J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5):1401--1421, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... literature relies on the computation of the Delaunay triangulation which may require an arithmetic precision four times the one used to represent the input data [5] References where the performance of geometric computations is measured also in terms of the required arithmetic precision include [2, 3, 4, 16]. The remainder of the paper is organized as follows. Preliminaries are in Section 2. A unifying approach to the computation of fi skeletons and fl graphs is presented in Section 3. In the same section the robust algorithm for Gabriel graphs is described. Section 4 deals with the computation of ....

....by using double precision integer arithmetic. Thus, we can identify a trade off between time complexity and numerical precision required by algorithms that compute Gabriel graphs. In the next theorem we show how to reduce the trade off. We adopt the degree model of computation introduced in [2, 16] and analyze the performance of Algorithm Right fi region in terms of required numerical precision to compute Gabriel graphs. In this model of computation the robustness of a geometric algorithm is evaluated by looking at the irreducible polynomial of highest algebraic degree whose sign is ....

J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5) 1401--1421, 2000.

....3. Moller and Trumbore [8] have a single step process for ray triangle intersection that could be modified to address these two concerns for triangles, but not for polygons. Recently, researchers in computational geometry have been evaluating the arithmetic precision of basic geometric algorithms [3, 4, 7] by studying the degrees of polynomials computed to resolve geometric tests. In this note, we consider the ray polygon intersection test, and derive a simple, degree three algorithm that handles all degeneracies. The next section shows that a standard pointin polygon test is degree two. Section ....

J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5):1401--1421, 2000.

....of a computation greatly a#ects the CPU time necessary to carry it out, the degree of a geometric algorithm should be considered as important as the asymptotic time complexity and should correspondingly play a major role in the design, or re design, of a geometric algorithm (see, e.g. Refs. [6, 7, 20]) As any library, GeomLib may su#er from a relative ine#ciency: providing generality usually requires an overhead with respect to an ad hoc program to solve a certain problem. As described before, however, one of the main purposes of GeomLib is to provide a framework for rapid prototyping of ....

J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5):1401--1421, 2000.

....of this instance on the arithmetic. Here, geometric computations impose subtle dependencies on modules that make the combinations of modules intrinsically harder. The demand of geometric computations on the arithmtic has been formalized [22, 23] and studied for a few basic geometric problems [22, 23, 24], but further research on the arithmetic demand as well as on an easy to use documentation of this demand is still needed. Ignoring the simplifying assumptions, such as relying on sufficient exactness of the built in arithmetic, would violate our understanding of correctness. Exactness should ....

J.-D. Boissonnat and F. Preparata, `Robust plane sweep for intersecting segments', Technical Report 3270, INRIA, Sophia-Antipolis, France, September 1997.

....algebraic curves (e.g. circular arcs) algorithms need to determine the sign of a polynomial of a rather high degree [14] Carrying out one such operation robustly may be costly. Redesigning algorithms so that they use lower degree predicates was recently proposed as a means to enhance robustness [13], 14] Indeed, robustness issues seem to be the most critical in the passage from theory to practice in geometric algorithms. Ignoring these issues can result in unreliable or incorrect programs. This has led to an intensive study in recent years. We brie y mention the main approaches to handling ....

J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. Report TR 3270, INRIA, Sophia Antipolis, Sept. 1997.

....in practice depends on the demand of this instance on the arithmetic. Here, geometric computations impose subtle dependencies on modules that make the combinations of modules intrinsically harder. The arithmetic demand of geometric computations has been studied for a few basic geometric problems [BP97, BMS94, LPT97] but further research on the arithmetic demand as well as on an easy to use documentation of this demand is still needed. Ignoring the simplifying assumptions, such as relying on suOEcient exactness of the built in arithmetic, would violate our understanding of correctness. ....

J.-D. Boissonnat and F. Preparata. Robust plane sweep for intersecting segments. Technical Report 3270, INRIA, Sophia-Antipolis, France, September 1997.

....practice depends on the demand of this instance on the arithmetic. Here, geometric computations impose subtle dependencies on modules that make the combinations of modules intrinsically harder. The arithmetic demand of geometric computations has been studied for a few basic geometric problems [BP97, BMS94, LPT97] but further research on the arithmetic demand as well as on an easy to use documentation of this demand is still needed. Ignoring the simplifying assumptions, such as relying on sufficient exactness of the built in arithmetic, would violate our understanding of correctness. ....

J.-D. Boissonnat and F. Preparata. Robust plane sweep for intersecting segments. Technical Report 3270, INRIA, Sophia-Antipolis, France, September 1997.

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J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5):14011421, 2000.

....of the algorithm follows using the same arguments as in Ref. 9] By the same observations the number of site and spike events is O(n) Thus, the time complexity of the algorithm is O(n log n) 4. The degree of the plane sweep algorithm Let s first review some definitions and notation from Refs. [15,5]. An algorithm has degree d if its test computations (predicates) involve the evaluation of multivariate polynomials of arithmetic degree at most d Ref. 15] The arithmetic degree of a polynomial is the maximum arithmetic degree of its monomials, and the arithmetic degree of a monomial is the sum ....

....is not constant. Clearly the degree of a predicate is the maximum degree of its elementary predicates and the degree of an algorithm is the maximum degree of its predicates. For more information on the degree of an algorithm and its implication on the speed and robustness of the algorithm see Ref. [5]. All input data are considered to be b bit integers. Following the notation of Ref. 15] an unspecified multivariate polynomial of degree s over input variables is denoted by ff . A specific term ae, which is known to be a polynomial of degree s over input variables, can be written as ff ....

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J.D. Boissonnat, F. Preparata, "Robust plane sweep for intersecting segments", SIAM J. Computing, to appear.

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J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM Jour'nal on Computing, 29(5):1401 1421, 2000.

....[13] we consider the degree of the predicates as an additional measure of the complexity of problems and algorithms, and intend to elucidate the relationship between time complexity and degree of the predicates. Related research can be found in Knuth s seminal work [12] and in some recent papers [3, 4, 10]. In this paper, we consider the problem of reporting the k intersecting pairs among a set of n x monotone curve segments. We address the red blue case, where this set is partitioned into two subsets of non intersecting segments. This problem can be solved in optimal O(n log n k) time [1, 6, 9] ....

J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5):14011421, 2000.

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J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput., 29(5):1401--1421, 2000.

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J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. Tech. Rep. RR-3270, INRIA Sophia Antipolis, 1997. SIAM J. Comput., to appear.

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J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. Research Report 3270, INRIA, 1997.

No context found.

J-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. Research Report 3270, INRIA, Sophia Antipolis, September 1997.

No context found.

J-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. SIAM J. Comput. to appear.

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J.-D. Boissonnat and F. P. Preparata. Robust plane sweep for intersecting segments. Research Report 3270, INRIA, Sophia Antipolis, Sept. 1997.

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