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Geometry and Generation of a New Graph Planarity Game

Rutger Kraaijer, Marc van Kreveld, Wouter Meulemans, Andre van Renssen
2018 2018 IEEE Conference on Computational Intelligence and Games (CIG)  
We introduce a new abstract graph game, Swap Planarity, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge.  ...  We analyze this puzzle game using concepts from graph theory and graph drawing, computational geometry, and complexity.  ...  We thank the organizers and participants of the workshop for providing a fun and stimulating research environment.  ... 
doi:10.1109/cig.2018.8490404 dblp:conf/cig/KraaijerKMR18 fatcat:4nq6fwpgdjhp5ann2lz5zubj4e

On Nonogram and Graph Planarity Puzzle Generation

Marc J. van Kreveld
2018 Canadian Conference on Computational Geometry  
We also present new nonogram and graph planarity puzzles.  ...  We will focus on puzzles with a geometric component where techniques from discrete and computational geometry can be employed to generate them.  ...  Graph planarity puzzles Planarity [10] is a popular abstract puzzle game that is widely available.  ... 
dblp:conf/cccg/Kreveld18 fatcat:iiiji2cqjvc2rivtekim6x4yj4

Computational Algorithm for Determining the Generic Mobility of Floating Planar and Spherical Linkages [chapter]

Offer Shai, Andreas Müller
2013 Mechanisms and Machine Science  
this paper, which always finds the correct generic mobility of any planar and spherical mechanism.  ...  Its foundation is a novel representation of constraints by means of a constraint graph.  ...  In this paper we introduce a new type of graph, termed mixed constraint graph . In this graph a vertex can represent a rigid body, , as well as points, .  ... 
doi:10.1007/978-94-007-7214-4_22 fatcat:dnood5et5jglrgsfz5datu4irq

Dots & Polygons

Kevin Buchin, Mart Hagedoorn, Irina Kostitsyna, Max van Mulken, Jolan Rensen, Leo van Schooten, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry  
We present a new game, Dots & Polygons, played on a planar point set. We prove that its NP-hard and discuss strategies for the case when the point set is in convex position.  ...  We introduce a more geometric variant of this game: Dots & Polygons. The game is played on a planar point set P of size n.  ...  Furthermore, triangle packing is polynomial-time solvable in planar graphs with maximum degree three [8] , and thus can no longer be used to justify the hardness of the VCP in planar cubic graphs.  ... 
doi:10.4230/lipics.socg.2020.79 dblp:conf/compgeom/BuchinHKMRS20 fatcat:t4u2lbparrhyxcrlvegoo2p65y

Page 1622 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
In fact, though the authors do not obtain new examples of finite generalized polygons, they construct in a fairly uniform way almost all known examples of generalized n-gons, n = 4,6.  ...  The authors prove the following nice charac- terization of such planar spaces: the planar space can be (i) the sum of a point and a projective plane minus one point, or (ii) the sum of a point and a Fano  ... 

Angular rigidity in 3D: combinatorial characterizations and algorithms

Audrey Lee-St. John, Ileana Streinu
2009 Canadian Conference on Computational Geometry  
We give a complete combinatorial characterization for generic minimal rigidity in two new models: lineplane-and-angle and body-and-angle structures.  ...  They also offer a rich source of interesting open questions in computational geometry. Although an active area of research for over 10 years [11] , their study has proven to be very challenging.  ...  See [7] for sparsity concepts (including tight graphs) and pebble game algorithms. Proof sketch.  ... 
dblp:conf/cccg/JohnS09 fatcat:lvpwus4cnfepbfijp755gpk2vm

Designing Art Galleries

Toon van Benthem, Kevin Buchin, Irina Kostitsyna, Stijn Slot, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry  
We present a method for generating interesting levels based on several NP-hardness reductions for a puzzle game based on the Art Gallery problem.  ...  The constructions described can be used to generate new levels, starting from an instance of the respective original problem, for the Art Gallery game. Planar 3SAT.  ...  In the final construction we use a planar embedding of the graph to create the Art Gallery level. Figure 8 shows an example of a generated level. Geometric Hitting Set.  ... 
doi:10.4230/lipics.socg.2020.80 dblp:conf/compgeom/BenthemBKS20 fatcat:2gfowgnw2bb7veb7pbmmrwioii

Page 3128 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
planar symmetries” * 00016 * 00014 * 00009 * 00018 “The trivial object and the non-triviality of a semantically closed theory with descriptions” Essen, 1997 Festschrift: Lange, Leo Jerome Vainikko, Gennadi  ...  of Groups and Algebras, Ist Euro Computers and Games, Ist International, CG’98 * 68137 Continued Fractions: From Analytic Number Theory to Constructive Approximation, International * 00018 Graph Connections  ... 

Book announcements

1990 Discrete Applied Mathematics  
Planarity (A nearly complete sketch of the proof. Connectivity and region boundaries. Edge contraction and connectivity. Planarity theorems for 3-connected graphs.  ...  Chapter 7: Implementations Dependent on Many and/or Very Strong Properties. A class of simple games- definitions whose range and domain are finite.  ... 
doi:10.1016/0166-218x(90)90074-m fatcat:uhwd4fl3wvcetkvers2zklsbry

Page 4952 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
The proof relies on the circle packing theorem, which has recently become a useful tool for studying planar graphs, because, as the authors state, “it endows the graph with a geometry that is better, for  ...  When a random walk on a graph G is transient, it is natural to ask at what speed it escapes from the starting point, and how this relates to the geometry of G.  ... 

Finding and Maintaining Rigid Components

Audrey Lee, Ileana Streinu, Louis Theran
2005 Canadian Conference on Computational Geometry  
We give the first complete analysis that the complexity of finding and maintaining rigid components of planar bar-and-joint frameworks and arbitrary d-dimensional body-and-bar frameworks, using a family  ...  To this end, we introduce a new data structure problem called union pairfind, which maintains disjoint edge sets and supports pair-find queries of whether two vertices are spanned by a set.  ...  Rigidity of planar bar-and-joint frameworks is well-understood and characterized by Laman graphs.  ... 
dblp:conf/cccg/LeeST05 fatcat:525rnfy7czekphrmumxvz5ggie

A video joystick from a toy

Gary Bradski, Victor Eruhimov, Sergey Molinov, Valery Mosyagin, Vadim Pisarevsky
2001 Proceedings of the 2001 workshop on Percetive user interfaces - PUI '01  
The paper describes an algorithm for 3D reconstruction of a toy composed from rigid bright colored blocks with the help of a conventional video camera.  ...  We also present the algorithm for extracting the color structure and matching feature points across the frames and discuss robust structure from motion and recognition connected with the subject.  ...  CONCLUSION The paper is devoted to a new type of visual interface for interactive computer games.  ... 
doi:10.1145/971478.971518 fatcat:kavzx3s2gjgcve65rpnsg6flsy

Mathematical ideas in non-western cultures

Marcia Ascher
1984 Historia Mathematica  
Graphs and Mazes: Traversing continuous closed paths without retracing any segment; a Shongo children's game; the KGnigsberg bridge problem; Euler's theorem; connectedness; planar graphs:  ...  Games, gods and gambling. London: Griffin. Deacon, A. B. 1934. Geometrical drawings from Malekula and other islands of the New Hebrides, edited by C. H. Wedgwood.  ... 
doi:10.1016/0315-0860(84)90006-5 fatcat:rnusraunbffqlkqvy3m5xj25ea

Table of contents

2018 2018 IEEE Conference on Computational Intelligence and Games (CIG)  
. . . . . . . 181 Sam Ganzfried and Qinyung Sun Geometry and Generation of a New Graph Planarity Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Rutger Kraaijer, Marc van Kreveld,  ...  Purmonen, Richard Meurling, Bartlomiej Kozakowski and Lele Cao A Critical Analysis of Punishment in Public Goods Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Garrison W.  ... 
doi:10.1109/cig.2018.8490418 fatcat:52t3qk7u6vbtvmfyieskij2ff4

GPU based multi-histogram volume navigation for virtual bronchoscopy

Ruida Cheng, Sheng Xu, Alexandra Bokinsky, Evan McCreedy, William Gandler, Bradford J. Wood, Matthew J. McAuliffe
2014 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society  
WildMagic is a C++ game engine [15] that provides the low-level geometry routines and complete high-level scene graph management for game applications.  ...  From the model space, the image scene graph tree contains all the 3D geometry objects in the game scene.  ... 
doi:10.1109/embc.2014.6944330 pmid:25570698 pmcid:PMC5990254 dblp:conf/embc/Cheng0BMGWM14 fatcat:kzyeb63jgvejpevfwrk3flh6wa
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