•   When: Wednesday, December 07, 2016 from 04:00 PM to 06:00 PM
•   Speakers: Evan Behar
•   Location: ENGR 2901
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The Minkowski sum is an important operation in a wide variety of applications, including robotic motion planning, computer animation, physical simulation, rapid prototyping, and computer-aided design, as well as being the fundamental operation in computing configuration spaces of objects. In many applications, however, the objects provided are transformed over time by means of rotation, scaling, or localized deformation, or make use of significantly similar or repeated geometry. Due to the complexity of the Minkowski sum, it is often not practical to recompute the Minkowski sum after each transformation. In this work, I present methods for dynamically updating the Minkowski sum boundaries of convex triangle meshes under common transformations, and I introduce both a new structure called the convex map, which allows these techniques to be extended to non-convex inputs, and the concept of local Minkowski sums, which allows incremental updates of relevant portions of the Minkowski sum boundary at interactive rates.