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GOOD NEWS: PARTITIONING A SIMPLE POLYGON BY COMPASS DIRECTIONS

MARC VAN KREVELD, IRIS REINBACHER
2004 International journal of computational geometry and applications  
Criteria for a good NEWS partition There are many criteria one can use to partition a country into four regions by compass directions.  ...  Figure 1 : 1 Three partitions of Austria by compass directions. initialize by computing a vertical line that has area A left of it.  ... 
doi:10.1142/s0218195904001469 fatcat:wlgzzrfxsvhk5aaofvcdtqsma4

Good NEWS

Marc van Kreveld, Iris Reinbacher
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
Criteria for a good NEWS partition There are many criteria one can use to partition a country into four regions by compass directions.  ...  Figure 1 : 1 Three partitions of Austria by compass directions. initialize by computing a vertical line that has area A left of it.  ... 
doi:10.1145/777792.777804 dblp:conf/compgeom/KreveldR03 fatcat:5ftkje3z2vhnpmxyuwu5m3jj6i

Separation-Sensitive Collision Detection for Convex Objects [article]

Jeff Erickson, Leonidas J. Guibas, Jorge Stolfi, Li Zhang
1998 arXiv   pre-print
We can then bound the number of events by the combinatorial size of a certain cover of the motion path by balls.  ...  Variants of these data structures are also shown that exhibit hysteresis---after a separation certificate fails, the new certificate cannot fail again until the objects have moved by some constant fraction  ...  The Compass Hierarchy For the compass hierarchy we introduce O(n) zerolength edges into P , whose outer normals form a regular recursive lattice on the unit circle, in the standard compass directions (  ... 
arXiv:cs/9809035v2 fatcat:b3aquazovbbqfg7cvz6vv365ua

Book Review: Rational Geometry, a Text-book for the Science of Space

S. C. Davisson
1905 Bulletin of the American Mathematical Society  
This definition is not so good as the one given by the " Foundations," as it savors of the need of compasses for the construction of a sect product, although the compasses are not really necessary.  ...  The author points out that the equality of polygons as to content is a constructible idea with nothing new about it but a definition.  ... 
doi:10.1090/s0002-9904-1905-01217-9 fatcat:5qjxh7k6qzghhh3ni5jb5neejq

An immersed boundary/level-set method for incompressible viscous flows in complex geometries with good conservation properties

Yoann Cheny, Olivier Botella
2009 European Journal of Computational Mechanics  
This paper concerns the development of a new Cartesian grid / immersed boundary (IB) method for the computation of incompressible viscous flows in irregular geometries.  ...  In this paper, we present an IB method (the LS-STAG method) based on the Cartesian MAC method where the irregular boundary is represented by its level-set function.  ...  Due to page limitations, we did not include in this paper the proofs of the conservation of total mass and momentum by the LS-STAG method.  ... 
doi:10.13052/ejcm.18.561-587 fatcat:z6hxinx3bfayxk2tzmwy4fig7i

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel [article]

Troy Wilson, Stefan B. Williams
2016 arXiv   pre-print
New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage.  ...  Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP).  ...  Acknowledgments This work is supported by the Department of Education and Training through the Australian Postgraduate Awards (APA) scheme and the Australian Research Council (ARC) through the Future Fellowships  ... 
arXiv:1603.06324v2 fatcat:racss2kilfctbk5r3i3bp6xrse

Meeting in a Polygon by Anonymous Oblivious Robots [article]

Giuseppe A. Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, Masafumi Yamashita
2019 arXiv   pre-print
Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon.  ...  For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial  ...  We thank Francesco Veneziano for a clarifying discussion.  ... 
arXiv:1705.00324v4 fatcat:il4pe72a3bbbnpmpid6xpkwebu

Managing cohort movement of mobile sensors via GPS-free and compass-free node localization

Hüseyin Akcan, Vassil Kriakov, Hervé Brönnimann, Alex Delis
2010 Journal of Parallel and Distributed Computing  
Our first algorithm, GPS-free Directed Localization (GDL) assumes the availability of a simple digital compass on each sensor node.  ...  We relax this requirement in our second algorithm termed GPS and Compass-free Directed Localization (GCDL).  ...  When a boundary is reached, a new direction of movement must be chosen. In our simulations, we implement this as a ricochet off the boundary surface.  ... 
doi:10.1016/j.jpdc.2010.03.007 fatcat:k47fiwmxw5allowpwstujelsve

Hardness and Approximation of Minimum Convex Partition [article]

Nicolas Grelier
2021 arXiv   pre-print
We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum  ...  We say that a point set is k-directed if the (straight) lines containing at least three points have up to k directions. We present an O(k)-approximation algorithm running in n^O(k)-time.  ...  Then, after a new scaling, we can replace each polygon by a wire, in a grid which is still of size Θ(|V | 2 ).  ... 
arXiv:1911.07697v3 fatcat:3k5aajdkmbeqzcwg3i6ttv3b7m

Archaeological News

1890 The American Journal of Archaeology and of the History of the Fine Arts  
But it was placed in direct communication with the market by a three-gated Propylaion which has been found in good preservation, and on the axis of the gate of Athena Archegetis.  ...  , a long straight neck placed on the remainder of the body formed by a simple quadrangle.  ... 
doi:10.2307/496010 fatcat:nlb62mjcxre6dp3yk7ufo5ewxa

Archaeological News

James M. Paton
1904 American Journal of Archaeology  
The purchases of the year were directed to filling gaps in order to produce good typical examples of the art of each period.  ...  -A New Oculist's Seal. -HARON DE VILLEFOSSE reports the discovery at Boulogne-sur-Mer by Dr. Sauvage of a new oculist's seal.  ...  latter being accompanied by Felix and Stephen Diaconus, the former by Adanctus and St.  ... 
doi:10.2307/497084 fatcat:sacrv33lsrhl5b6ed2niffvvnm

Page 4587 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations.  ...  Such curves form a class of rational Bézier curves which are characterized by control points on radial directions and by weights equal to the inverse of the polar radius.  ... 

Acquiring new spatial intuitions: Learning to reason about rotations☆

John R. Pani, Julia H. Chariker, Thomas E. Dawson, Nathan Johnson
2005 Cognitive Psychology  
There are certain simple rotations of objects that most people cannot reason about accurately.  ...  Using virtual reality techniques, this project investigated the nature of learning to reason across the domain of simple rotations.  ...  nearly a minute and then indicate a direction for the axis that is incorrect by 35°or more.  ... 
doi:10.1016/j.cogpsych.2005.06.002 pmid:16165120 fatcat:s6rmllxcmnaxzjugligj6gy52e

Zone and polygon menus

Shengdong Zhao, Maneesh Agrawala, Ken Hinckley
2006 Proceedings of the SIGCHI conference on Human Factors in computing systems - CHI '06  
An experiment shows that Zone and Polygon menus can successfully increase breadth by a factor of 2 or more over orientation-based marking menus, while maintaining high selection speed and accuracy.  ...  We present Zone and Polygon menus, two new variants of multi-stroke marking menus that consider both the relative position and orientation of strokes.  ...  We can provide scaleindependence by creating a single open-ended zone in each radial direction from the origin of the coordinate system as shown in Figure 2b .  ... 
doi:10.1145/1124772.1124933 dblp:conf/chi/ZhaoAH06 fatcat:kve2ztgstnh2lnzir7hkpo5rvy

Vortex maze construction

Jie Xu, Craig S. Kaplan
2007 Journal of Mathematics and the Arts  
In general, the problem is a very subtle and complex one, as it relies both on formal mathematical measures of the maze's geometry and on ineffable properties of human perception.  ...  We then render each cell of the grid as a vortex, where there is a label at each compass heading precisely if the cell's wall in that direction has been erased.  ...  A good maze is simultaneously a work of art and a complex puzzle.  ... 
doi:10.1080/17513470701225236 fatcat:efxzspzfwbek5dgblj26qojeiq
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