Arrangements in Geometry: Recent Advances and Challenges

We review recent progress in the study of arrangements in computational and combinatorial geometry, and discuss several open problems and areas for further research. In this talk I will survey several recent advances in the study of arrangements of curves and surfaces in the plane and in higher dimensions. This is one of the most basic structures in computational and combinatorial geometry. Arrangements appear in a variety of application areas, such as geometric optimization, robotics, graphics and modelling, and molecular biology, just to name a few. Arrangements also possess their own rich structure, which has fueled extensive research for the past 25 years (although, if one wishes, one can find the first trace of them in a study by Steiner in 1826 [37]). While considerable progress has been made, it has left many “hard nuts” that still defy a solution. The aim of this talk is to present these difficult problems, describe what has been done, and what are the future challenges. ...

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Micha Sharir
• Keywords: Arrangements, Combinatorial Geometry, ESA 2007, Surfaces