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.
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