Computational geometry: an introduction
Computational geometry: an introduction
On translating a set of objects in 2- and 3-dimensional space
Computer Vision, Graphics, and Image Processing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Separating two simple polygons by a sequence of translations
Discrete & Computational Geometry
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
An efficient output-sensitive hidden surface removal algorithm and its parallelization
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
The complexity and construction of many faces in arrangements of lines and of segments
Discrete & Computational Geometry - Special issue on the complexity of arrangements
A survey of motion planning and related geometric algorithms
Geometric reasoning
Cutting hyperplane arrangements
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Stabbing and ray shooting in 3 dimensional space
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Efficient ray shooting and hidden surface removal
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Reporting points in halfspaces
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Diameter, width, closest line pair, and parametric searching
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Finding stabbing lines in 3-space
Discrete & Computational Geometry
Efficient Spatial Point Location (Extended Abstract)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
The Complexity and Decidability of Separation
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Separating a Polyhedron by One Translation from a Set of Obstacles (Extended Abstract)
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
On translating a set of rectangles
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
New bounds for lower envelopes in three dimensions, with applications to visibility in terrains
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
Recent Developments in the Theory of Arrangements of Surfaces
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
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We study some combinatorial and algorithmic problems onsets of lines and polyhedral objects in 3-space. Our main resultsinclude:(1) An On32clogn upper bound on the worst case complexity of the setof lines missing a star-shaped compact polyhedron withn edges.(2) Given a star-shaped compact polyhedron P withn edges we can compute on-line theshadow of P from a query directionv in almost-optimal output-sensitivetime O(k log4n), where k is thesize of the shadow. The storage used by the data structure isO(n3+&egr;.(3) An On32clogn upper bound on the worst case complexity of the setof lines that can be moved to infinity without intersecting a set ofn given lines. This bound is almosttight.(4) AnO(n1.5+&egr;)randomized expected time algorithm that tests the separation property:there exists a direction v alongwhich a set of n red lines can betranslated away from a set of n bluelines without collisions?(5) Computing the intersection of two polyhedral terrains in3-space with n edges in timeO(n4/3+&egr; +k1/3n1+&egr; + klog2 n), where k is the size of the output, and&egr; 0 an arbitrary small but fixed constant. This algorithmimproves on the best previous result of Chazelle et al. [7]The tools used to obtain these results include Plu¨ckercoordinates of lines, random sampling and polarity transformations in3-space.