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Cutting triangular cycles of lines in space

Boris Aronov, Vladlen Koltun, Micha Sharir
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
We show that n lines in 3-space can be cut into O(n 2−1/69 log 16/69 n) pieces, such that all depth cycles defined by triples of lines are eliminated.  ...  This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.  ...  Agarwal, Sariel Har-Peled and Shakhar Smorodinsky for insightful suggestions concerning the material presented in this paper.  ... 
doi:10.1145/780619.780622 fatcat:li7jdtqyqbaaba6hsmc77n4qum

Cutting Triangular Cycles of Lines in Space

Boris Aronov, Vladlen Koltun, Micha Sharir
2004 Discrete & Computational Geometry  
We show that n lines in 3-space can be cut into O(n 2−1/69 log 16/69 n) pieces, such that all depth cycles defined by triples of lines are eliminated.  ...  This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.  ...  Agarwal, Sariel Har-Peled, and Shakhar Smorodinsky for insightful suggestions concerning the material presented in this paper.  ... 
doi:10.1007/s00454-004-1123-5 fatcat:fyzbczd3tnch7mmiy4xhfhmzam

Cutting triangular cycles of lines in space

Boris Aronov, Vladlen Koltun, Micha Sharir
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
We show that n lines in 3-space can be cut into O(n 2−1/69 log 16/69 n) pieces, such that all depth cycles defined by triples of lines are eliminated.  ...  Cycles of length three are called triangular. See Figure 1 (a).  ...  Agarwal, Sariel Har-Peled and Shakhar Smorodinsky for insightful suggestions concerning the material presented in this paper.  ... 
doi:10.1145/780542.780622 dblp:conf/stoc/AronovKS03 fatcat:cdprgldabbc2jnilxpku57qkqu

Almost Tight Bounds for Eliminating Depth Cycles in Three Dimensions [article]

Boris Aronov, Micha Sharir
2016 arXiv   pre-print
Given n non-vertical lines in 3-space, their vertical depth (above/below) relation can contain cycles.  ...  We also discuss several algorithms for constructing a small set of cuts so as to eliminate all depth-relation cycles among the lines (minimizing such a set, for the case of line segments, is known to be  ...  ) on the number of so-called joints in a collection of n lines in 3-space.  ... 
arXiv:1512.00358v2 fatcat:2crpo4y7pjagzagbewscgysw6i

Almost Tight Bounds for Eliminating Depth Cycles in Three Dimensions

Boris Aronov, Micha Sharir
2017 Discrete & Computational Geometry  
Given n non-vertical lines in 3-space, their vertical depth (above/below) relation can contain cycles.  ...  Previous results on this topic could only handle restricted cases of the problem (such as handling only triangular cycles, by Aronov, Koltun, and Sharir, or only cycles in grid-like patterns, by Chazelle  ...  ) on the number of so-called joints in a collection of n lines in 3-space.  ... 
doi:10.1007/s00454-017-9920-9 fatcat:qdq6zxhxwndglhav3gtwmfjvka

Almost tight bounds for eliminating depth cycles in three dimensions

Boris Aronov, Micha Sharir
2016 Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016  
Given n non-vertical lines in 3-space, their vertical depth (above/below) relation can contain cycles.  ...  Previous results on this topic could only handle restricted cases of the problem (such as handling only triangular cycles, by Aronov, Koltun, and Sharir, or only cycles in grid-like patterns, by Chazelle  ...  ) on the number of so-called joints in a collection of n lines in 3-space.  ... 
doi:10.1145/2897518.2897539 dblp:conf/stoc/AronovS16 fatcat:4tglsk3ntbgqtl3b3jmi2fyoq4

Kirigami skins make a simple soft actuator crawl

Ahmad Rafsanjani, Yuerou Zhang, Bangyuan Liu, Shmuel M. Rubinstein, Katia Bertoldi
2018 Science Robotics  
First, we showed that this transformation was accompanied by a dramatic change in the frictional properties of the surfaces.  ...  We designed highly stretchable kirigami surfaces in which mechanical instabilities induce a transformation from flat sheets to 3D-textured surfaces akin to the scaled skin of snakes.  ...  (B) Displacement of the center of mass (solid line), head (dashed line), and tail (dotted line) of the crawlers versus number of cycles.  ... 
doi:10.1126/scirobotics.aar7555 pmid:33141681 fatcat:wpidvlr5kjcavbjagbshklee6a

Biomechanical Stability of the Sacroiliac Joint with Differing Implant Configurations in a Synthetic Model

Andrew L Freeman, Joan E Bechtold, David W Polly
2021 The International Journal of Spine Surgery  
Linear, triangular, and angled (10° or 20°) implant patterns were used with spacing of 13 or 22 mm between implants.  ...  Triangular SIJ fusion implants were tested in six patterns using three implants, and two patterns with two implants (n = 5/pattern).  ...  (no cycling) at 7.5 Nm. 26, 30, 31 Authors of a finite element analysis (FEA) of the SIJ evaluated in line and transarticular placement of triangular titanium implants with a varying number of implants  ... 
doi:10.14444/8117 pmid:34625453 pmcid:PMC8651206 fatcat:4fwt6joif5dnjg5wszca3tmh44

Removing Depth-Order Cycles Among Triangles: An Efficient Algorithm Generating Triangular Fragments [article]

Mark de Berg
2017 arXiv   pre-print
Thus the most natural version of the problem is still wide open: Can we cut any collection of n disjoint triangles in R^3 into a subquadratic number of triangular fragments that admit a depth order?  ...  We answer this question by presenting an algorithm that cuts any set of n disjoint triangles in R^3 into O(n^7/4polylog n) triangular fragments that admit a depth order.  ...  In the special case of lines (or line segments) one can easily get rid of all cycles using O(n 2 ) cuts: project the lines onto the xy-plane and cut each line at its intersection points with the other  ... 
arXiv:1701.00679v2 fatcat:rluksjuvdnaa7ifnu2klnwxtha

USING COMPUTER SIMULATION IN LEAN MANUFACTURING IMPLEMENTATION

S. Seleem, M. Helal, A. Elassal
2014 The International Conference on Applied Mechanics and Mechanical Engineering  
Converting the assembly line into a lean production system led to cutting off work-inprocess by about 82%, reducing cycle time by 30%, and decreasing model changeover time from 127.5 min to 11.5 min, in  ...  A methodology has been developed and used as a framework to utilize various lean manufacturing tools in analyzing configuration and performance of the assembly line and identifying the present forms of  ...  of cycle time in most operations are greater than line targeted cycle time.  ... 
doi:10.21608/amme.2014.35711 fatcat:yacmucgz5vazxdlyvxpx6rypqe

Removing Depth-Order Cycles among Triangles: An Efficient Algorithm Generating Triangular Fragments

Mark de Berg
2017 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)  
Thus the most natural version of the problem is still wide open: Is it possible to cut any collection of n disjoint triangles in R 3 into a subquadratic number of triangular fragments that admit a depth  ...  We answer this question by presenting an algorithm that cuts any set of n disjoint triangles in R 3 into O(n 7/4 polylog n) triangular fragments that admit a depth order.  ...  [5] obtained a subquadratic upper bound for general sets of lines, but they only get of all triangular cycles-that is, cycles consisting of three lines-and their bounds are only slightly subquadratic  ... 
doi:10.1109/focs.2017.33 dblp:conf/focs/Berg17 fatcat:dvm2yqzndffbtmyulmzp6iqw2e

Spectral statistics of a system with sharply divided phase space

Jure Malovrh, Tomaz Prosen
2002 Journal of Physics A: Mathematical and General  
of phase space can be computed analytically or at least rigorously estimated from below.  ...  We construct a family of non-Kolmogorov-Arnold-Moser (non-KAM) piecewise-linear continuous 2D area-preserving maps which have sharply divided phase space with regions of regular elliptic and chaotic hyperbolic  ...  Figure 2 . 2 A magnified view of the region near a 1-cycle elliptic island with ε = 1.3 (slightly different to that infigure 1). The straight vertical line is the cut at x = 1/2.  ... 
doi:10.1088/0305-4470/35/10/312 fatcat:ph2ui3ioibhprcgugo75r3snea

Removing Depth-Order Cycles Among Triangles: An Algorithm Generating Triangular Fragments

Mark de Berg
2019 Discrete & Computational Geometry  
More than 25 years ago, inspired by applications in computer graphics, Chazelle et al. studied the following question: is it possible to cut any set of n lines or other objects in R 3 into a subquadratic  ...  Thus the following natural version of the problem is still wide open: is it possible to cut any collection of n disjoint triangles in R 3 into a subquadratic number of triangular fragments that admit a  ...  (ii) A bipartite weaving cycles-that is, cycles consisting of three lines-and their bounds are only slightly subquadratic: they use O(n 2−1/69 log 16/69 n) cuts to remove all triangular cycles.  ... 
doi:10.1007/s00454-019-00102-0 fatcat:lmqdzznahbc2nfecemmm4iaafi

Page 1243 of American Society of Civil Engineers. Collected Journals Vol. 113, Issue 6 [page]

1987 American Society of Civil Engineers. Collected Journals  
Lower cut-off, equal to the AASHTO fatigue limit of 110 MPa (16 ksi) for over 2,000,000 cycles of loading. 4.  ...  The number of cycles to fatigue failure is ambiguous in this case.  ... 

Euclid's Postulate as a Property of Matter

G. H. Bryan
1911 Mathematical Gazette  
At the same time, while Euclidean straight lines intersect in only one point, ideal lines may cut in two points.  ...  At the same time, while Euclidean straight lines intersect in only one point, ideal lines may cut in two points.  ...  The explanation depends on the general theorem that the area, reckoned algebraically, swept out by a line of fixed length in a complete cycle, is equal to the difference of the areas described by its ends  ... 
doi:10.2307/3604903 fatcat:djtresrk2zbttbm7wzz6dtdk7m
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