Polygonal Surface Advection applied to Strange Attractors

Strange attractors of 3D vector field flows sometimes have a fractal geometric structure in one dimension, and smooth surface behavior in the other two. General flow visualization methods show the flow dynamics well, but not the fractal structure. Here we approximate the attractor by polygonal surfa...

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Bibliographic Details
Published in:Computer graphics forum 2010-09, Vol.29 (7), p.2281-2290
Main Authors: Yan, S., Max, N., Ma, K.-L.
Format: Article
Language:English
Subjects:
and systems
Approximation
Chaos theory
Computer based modeling
Computer graphics
Fractal analysis
Fractal geometry
Fractals
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
languages
Mathematical analysis
Polygons
Preserves
Studies
Subdivisions
Three dimensional
Turbulent flow
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Summary:Strange attractors of 3D vector field flows sometimes have a fractal geometric structure in one dimension, and smooth surface behavior in the other two. General flow visualization methods show the flow dynamics well, but not the fractal structure. Here we approximate the attractor by polygonal surfaces, which reveal the fractal geometry. We start with a polygonal approximation which neglects the fractal dimension, and then deform it by the flow to create multiple sheets of the fractal structure. We use adaptive subdivision, mesh decimation, and retiling methods to preserve the quality of the polygonal surface in the face of extreme stretching, bending, and creasing caused by the flow. A GPU implementation provides efficient visualization, which we also apply to other turbulent flows.
ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2010.01817.x