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- W2012313215 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." @default.
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- W2012313215 date "1997-10-01" @default.
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- W2012313215 title "Vertical Decomposition of a Single Cell in a Three-Dimensional Arrangement of Surfaces" @default.
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- W2012313215 doi "https://doi.org/10.1007/pl00009319" @default.
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