## DYMSUM: Dynamic Minkowski Sum

#### Emily Behar, Jyh-Ming Lien

##### Overview

In this work, we developed a method that efficiently computes the Minkowski sum of*rotating convex polyhedra*. It is well known that the Minkowski sum of two polyhedra can be dramatically different from the Minkowski sum of the same polyhedra after rotation. To the best of our knowledge, all existing methods recompute a new Minkowski sum every time when the input polyhedra rotates. A main problem of recomputing the Minkowski sum from scratch is that it requires the same computation even when a small amount of rotation is applied. Computing the Minkowski sum of polyhedra undergoing small rotations can be found in many problems, such as

*general penetration depth*estimation for physically-based simulation and

*configuration-space obstacle*approximation for robotic motion planning.

##### Video

- A higher resolution video can be downloaded here: divx.avi 84MB.

##### Publications

Dynamic Minkowski Sum of Convex Shapes, Emily Behar and Jyh-Ming Lien,

Web Site / Paper (pdf) / BibTeX

*In Proc. IEEE Int. Conf. Robot. Autom. (ICRA)*, May 2011Web Site / Paper (pdf) / BibTeX

**Minkowski Sums of Rotating Convex Polyhedra**, Jyh-Ming Lien, Proceedings of the ACM Symposium on Computational Geometry (SoCG), College Park, Maryland. Video Abstract, Jun. 2008.

Full text: Proceedings (pdf) Video (divx.avi)

##### Technical Reports

Dynamic Minkowski Sum of Convex Shapes, Emily Behar, Jyh-Ming Lien, Department of Computer Science, George Mason University, (Technical Report), 2010

Web Site / Paper (pdf) / BibTeX

Web Site / Paper (pdf) / BibTeX

List of MASC Research Pages