Counting and cutting cycles of lines and rods in space

DOI10.1016/0925-7721(92)90009-HzbMath0748.68082OpenAlexW2010761427WikidataQ56970893 ScholiaQ56970893MaRDI QIDQ1194306

Leonidas J. Guibas, Micha Sharir, Raimund Seidel, Bernard Chazelle, Richard Pollack, Jack Scott Snoeyink, Herbert Edelsbrunner

Publication date: 27 September 1992

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0925-7721(92)90009-h

zbMATH Keywords

cycleline segmentsincidenceshidden surface removaldepth sortrendering algorithmsthree-dimensional objects

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (24)

Efficient ray shooting and hidden surface removal ⋮ On joints in arrangements of lines in space and related problems ⋮ Joints of varieties ⋮ Weaving patterns of lines and line segments in space ⋮ Book review of: L. Guth, Polynomial methods in combinatorics ⋮ On the multilinear restriction and Kakeya conjectures ⋮ The shortest watchtower and related problems for polyhedral terrains ⋮ Lines in space: Combinatorics and algorithms ⋮ On lines and joints ⋮ Incidence bounds on multijoints and generic joints ⋮ Joints tightened ⋮ On lines, joints, and incidences in three dimensions ⋮ Non-transversal multilinear duality and joints ⋮ Eliminating depth cycles among triangles in three dimensions ⋮ Algebraic methods in discrete analogs of the Kakeya problem ⋮ Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications ⋮ Removing depth-order cycles among triangles: an algorithm generating triangular fragments ⋮ The joints problem for matroids ⋮ On the Erdős distinct distances problem in the plane ⋮ Counting multijoints ⋮ Almost tight bounds for eliminating depth cycles in three dimensions ⋮ Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory ⋮ Efficient hidden surface removal for objects with small union size ⋮ Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type

Cites Work

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• Extremal problems in discrete geometry
• Combinatorial complexity bounds for arrangements of curves and spheres
• Rigidity and polarity. II: Weaving lines and tensegrity frameworks
• Algorithms for bichromatic line-segment problems and polyhedral terrains
• Lines in space: Combinatorics and algorithms
• An optimal algorithm for intersecting line segments in the plane

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