Arrangements and their Applications in Robotics : Recent
نویسندگان
چکیده
We survey a collection of recent combinatorial and al-gorithmic results in the study of arrangements of low-degree algebraic surface patches in three or higher dimensions. The new results extend known results involving 2-dimensional arrangements, and they almost settle several conjectures posed eight years ago. Arrangements play a central role in the design and analysis of geometric algorithms, and they arise in a variety of seemingly unrelated applications. In this survey we concentrate on the application of the new results to problems involving collision-free motion planning with three degrees of freedom, and visibility over polyhedral terrains.
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