Geometry-guided synthesis of patterns and textures

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Ornamentation-the decoration of surfaces with patterns or textures-has been a form of human artistic expression since prehistory. This practice remains vital today: ornamental patterns can be found in product packaging, graphic design, clothing, interior design, and architecture, not to mention computer-generated environments. Ornamentation is useful in any context where a drawing or surface might benefit from extra visual impact, or as a means of breaking up a blank architectural form with detail at a human scale. The simplest varieties of ornamentation are flat, repeating geometric patterns that you might find printed on fabrics for clothing or upholstery. These patterns give life to the objects and surfaces to which they are applied, but they do not typically adapt or conform to those surfaces. When sewing a garment from a set of printed fabric pieces, we accept that the pattern will jump discontinuously at the seams. A flat pattern applied in an architectural setting will appear to fold or tear when wrapped around a building with a curved skin. The goal of this research is to invent new mathematical and computational techniques that will enhance our abilities to design, apply, and evaluate ornamentation. I will consider three main research objectives that contribute to this goal. I will study the expressivity of computer ornamentation, giving artists and designers more control over the styles and shapes of features in a pattern, and a broader range of surfaces to which patterns can be applied without producing seams or tears. I will investigate the application of ornamentation in new spaces, including patterns that adapt seamlessly to surfaces like garments, assembled from multiple disconnected pieces, and animated patterns in two dimensions of space and one of time. Finally, I will explore the evaluation of ornamentation, using ideas from perceptual psychology to provide a rigorous scientific basis for measuring and comparing the quality of patterns. This research program will allow me to train numerous graduate and undergraduate students in the latest techniques in the intersection of geometry and computer graphics. Students will develop their mathematical, programming, and communication skills, and emerge with a broad interdisciplinary view of scientific research, prepared for careers in academia or in industrial research and development. My students and I will create tools that artists and designers can use to draw patterns with greater flexibility, control, and expressive range than they could before. Artists will also be able to apply their patterns in a wider range of decorative contexts. These tools, whether as standalone commercial or open-source software, or add-ons for popular packages like Adobe Illustrator, will find exciting commercial and industrial applications in the worlds of art, design, and architecture.