Cited By
View all- Kim TAugsdörfer UWallner J(2015)Quaternion Julia set shape optimizationProceedings of the Eurographics Symposium on Geometry Processing10.1111/cgf.12705(167-176)Online publication date: 6-Jul-2015
Subdivision schemes and attractors
Authors: 
S. Schaefer, D. Levin, R. GoldmanAuthors Info & Claims
S. Schaefer, D. Levin, R. GoldmanAuthors Info & ClaimsAbstract
Subdivision schemes generate self-similar curves and surfaces. Therefore there is a close connection between curves and surfaces generated by subdivision algorithms and self-similar fractals generated by Iterated Function Systems (IFS). We demonstrate that this connection between subdivision schemes and fractals is even deeper by showing that curves and surfaces generated by subdivision are also attractors, fixed points of IFS's. To illustrate this fractal nature of subdivision, we derive the associated IFS for many different subdivision curves and surfaces without extraordinary vertices, including B-splines, piecewise Bezier, interpolatory four-point subdivision, bicubic subdivision, three-direction quartic box-spline subdivision and Kobbelt's √3-subdivision surfaces. Conversely, we shall show how to build subdivision schemes to generate traditional fractals such as the Sierpinski gasket and the Koch curve, and we demonstrate as well how to control the shape of these fractals by adjusting their control points.
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- Subdivision schemes and attractors
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- SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
- EUROGRAPHICS: The European Association for Computer Graphics
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Eurographics Association
Goslar, Germany
Publication History
Published: 04 July 2005
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SGP '05
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- SIGGRAPH
- EUROGRAPHICS
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SGP '05 Paper Acceptance Rate 22 of 87 submissions, 25%;
Overall Acceptance Rate 64 of 240 submissions, 27%
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View all- Kim TAugsdörfer UWallner J(2015)Quaternion Julia set shape optimizationProceedings of the Eurographics Symposium on Geometry Processing10.1111/cgf.12705(167-176)Online publication date: 6-Jul-2015