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Combinatorial Shape Decomposition [chapter]

Ralf Juengling, Melanie Mitchell
Advances in Visual Computing  
We formulate decomposition of two-dimensional shapes as a combinatorial optimization problem and present a dynamic programming algorithm that solves it.  ...  Bottou's Lush programming environment, and obtained the shape data for our experiments from R. Lakaemper.  ...  In this paper we present a novel shape-decomposition algorithm, aimed at capturing some of the heuristics used by humans when parsing shapes.  ... 
doi:10.1007/978-3-540-76856-2_18 dblp:conf/isvc/JuenglingM07 fatcat:vpnc3u5qhndsho7676za6iuove

Computing and Visualizing a Graph-Based Decomposition for Non-manifold Shapes [chapter]

Leila De Floriani, Daniele Panozzo, Annie Hui
2009 Lecture Notes in Computer Science  
We present a new tool for visualizing the shape decomposition and its graph as an effective support to modeling, analyzing and understanding non-manifold shapes.  ...  The topological structure of a non-manifold shape can be analyzed through its decomposition into a collection of components with a simpler topology.  ...  The combinatorial structure of the MC-decomposition graph and the topological structure of the MC-components themselves are related to the topology of the original nonmanifold shape.  ... 
doi:10.1007/978-3-642-02124-4_7 fatcat:2khqhahby5h3xnaegp6l2gqwaq

A census of tetrahedral hyperbolic manifolds [article]

Evgeny Fominykh, Stavros Garoufalidis, Matthias Goerner, Vladimir Tarkaev, Andrei Vesnin
2015 arXiv   pre-print
Following an earlier publication by three of the authors, we give a census of all tetrahedral manifolds and all of their combinatorial tetrahedral tessellations with at most 25 (orientable case) and 21  ...  Our isometry classification uses certified canonical cell decompositions (based on work by Dunfield, Hoffman, Licata) and isomorphism signatures (an improvement of dehydration sequences by Burton).  ...  We first guess exact values z i from the approximated shapes reported by SnapPy.  ... 
arXiv:1502.00383v2 fatcat:5xqu4x65t5d7jelcm3gh2altju

A Census of Tetrahedral Hyperbolic Manifolds

Evgeny Fominykh, Stavros Garoufalidis, Matthias Goerner, Vladimir Tarkaev, Andrei Vesnin
2016 Experimental Mathematics  
Following an earlier publication by three of the authors, we give a census of all tetrahedral manifolds and all of their combinatorial tetrahedral tessellations with at most 25 (orientable case) and 21  ...  Our isometry classification uses certified canonical cell decompositions (based on work by Dunfield, Hoffman, Licata) and isomorphism signatures (an improvement of dehydration sequences by Burton).  ...  We first guess exact values z i from the approximated shapes reported by SnapPy.  ... 
doi:10.1080/10586458.2015.1114436 fatcat:qpsgwhkemjbnbe75jbjoky74ii

An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components [chapter]

M. Mostefa Mesmoudi, Leila De Floriani, Franco Morando, Enrico Puppo
2005 Mathematics and Visualization  
We present a decomposition algorithm, whose complexity is slightly super-linear in the total number of simplexes.  ...  To this aim, we have developed a combinatorial approach based on decomposing a non-manifold d-dimensional object into an assembly of more regular components, that we call initial quasi-manifolds.  ...  Moreover, since our decomposition operates locally, we can use this approach to define a measure of "shape complexity" at each non-manifold singularity, and thus to guide a complexity-preserving shape  ... 
doi:10.1007/3-540-26808-1_4 fatcat:nax5mjztnfgndluexxsj2pfav4

Graphical objects

Jonas Gomes, Bruno Costa, Lucia Darsa, Luiz Velho
1996 The Visual Computer  
In a decomposition representation, the combinatorial must be specified explicitly so that the object shape can be reconstructed from its representation.  ...  Decomposition Shape Representation In a decomposition representation, the object shape is decomposed into a family of subsets. This representation uses the well known "divide and conquer" paradigm.  ... 
doi:10.1007/s003710050064 fatcat:qpnceqefmvbwjfwxcq3zre3v4e

Graphical objects

Jonas Gomes, Bruno Costa, Lucia Darsa, Luiz Velho
1996 The Visual Computer  
In a decomposition representation, the combinatorial must be specified explicitly so that the object shape can be reconstructed from its representation.  ...  Decomposition Shape Representation In a decomposition representation, the object shape is decomposed into a family of subsets. This representation uses the well known "divide and conquer" paradigm.  ... 
doi:10.1007/bf01782289 fatcat:uhktwkgwxrchjgu6hjtqup4et4

Decomposition Search: A Combinatorial Games Approach to Game Tree Search, with Applications to Solving Go Endgames

Martin Müller
1999 International Joint Conference on Artificial Intelligence  
The method does not use traditional minimax search algorithms such as alpha-beta, but relies on concepts from combinatorial game theory to do locally restricted searches.  ...  We develop a new method called decomposition search for computing minimax solutions to games that can be partitioned into independent subgames.  ...  Practical limits are highly game-specific, and depend on the shape of local game graphs built during LCGS and on the complexity of the combinatorial games involved.  ... 
dblp:conf/ijcai/Muller99 fatcat:nvr5hfadxfbudhw44cudrgbcm4

A Robustness Study for the Extraction of Watertight Volumetric Models from Boundary Representation Data

Markus Wilhelm Jahn, Patrick Erik Bradley
2022 ISPRS International Journal of Geo-Information  
previous results by presenting the unpublished used algorithms to find inner disjoint (d+1)-dimensional simplicial complexes from a set of intersecting d-dimensional simplicial complexes which partly shape  ...  Some could shape hulls (2-dimensional sphere), which seem to show a combinatorial Euler characteristic of two (see Section 3.3 Euler's polyhedron formula of Theorem 1).  ...  The combinatorial Euler characteristics are calculated for each decomposition type presented as a distribution over the number of spatial objects which share the same combinatorial Euler characteristic  ... 
doi:10.3390/ijgi11040224 fatcat:omh7foyrb5d25juzri4bit7yjy

Non-manifold Decomposition in Arbitrary Dimensions [chapter]

Leila De Floriani, Mostefa Mohammed Mesmoudi, Franco Morando, Enrico Puppo
2002 Lecture Notes in Computer Science  
Therefore, we define d-quasi-manifolds, a decidable superset of the class of combinatorial d-manifolds that coincides with d-manifolds in dimension less or equal than two.  ...  This result provides a rigorous starting point for our future work, which includes designing efficient data structures for non-manifold modeling, as well as defining a notion of measure of shape complexity  ...  This notion will be used to define a measure of the amount of shape complexity at each non-manifold point.  ... 
doi:10.1007/3-540-45986-3_6 fatcat:nby5mtrdlnch3cezenmf72cnji

Crossing Stocks and the Positive Grassmannian I: The Geometry Behind Stock Market

Ovidiu Sorin Racorean
2014 Social Science Research Network  
It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape.  ...  From this point on the financial and combinatorial concepts are netted together to build a bridge connecting the stock market to a beautiful geometrical object that will be called stock market polytope  ...  the final geometrical shape picture of stock market is reached.  ... 
doi:10.2139/ssrn.2512437 fatcat:mw6ocqemafbrhghelvcl72hcze

Crossing Stocks and the Positive Grassmannian I: The Geometry behind Stock Market [article]

Ovidiu Racorean
2014 arXiv   pre-print
It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape.  ...  From this point on the financial and combinatorial concepts are netted together to build a bridge connecting the stock market to a beautiful geometrical object that will be called stock market polytope  ...  the final geometrical shape picture of stock market is reached.  ... 
arXiv:1402.1281v2 fatcat:g4fywilarzawdp2pvylhoqijge

Rational tableaux and the tensor algebra of gln

John R Stembridge
1987 Journal of combinatorial theory. Series A  
In particular, these characters give a combinatorial explanation for the known connection between the decomposition of glFk and the decomposition of tensor products of irreducible Sk-modules.  ...  We reformulate this problem into the combinatorial framework we have developed, and prove the existence of a recursive, insertion-type algorithm that describes this decomposition (Sect. 6).  ...  As an application, we use this description to give combinatorial explanations of a family of generating functions found by Hanlon [3] which describe the decomposition of gl,Ok in certain limiting cases  ... 
doi:10.1016/0097-3165(87)90077-x fatcat:kc626rvg4vb6dpri72p3wkrwvm

Shape Convergence for Aggregate Tiles in Conformal Tilings [article]

Richard Kenyon, Kenneth Stephenson
2017 arXiv   pre-print
We prove that aggregate tiles within T_n converge in shape as n→∞ to their associated Euclidean tiles in T.  ...  An intriguing aspect of shape convergence is that the purely combinatorial data in K and τ encode precise Euclidean shapes.  ...  As noted earlier, if we ignore the metric properties of T , we are left with a cell decomposition of a topological plane, which we treat as a combinatorial tiling and denote by K.  ... 
arXiv:1703.04371v1 fatcat:ll2nvml4pzgkvbzqaeli3uohn4

The complex of pant decompositions of a surface [article]

Silvia Benvenuti, Riccardo Piergallini
2007 arXiv   pre-print
We exhibit a set of edges (moves) and 2-cells (relations) making the complex of pant decompositions on a surface a simply connected complex.  ...  Once again, the shape of the bigons changes when lifted from the combinatorial setting to the new one, as depicted in Figure 29 , while all the other combinatorial cells maintain their shape.  ...  Notice that the shape of the bigons and that of the pentagons change when lifted to the decorated setting, as depicted in Figure 25 , while all the other combinatorial cells maintain their shape.  ... 
arXiv:0710.1483v2 fatcat:j4auqkkjtrgkrfiwiybizvva6q
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