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Vertical Decomposition of a Single Cell in a Three-Dimensional Arrangement of Surfaces (1997)

Schwarzkopf, O. ; Sharir, M.

Springer

Discrete & computational geometry 18 (1997), S. 269-288

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ISSN: 1432-0444

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract. Let Σ be a collection of n algebraic surface patches in ${\Bbb R}^3$ of constant maximum degree b, such that the boundary of each surface consists of a constant number of algebraic arcs, each of degree at most b as well. We show that the combinatorial complexity of the vertical decomposition of a single cell in the arrangement ${\cal A}(\Sigma)$ is O(n^{2+ɛ}), for any ɛ 〉 0, where the constant of proportionality depends on ɛ and on the maximum degree of the surfaces and of their boundaries. As an application, we obtain a near-quadratic motion-planning algorithm for general systems with three degrees of freedom.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00009319

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