On obstructions in relation to a fixed viewpoint

108 Efficient, randomized algorithms are given for the following problems: (1) construction of levels of order 1 to k in an arrangement of hyperplanes in any dimension; (2) construction of higher order Voronoi diagrams of order 1 to k in any dimension; (3) hidden surface removal for completely general scenes (intersecting and curved faces are allowed). A combinatorial tool in the form of a mathematical series called a θ series is associated with a configuration of polytopes in R^d. It is used to study the combinatorial, as well as algorithmic, complexity of the geometric problems under consideration