Professor Kaplan studies the application of computer graphics 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 and 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; traditional Chinese and European papercutting; and graphic design based on calligraphy.
Professor Kaplan has also conducted research and maintains interests in human-computer interaction, computational geometry (including computational aspects of tiling theory) and programming language design.