Physics and mathematics of marbling

Duration: 46 mins 46 secs

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Description:	Jaffer, A Tuesday 28th November 2017 - 11:10 to 11:50


Created:	2017-11-30 13:27
Collection:	Growth form and self-organisation
Publisher:	Isaac Newton Institute
Copyright:	Jaffer, A
Language:	eng (English)


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

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

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