Slices of Minkowski Diierences and Satellite Antenna Layout

Satellite layout is a very hard task because available space for the instruments is small and the physical constraints on the layout are strong. In this article, we show how some physical layout constraints can be modeled geometrically and how Minkowski operations can be used to place instruments, and in particular antennas. The crucial step consists in placing an antenna by translation onto a satellite wall. The admissible space is therefore two-dimensional, although the instrument is three-dimensional. We propose an algorithm to eeciently compute the admissible space and describe its implementation. Experimental results on realistic examples are given.