Solid Mathematical Marbling.

Years of research have been devoted to computer-generated two-dimensional marbling. However, three-dimensional marbling has yet to be explored. In this paper, we present mathematical marbling of three-dimensional solids which supports a compact random-access vector representation. Our solid marbling textures are created by composing closed-form 3D pattern tool functions. These tool functions are an injection function and five deformation functions. The injection function is used to generate basic patterns, and the deformation functions are responsible for transforming the basic pattern into complex marbling effects. The resulting representation is feature preserving and resolution-independent. Our approach can render high-quality images preserving both the sharp features and the smooth color variations of a solid texture. When implemented on the GPU, our representation enables efficient color evaluation during the real-time solid marbling texture mapping. The color of a point in the volume space is computed by the 3D pattern tool functions from its coordinates. Our method consumes very little memory because only the mathematical functions and their corresponding parameters are stored. In addition, we develop an intuitive user interface and a genetic algorithm to facilitate the solid marbling texture authoring process. We demonstrate the effectiveness of our approach through various solid marbling textures and 3D objects carved from them.

Solid Mathematical Marbling.

Years of research have been devoted to computer-generated 2D marbling, whereas 3D marbling has yet to be explored. The proposed mathematical marbling of 3D solids supports a compact random-access vector representation, creating solid marbling textures by composing closed-form 3D pattern tool functions. The resulting representation is feature-preserving and resolution-independent, and it consumes very little memory. To facilitate the solid-marbling texture authoring process, the authors also developed an intuitive user interface and a genetic algorithm.

Mathematical marbling.

In this paper, the proposed method takes a mathematical approach with closed-form expressions to simulate marbling. This method improves control, ease of implementation, parallelism, and speed, enabling real-time visual feedback and creation of vivid flowing animations. Users can start designs from a blank sheet, raster images, or videos.