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Reference

Craig S. Kaplan: Curve Evolution Schemes for Parquet Deformations. In: Bridges 2010. Pages 95–102

DOI

Abstract

In this paper, I consider the question of how to carry out aesthetically pleasing evolution of the curves that make up the edges in a parquet deformation. Within the framework of simple arrangements of square tiles, I explore curve evolution models based on grids, iterated function systems, and organic labyrinthine paths.

Extended Abstract

Bibtex

Used References

[1] Marc Alexa, Daniel Cohen-Or, and David Levin. As-rigid-as-possible shape interpolation. In SIG- GRAPH ’00: Proceedings of the 27th annual conference on Computer graphics and interactive tech- niques, pages 157–164, New York, NY, USA, 2000. ACM Press/Addison-Wesley Publishing Co.

[2] David Douglas and Thomas Peucker. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer, 10(2):112–122, 1973.

[3] George Hart. Growth forms. In Craig S. Kaplan and Reza Sarhangi, editors, Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture, pages 207–214. InType Libra, 2009.

[4] Douglas Hofstadter. Metamagical Themas: Questing for the Essence of Mind and Pattern. Bantam Books, 1986.

[5] William S. Huff. The Parquet Deformations, from the Basic Design Studio of William S. Huff at Carnegie-Mellon University, Hochschule f ̈ur Gestaltung and State University of New York at Buffalo from 1960 to 1980. Unpublished.

[6] Craig S. Kaplan. Metamorphosis in Escher’s art. In Bridges 2008: Mathematical Connections in Art, Music and Science, pages 39–46, 2008.

[7] Craig S. Kaplan. Introductory Tiling Theory for Computer Graphics. Morgan & Claypool, 2009.

[8] Craig S. Kaplan and Robert Bosch. TSP art. In Bridges 2005: Mathematical Connections in Art, Music and Science, pages 301–308, 2005.

[9] Xiaofeng Mi, Doug DeCarlo, and Matthew Stone. Abstraction of 2d shapes in terms of parts. In NPAR ’09: Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering, pages 15–24, New York, NY, USA, 2009. ACM.

[10] Hans Pedersen and Karan Singh. Organic labyrinths and mazes. In NPAR ’06: Proceedings of the 4th international symposium on Non-photorealistic animation and rendering, pages 79–86. ACM Press, 2006.

[11] Thomas W. Sederberg, Peisheng Gao, Guojin Wang, and Hong Mu. 2D shape blending: An intrinsic solution to the vertex path problem. In James T. Kajiya, editor, Computer Graphics (SIGGRAPH ’93 Proceedings), volume 27, pages 15–18, August 1993.


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http://archive.bridgesmathart.org/2010/bridges2010-95.pdf

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http://archive.bridgesmathart.org/2010/bridges2010-95.html