Modular Line-Based Halftoning via Recursive Division

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Abdalla Ahmed: Modular Line-Based Halftoning via Recursive Division. In: Computational Aesthetics 2014.



We present a new approach for stippling by recursively dividing a grayscale image into rectangles with equal amount of ink, then we use the resulting structure to generate novel line-based halftoning techniques. We present four different rendering styles which share the same underlying structure, two of which bear some similarity to Bosch-Kaplan's TSP Art and Inoue-Urahama's MST Halftoning. The technique we present is fast enough for real time interaction, and at least one of the four rendering styles is well-suited for maze construction.

Extended Abstract


author = {Ahmed, Abdalla G. M.},
title = {Modular Line-based Halftoning via Recursive Division},
booktitle = {Proceedings of the Workshop on Non-Photorealistic Animation and Rendering},
series = {NPAR '14},
year = {2014},
isbn = {978-1-4503-3020-6},
location = {Vancouver, British Columbia, Canada},
pages = {41--48},
numpages = {8},
url = { },
doi = {10.1145/2630397.2630403},
acmid = {2630403},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {halftoning, line art, maze, non-photorealistic rendering, stippling},

Used References

Ergun Akleman , Qing Xing , Pradeep Garigipati , Gabriel Taubin , Jianer Chen , Shiyu Hu, Special Section on Expressive Graphics: Hamiltonian cycle art: Surface covering wire sculptures and duotone surfaces, Computers and Graphics, v.37 n.5, p.316-332, August, 2013

Robert Bosch , Adrianne Herman, Continuous line drawings via the traveling salesman problem, Operations Research Letters, v.32 n.4, p.302-303, July, 2004

Bosch, R. 2011. Opt Art: Special Cases. In Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture, Tessellations Publishing, Phoenix, Arizona, R. Sarhangi and C. H. Séquin, Eds., 249--256. Available online at

Cameron Browne, Chaos and Graphics: Truchet curves and surfaces, Computers and Graphics, v.32 n.2, p.268-281, April, 2008

Cirulli, G., 2014. 2048, March. Available online at, as of Apr. 14, 2014.

Kohei Inoue , Kiichi Urahama, Chaos and Graphics: Halftoning with minimum spanning trees and its application to maze-like images, Computers and Graphics, v.33 n.5, p.638-647, October, 2009

Kaplan, C. S., and Bosch, R. 2005. Tsp art. In Renaissance Banff: Mathematics, Music, Art, Culture, Canadian Mathematical Society, Banff, Alberta, R. Sarhangi and R. V. Moody, Eds., 301--308. Available online at

Victor Ostromoukhov , Roger D. Hersch, Artistic screening, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.219-228, September 1995

Hans Pedersen , Karan Singh, Organic labyrinths and mazes, Proceedings of the 4th international symposium on Non-photorealistic animation and rendering, June 05-07, 2006, Annecy, France

Pnueli, Y., and Bruckstein, A. M. 1996. Gridless halftoning: A reincarnation of the old method. Graphical Models and Image Processing 58, 1, 38--64.

Pullen, W. D. Maze Creation Algorithms. Available online at, as of Apr. 14, 2014.

Reimann, D. A. 2012. Modular knots from simply decorated uniform tessellations. In Proceedings of ISAMA 2012: Eleventh Interdisciplinary Conference of the International Society of the Arts, Mathematics, and Architecture, 63--69.

Secord, A. 2002. Random Marks on Paper: Non-Photorealistic Rendering with Small Primitives. Master's thesis, Department of Computer Science, UBC.

Adrian Secord, Weighted Voronoi stippling, Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering, June 03-05, 2002, Annecy, France

Smith, C., and Boucher, P. 1987. The Tiling Patterns of Sebastian Truchet and the Topology of Structural Hierarchy. Leonardo 20(4), 373--385.

Luiz Velho , Jonas de Miranda Gomes, Digital halftoning with space filling curves, ACM SIGGRAPH Computer Graphics, v.25 n.4, p.81-90, July 1991

Jie Xu , Craig S. Kaplan, Image-guided maze construction, ACM SIGGRAPH 2007 papers, August 05-09, 2007, San Diego, California


Full Text

[extern file]

intern file

Sonstige Links