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Finite-resolution computational geometry

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2 Author(s)

Geometric algorithms are usually designed with continuous parameters in mind. When the underlying geometric space is intrinsically discrete, as is the case for computer graphics problems, such algorithms are apt to give invalid solutions if properties of a finite-resolution space are not taken into account. In this paper we discuss an approach for transforming geometric concepts and algorithms from the continuous domain to the discrete domain. As an example we consider the discrete version of the problem of finding all intersections of a collection of line segments. We formulate criteria for a satisfactory solution to this problem, and design an interface between the continuous domain and the discrete domain which supports certain invariants. This interface enables us to obtain a satisfactory solution by using plane-sweep and a variant of the continued fraction algorithm.

Published in:

Foundations of Computer Science, 1986., 27th Annual Symposium on

Date of Conference:

27-29 Oct. 1986