L-systems in Geometric Modeling

Przemyslaw Prusinkiewicz
(University of Calgary)
Mitra Shirmohammadi
(University of Calgary)
Faramarz Samavati
(University of Calgary)

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.

Invited Presentation in Ian McQuillan and Giovanni Pighizzini: Proceedings Twelfth Annual Workshop on Descriptional Complexity of Formal Systems (DCFS 2010), Saskatoon, Canada, 8-10th August 2010, Electronic Proceedings in Theoretical Computer Science 31, pp. 3–14.
Published: 7th August 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.31.3 bibtex PDF

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