Volumetric Modeling with Diffusion Surfaces

Kenshi Takayama, Olga Sorkine-Hornung, Andrew Nealen, Takeo Igarashi

Volumetric Modeling with Diffusion Surfaces


The modeling of volumetric objects is still a difficult problem. Solid texture synthesis methods enable the design of volumes with homogeneous textures, but global features such as smoothly varying colors seen in vegetables and fruits are difficult to model. In this paper, we propose a representation called diffusion surfaces (DSs) to enable modeling such objects. DSs consist of 3D surfaces with colors defined on both sides, such that the interior colors in the volume are obtained by diffusing colors from nearby surfaces. A straightforward way to compute color diffusion is to solve a volumetric Poisson equation with the colors of the DSs as boundary conditions, but it requires expensive volumetric meshing which is not appropriate for interactive modeling. We therefore propose to interpolate colors only locally at user-defined cross-sections using a modified version of the positive mean value coordinates algorithm to avoid volumetric meshing. DSs are generally applicable to model many different kinds of objects with internal structures. As a case study, we present a simple sketch-based interface for modeling objects with rotational symmetries that can also generate random variations of models. We demonstrate the effectiveness of our approach through various DSs models with simple non-photorealistic rendering techniques enabled by DSs.


accompanying video (with narration)


We thank Wilmot Li and Doug DeCarlo for their helpful suggestions on illustrative renderings, Murphy Stein for his narration of the accompanying video, and the anonymous reviewers for their valuable comments and feedback. This work was supported in part by the National Science Foundation (grants IIS- 0905502 and IIS-0916845), JSPS, JST ERATO, and NYU URCF.