Many of the surfaces we encounter in the shape analysis and geometry processing pipelines are actually boundaries of volumetric objects rather than thin, two-dimensional sheets. Somewhat counter to intuition, accounting for volumetric structure in algorithms for tasks like parameterization, meshing, and retrieval is not as simple as incrementing the dimension in well-known algorithms. Instead, a new set of geometric and topological challenges arises. In this talk, I will outline efforts to lift geometry processing to three dimensions, yielding a practical toolbox for understanding and processing volumetric shape.
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