Silvia Sellán - A deep dive into Swept Volumes

June 1st 2021. MIT CSAIL
Abstract:
Given a solid 3D shape and a trajectory of it over time, we compute its swept volume - the union of all points contained within the shape at some moment in time. We consider the representation of the input and output as implicit functions, and lift the problem to 4D spacetime, where we show the problem gains a continuous structure which avoids expensive global searches. We exploit this structure via a continuation method which marches and reconstructs the zero level set of the swept volume, using the temporal dimension to avoid erroneous solutions. We show that, compared to other methods, our approach is not restricted to a limited class of shapes or trajectories, is extremely robust, and its asymptotic complexity is an order lower than standards used in the industry, enabling its use in applications such as modeling, constructive solid geometry, and path planning.
Bio:
Silvia Sellán (dgp.toronto.edu...) is a second-year PhD student at the University of Toronto, supervised by professor Alec Jacobson. She has interned twice at Adobe Research and twice at the Fields Institute of Mathematical Sciences, and has published three first-author papers at ACM SIGGRAPH. Her research focuses on specific geometry processing challenges one encounters in data captured from the real world, and geometric data aimed at fabrication.