Abstract: To create a new, flexible system for volume illustration, we have explored the use of Wang Cubes, the 3D extension of 2D Wang Tiles. We use small sets of Wang Cubes to generate a large variety of nonperiodic illustrative 3D patterns and texture, which otherwise would be too large to use in real applications. We also develop a direct volume rendering framework with the generated patterns and textures. Our framework can be used to render volume datasets effectively and a variety of rendering styles can be achieved with less storage.

Specifically, we extend the nonperiodic tiling process of Wang Tiles to Wang Cubes and modify it for multipurpose tiling. We automatically generate isotropic Wang Cubes consisting of 3D patterns or textures to simulate various illustrative effects. Anisotropic Wang Cubes are generated to yield patterns by using the volume data, curvature, and gradient information. We also extend the definition of Wang Cubes into a set of different sized cubes to provide multiresolution volume rendering. Finally, we provide both coherent 3D geometry-based and texture-based rendering frameworks that can be integrated with arbitrary feature exploration methods.