# Prof. Phan Thanh An - The Law of Cosines for Computing Geometric Shortest Paths on a Convex Polytope in 3D

**Abstract**In this talk, we present efficient algorithms for two problems: computing exact geometric shortest paths joining a fixed source point to all given points and computing an exact geometric shortest paths joining two points on the surface of a convex polytope in three-dimensional space using the concept of funnels on the surface.

To obtain such funnels, straightest geodesics and the law of cosines in a triangle are used. We do not rely on unfolding of the polytope.

For the first problem, the corresponding algorithm is implemented in Python and is compared with Chen and Han‘s algorithm. This is a joint work with Tran Van Hoai and Vuong Ba Thinh.

For the second problem, some numerical examples using JavaView are presented.

**Biography**Dr. Phan Thanh An is a visiting professor at the Institute of Mathematics and Computer Sciences (ICMC), University of São Paulo, Brasil. He completed his PhD in the field of optimization at the Vinh University in Vietnam in 1999 under the supervision of Professors Hoang Xuan Phu and Nguyen Nhuy. Since then he has worked as a researcher at the Hanoi Institute of Mathematics, Vietnam (as an associate professor of the institute since 2009), and has specialized in the use of optimization methods (the method of orienting curves and the method of multiple shooting) for solving computational geometry problems. During the years 2009-2014 he worked at the Center for Computational and Stochastic Mathematics (CEMAT) of the Instituto Superior Técnico, the University of Lisbon, Portugal and supervised successfully two PhD theses for this university in the research trend „Optimization approaches for computational geometry“. He regularly visits the Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany to collaborate with colleagues from the group “Simulation and Optimization” of the IWR on numerical optimization. He has also visited the Freie Universität Berlin, Germany since 2014 to collaborate with the Mathematical Geometry Processing working group on discrete geodesics. His research works can be found at his research website: https://sites.google.com/a/math.ac.vn/phan-thanh-an-s-homepage/

### Time & Location

Dec 13, 2018 | 03:00 PM

FU Berlin | Arnimallee 6 | Raum 108/109