Subdivision surfaces are used throughout Pixar's animation movies for the modeling of 3D objects. The variety of objects includes toys, furniture, machines, and architecture. The volume, center of mass, and inertia are important characteristics for the accurate design and physical simulation of these solids.

Using our new approach, we are able compute these moments with unprecedented ease and accuracy. Our framework also handles a broader variety of subdivision schemes than was possible before. In the talk, I present the mathematical derivation of the available methods that compute moment forms for curves and surfaces generated by stationary subdivision schemes. I conclude with open questions, possible extensions, and applications of the framework.

Linear algebra is the only prerequisite for the comprehension of the presented material. Familiarity with subdivision schemes is helpful.

Jan Hakenberg recently joined the Institute for Dynamic Systems and Control at ETH Zurich as a software engineer. The research projects he is involved in concern the control of autonomous vehicles.
In the past, he was a software architect for autonomous driving at NuTonomy, and for a nano-satellite project at Nanyang Technological University. Besides subdivision and geometry, he is interested in data-driven music composition.