## Abstract

Most mathematical marbling simulations generate patterns for texture mapping and surface decoration. We explore the application of three-dimensional deformations inspired by mathematical marbling as a suite of tools to enable creative shape design. Our tools are expressed as analytical functions of space and are volume-preserving vector fields, meaning that the modelling process preserves volumes and avoids self-intersections. Complicated deformations are easily combined to create complex objects from simple ones. To achieve smooth and high-quality shapes, we also present a mesh refinement and simplification algorithm adapted to our deformations. We show a number of examples of shapes created with our technique in order to demonstrate its power and expressiveness.

## Keywords

Computational geometry Shape modelling Volume-preserving vector fields Marbling art## Notes

### Acknowledgements

Shufang Lu was supported by the National Natural Science Foundation of China (Grant No. 61402410) and the China Scholarship Council. Xiaogang Jin was supported by the National Natural Science Foundation of China (Grant No. 61472351).

## Supplementary material

Supplementary material 1 (avi 23583 KB)

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