This paper explores a paradigm for producing geometrical algorithms in which logical decisions that depend on finite-precision numerical calculation cannot lead to failure. It applies this paradigm to the task of inte...
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This paper explores a paradigm for producing geometrical algorithms in which logical decisions that depend on finite-precision numerical calculation cannot lead to failure. It applies this paradigm to the task of intersecting two convex polyhedral objects. A key tool in this work is a method of perturbing embedding polyhedra in ways consistent with their topology.
An arrangement of n lines in the plane is considered. The lines divide the plane into convex regions and their sides are called edges. It is shown that the number of edges which can be joined to the x-axis by a segmen...
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An arrangement of n lines in the plane is considered. The lines divide the plane into convex regions and their sides are called edges. It is shown that the number of edges which can be joined to the x-axis by a segment intersecting less than k lines is Alt. Theta (nk). As an application, a range search algorithm is described. After preprocessing of an n-point set in the plane, it allows to report all points lying inside a given triangle with two sides parallel to the coordinate axes in O((log n) sup 2 + k) time (where k is the number of points reported), using O(n(log n) sup 2 ) storage.
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