Abstract

Co-authors: Shufang Lu (Zhejiang University of Technology), Xiaogang Jin (Zhejiang University), Fei Gao (Zhejiang University of Technology), Xiaoyang Mao (University of Yamanashi)

Ink marbling refers to techniques for creating intricate designs in colored inks floating on a liquid surface. If the marbling motions are executed slowly, then this layer of inks can be modeled as a two-dimensional incompressible Newtonian fluid. In this highly constrained model many common marbling techniques can be exactly represented by closed-form homeomorphisms. These homeomorphisms can be composed and compute the composite mapping at any resolution orders of magnitude faster than finite-element fluid-dynamics methods.Pictorial designs for flowers and animals use short strokes of a single stylus; presented is a closed form velocity field for Oseen fluid flow and its application to creating short stroke marbling homeomorphisms.These approaches extend to three-dimensions and allow creation of coherent marbled surfaces on any shape while avoiding the process of texture mapping entirely.

Related Links

• https://www.computer.org/csdl/mags/cg/2012/06/mcg2012060026.html  Mathematical Marbling
• https://www.youtube.com/watch?v=ZgVbIaKhC_4  Mathematical Marbling video
• https://www.computer.org/csdl/mags/cg/2017/02/mcg2017020090.html  Solid Mathematical Marbling
• https://arxiv.org/pdf/1702.02106  Oseen Flow in Ink Marblnig
• http://people.csail.mit.edu/jaffer/Marbling - Mathematical Marbling website