Research Statement
My research lies at the intersection of computer science, mathematics, and the arts, with a focus on transdisciplinary methodologies that bridge technical innovation and creative expression. Over nearly three decades, I have pursued a diverse research agenda encompassing computer graphics, geometric modeling, and topology, with particular emphasis on shape modeling, computer-aided sculpting, and manifold mesh generation. My work aims to push the boundaries of human creativity by enabling new forms of artistic, scientific, and engineering expression through computational tools.
A significant area of my research has been the development of topological mesh modeling techniques, particularly through the creation of the TopMod system. This manifold mesh modeling tool introduced innovative approaches for the construction and manipulation of 2-manifold and non-manifold surfaces, enabling artists and designers to explore complex geometries. TopMod has been widely adopted by artists and educators, with its impact extending to over 100 educational and creative projects showcased online. I have also delved deeply into mathematical topology, exploring new algorithms for shape generation and contributing to our understanding of geometrical and topological constraints in design.
Beyond technical modeling, my research incorporates artistic and cultural dimensions. As a professional cartoonist and illustrator, I leverage my creative background to design computational tools that resonate with artistic workflows. This unique perspective allows me to create systems that are not only functionally robust but also intuitively accessible to creative practitioners. My collaborations with students and professionals in art, architecture, and visualization have resulted in numerous projects that explore the interplay between aesthetics and computation.
In recent years, my focus has expanded to the exploration of links, knots, and woven structures, inspired by their applications in engineering, science, and visual art. I am particularly interested in developing systematic approaches to model these structures using computational geometry and topology. By combining artistic intuition with formal mathematical techniques, my research aims to uncover novel applications of knots and links in areas ranging from physical simulations and 3D printing to wearable design and biomimetic structures.
Education and mentorship are integral to my research ethos. I have supervised nearly 100 graduate students, many of whom now hold positions at leading companies such as PIXAR, Disney, DreamWorks, Google, and Facebook. My teaching philosophy emphasizes the integration of artistic creativity with technical rigor, fostering a new generation of researchers and practitioners who thrive at the confluence of disciplines.
Looking forward, my research aims to deepen the synergy between computation and creativity by exploring emerging fields such as AI-driven design, interactive storytelling, and computational aesthetics. By fostering collaborations across disciplines, I seek to develop innovative tools and frameworks that empower creators and address pressing challenges in visualization, communication, and design.
Overview
As a researcher, I am deeply interested in the introduction of new artistic concepts, styles, and techniques. I find great excitement in developing unconventional artistic approaches and continuously create computational tools and techniques to support this purpose. These tools and techniques enable me to produce a wide variety of artworks as proof of concept. My primary strength in research lies in organizing diverse teams with varying interests, where I define the problem and outline a rough solution. I have excelled in motivating my teams to explore these problems in detail, achieving impactful results despite limited resources. Working within a Master’s program with limited access to Ph.D. students, I have adapted by focusing on fresh ideas and creativity, producing compelling results with small teams and constrained resources.
I am particularly fascinated by non-representational sculptures and the unconventional architectural designs of figures such as Frank Gehry, Santiago Calatrava, and Norman Foster. These sculptural and architectural forms differ fundamentally from engineering shapes—they are large, one-of-a-kind objects where aesthetics take precedence over high precision. My research has focused on discovering new concepts for developing more intuitive and powerful shape modeling systems, enabling designers to create such unusual and aesthetically pleasing forms easily. My primary goals in shape modeling have been to ensure interactivity and enable topology changes, such as adding or deleting handles, opening or closing holes, and connecting or disconnecting objects. Traditional shape modeling methods, such as subdivision techniques and implicit methods, fail to fully meet these goals due to mathematical limitations: subdivision methods cannot handle topology changes, and implicit methods cannot guarantee interactivity. Much of my influential work in topological and implicit modeling has revolved around overcoming these mathematical constraints. My recent research seeks to develop new methods that allow users to intuitively design unique and aesthetic shapes, with applications in environmental design, cinema, games, and web design, alongside architecture and sculpture.
I classify my work based on the methods I use and the type of results achieved. My most influential contributions have been motivated by the creation of new sculptural forms and are, therefore, strongly related to shape modeling. Key topics in this area include topological mesh modeling, implicit modeling, and conceptual architecture. However, artistic depiction also plays a significant role in my research, encompassing works aimed at discovering new conceptual sculptural forms, such as 3D caricatures. This is one reason I refer to this area as artistic depiction rather than non-photorealistic rendering. Artistic depiction further includes innovations such as 3D Chinese painting, volume painting, cubist rendering, and video screening. My research in rendering and visualization covers not only visualization techniques but also practical developments such as our recent work on rendering hair with global illumination.
While my interest in shape modeling often focuses on non-representational forms, I also explore representational sculptural works, such as volume painting and 3D caricatures. Volume painting involves creating events in space-time through a sampling and reconstruction process that populates three-dimensional space with objects. Caricature, a personal passion of mine, has driven me to develop artistic methods to identify and exaggerate facial features, producing highly exaggerated 3D caricatures. Recently, I have refined these techniques further, creating new methods to construct 3D faces and caricatures.
My research is fundamentally motivated by artistic concerns, a shared characteristic of many computer graphics researchers. I develop and utilize scientific and mathematical methods to create artworks and have recently incorporated social science to inform my creative process. By combining shape modeling, rendering, and visualization, I aim to advance the boundaries of computational creativity, producing innovative tools and frameworks that resonate across disciplines.
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