materials are assumed to be optically dense such that multiple scattering can be approximated by a diffusion process described by the diffusion equation. For modeling heterogeneous materials, we present an algorithm for acquiring material properties from appearance measurements by solving an inverse diffusion problem. Our modeling algorithm incorporates a regularizer to handle the ill-conditioned inverse problem, an adjoint method to dramatically reduce the computational cost, and a hierarchical GPU implementation for further speedup. To display an object with known material properties, we present an algorithm that performs rendering by solving the diffusion equation with the boundary condition defined by the given illumination environment. This algorithm is centered around object representation by a polygrid, a grid with regular connectivity and an irregular shape, which facilitates the solution of the diffusion equation in arbitrary volumes. Because of the regular connectivity, our rendering algorithm can be implemented on the GPU for real-time performance. We demonstrate our techniques by capturing materials from physical samples and performing real-time rendering and editing with these materials.


Appearance modeling and rendering, diffusion approximation, subsurface scattering



 author = {Wang, Jiaping and Zhao, Shuang and 
 Tong, Xin and Lin, Stephen and Lin, Zhouchen and 
 Dong, Yue and Guo, Baining and Shum, Heung-Yeung},
 title = {Modeling and rendering of heterogeneous 
 translucent materials using the diffusion equation},
 journal = {ACM Trans. Graph.},
 issue_date = {March 2008},
 volume = {27},
 number = {1},
 month = mar,
 year = {2008},
 issn = {0730-0301},
 pages = {9:1--9:18},
 articleno = {9},
 numpages = {18},
 url = {},
 doi = {10.1145/1330511.1330520},
 acmid = {1330520},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {Appearance modeling and rendering, 
 diffusion approximation, subsurface scattering},



The snail in Figure 20 was modeled by Feiyang Tong. The authors thank Ming Jiang, Tie Zhou, Ruo Li and Guanquan Zhang for discussions on inverse diffusion, and the anonymousreviewers for their helpful suggestions and comments. This work was done when Shuang Zhao, and Yue Dong were visiting students in Microsoft Research Asia.