Craig Steven KaplanResearch interests

Professor Kaplan studies the application of mathematical and computational techniques in art, illustration, ornamentation, and design. This research area is rooted in computer graphics, but involves forays into art (to study historical sources) classical and computational geometry (to develop mathematical and computational models of ornament), and computer-aided design and manufacturing. His goal is to push forward the frontiers of computer graphics and geometry in order to put new tools in the hands of artists and designers. These tools should be sensitive to the artist's needs and desires---they should offer new aesthetic opportunities without usurping the artistic process.

Topics explored by Professor Kaplan in the past include: the art of M.C. Escher, particularly his regular divisions of the plane; the mathematical structure and generation of Islamic geometric patterns; black-and-white line art, especially mazes and labyrinths; the creation of pixel art illustrations from vector drawings; and the example-based synthesis and perceived aesthetics of discrete element textures.

Professor Kaplan is one of the organizers of the annual Bridges conference on art and mathematics, and serves as editor-in-chief of Journal of Mathematics and the Arts.

Degrees and awards

BMath (Waterloo), MS, PhD (Washington)

Representative publications

Z. AlMeraj, C.S. Kaplan, and P. Asente. Towards effective evaluation of geometric texture synthesis algorithms. In Proceedings of the Symposium on Non-Photorealistic Animation and Rendering, NPAR ‘13, pages 5–14. ACM Press, 2013.

T. Inglis, D. Vogel, and C.S. Kaplan. Rasterizing and antialiasing vector line art in the pixel art style. In Proceedings of the Symposium on Non-Photorealistic Animation and Rendering, NPAR ‘13, pages 25–32. ACM Press, 2013.

J. Xu and C. S. Kaplan. Image-guided maze construction. Proceedings of SIGGRAPH, 2007.

C.S. Kaplan. Introductory Tiling Theory for Computer Graphics.  Morgan & Claypool, 2009.

C.S. Kaplan and D.H. Salesin, Islamic Star Patterns in Absolute Geometry, ACM Transactions on Graphics, 23(2):97-119, 2004.

University of Waterloo
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