Topologically sweeping visibility complexes via pseudotriangulations
Michel Pocchiola,Gert Vegter +1 more
- Vol. 16, Iss: 4, pp 419-453
TLDR
This paper describes a new algorithm for constructing the set of free bitangents of a collection ofn disjoint convex obstacles of constant complexity, which is the first optimal algorithm that uses only linear space.Abstract:
This paper describes a new algorithm for constructing the set of free bitangents of a collection ofn disjoint convex obstacles of constant complexity. The algorithm runs in timeO(n logn + k), where,k is the output size, and uses,O(n) space. While earlier algorithms achieve the same optimal running time, this is the first optimal algorithm that uses only linear space. The visibility graph or the visibility complex can be computed in the same time and space. The only complicated data structure used by the algorithm is a splittable queue, which can be implemented easily using red-black trees. The algorithm is conceptually very simple, and should therefore be easy to implement and quite fast in practice. The algorithm relies on greedy pseudotriangulations, which are subgraphs of the visibility graph with many nice combinatorial properties. These properties, and thus the correctness of the algorithm, are partially derived from properties of a certain partial order on the faces of the visibility complex.read more
Citations
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Deformable Free-Space Tilings for Kinetic Collision Detection†:
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Geometric Graphs and Arrangements
TL;DR: In this article, the main mathematical part of the text contains only few citations and references to related material, and these additional bits of information are provided in the last section of each chapter, 'Notes and References'.
References
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An algorithm for planning collision-free paths among polyhedral obstacles
TL;DR: A collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects that transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object.
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Literate Programming
TL;DR: This anthology of essays from the inventor of literate programming also contains excerpts from the programs for TEX and METAFONT and CWEB, a system for Literate programming in C and related languages.
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A linear-time algorithm for a special case of disjoint set union
Harold N. Gabow,Robert E. Tarjan +1 more
TL;DR: A linear-time algorithm for the special case of the disjoint set union problem in which the structure of the unions (defined by a “union tree”) is known in advance that is useful in finding maximum cardinality matchings in nonbipartite graphs.