This thesis addresses satellite layout problems. The goal is to develop efficient algorithms that lead to Simple tools that help the design office engineer in his frequent layout problems. We propose an optimal algorithm that calculates a planar section of the Minlrowski sum of two convex polyhedra and an efficient algorithm that calculates the union of a set of polygons. We closely analyzed the numerical precision that is necessary for the two algorithms to work correctly and the handling of geometric degeneracíes that can be encountered. We developed the program GEOTOOLS for the placement of a sequence of equipment and in particular antennas that have a field of vision. GEOTOOLS allows interactive placement of a piece of equipment in a partially completed layout while visualizing the constraints imposed by this layout (the admissible space). The second part of this thesis discusses our experiences using GEOTOOLS on realistic models of satellites when placing sequences of antennas interactively and automatically.
