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Approximate Convex Intersection Detection with Applications to Width and Minkowski Sums

, College Park, MD , USA 1 David M. Mount 2 Université Clermont Auvergne , LIMOS, and INRIA Sophia Antipolis , France Approximation problems involving a single convex body in Rd have received a great deal

On the Combinatorial Complexity of Approximating Polytopes

Approximating convex bodies succinctly by convex polytopes is a fundamental problem in discrete geometry. A convex body K of diameter $diam(K)$ is given in Euclidean d-dimensional space, where $d$ is a constant. Given an error parameter eps > 0, the objective is to determine a polytope of minimum combinatorial complexity whose Hausdorff distance from K is at most eps diam(K). By...

The Effect of Corners on the Complexity of Approximate Range Searching

Given an n-element point set in ℝ d , the range searching problem involves preprocessing these points so that the total weight, or for our purposes the semigroup sum, of the points lying within a given query range η can be determined quickly. In ε-approximate range searching we assume that η is bounded, and the sum is required to include all the points that lie within η and may...