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Non-Euclidean Spring Embedders

S.G. Kobourov, K. Wampler
2005 IEEE Transactions on Visualization and Computer Graphics  
The method relies on extending the Euclidean notions of distance, angle, and force-interactions to smooth non-Euclidean geometries via projections to and from appropriately chosen tangent spaces.  ...  Generalizing the non-Euclidean spring embedders along the lines of [5, 7] should be possible.  ...  Spherical Geometry As a further example for generalizing spring embedders to non-Euclidean geometry we also consider spherical geometry.  ... 
doi:10.1109/tvcg.2005.103 pmid:16270867 fatcat:nhshmnhfrngdfbcuh4ezg6b3xi

Non-Euclidean Spring Embedders

S.G. Kobourov, K. Wampler
IEEE Symposium on Information Visualization  
The method relies on extending the Euclidean notions of distance, angle, and force-interactions to smooth non-Euclidean geometries via projections to and from appropriately chosen tangent spaces.  ...  Generalizing the non-Euclidean spring embedders along the lines of [5, 7] should be possible.  ...  placement(n, G ) position[n] := τ −1 x (x ) end end Figure 4 : 4 A generic Euclidean spring embedder and its non-Euclidean counterpart.  ... 
doi:10.1109/infvis.2004.49 dblp:conf/infovis/KobourovW04 fatcat:3p7fmrvlxjhdjh4swksmyh2jgi

Methodology and Techniques [chapter]

Dirk Knaust
2012 Developments in Sedimentology  
The method relies on extending the Euclidean notions of distance, angle, and force-interactions to smooth non-Euclidean geometries via projections to and from appropriately chosen tangent spaces.  ...  Generalizing the non-Euclidean spring embedders along the lines of [5, 7] should be possible.  ...  placement(n, G ) position[n] := τ −1 x (x ) end end Figure 4 : 4 A generic Euclidean spring embedder and its non-Euclidean counterpart.  ... 
doi:10.1016/b978-0-444-53813-0.00009-5 fatcat:ojtyvy2asnhm7mhuhhmf65li7q

Automatic graph clustering (system demonstration) [chapter]

Reinhard Sablowski, Arne Frick
1997 Lecture Notes in Computer Science  
As spring-embedder drawings tend to have related nodes close to each other, geometric proximity and statistical techniques [5] may be applied to compute clusterings from spring-embedder drawings as well  ...  One possible technique to visualize clusterings is to apply a spring-embedder algorithm [4] .  ... 
doi:10.1007/3-540-62495-3_63 fatcat:yysfcaeewrdh3jpnozhxpgfo2e

Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

Luca Castelli Aleardi, Gaspard Denis, Éric Fusy, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local  ...  While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders.  ...  (Spherical) Spring Embedders. While spring embedders are originally designed to produce 2D or 3D layouts, one can adapt them to non euclidean geometries.  ... 
doi:10.4230/lipics.sea.2018.24 dblp:conf/wea/AleardiDF18 fatcat:oonyafnkirdkjmwdr6csmzzfei

The spring bounces back: introducing the strain elevation tension spring embedding algorithm for network representation

Jonathan Bourne
2020 Applied Network Science  
This paper introduces the strain elevation tension spring embedding (SETSe) algorithm.  ...  SETSe is a novel graph embedding method that uses a physical model to project feature-rich networks onto a manifold with semi-Euclidean properties.  ...  It should also be noted that although SETSe is embedded in Euclidean space and the graph space, other non-Euclidean spaces can be used.  ... 
doi:10.1007/s41109-020-00329-4 fatcat:dzimluwdtrh2lmc3njhfmkerte

Spring Embedders and Force Directed Graph Drawing Algorithms [article]

Stephen G. Kobourov
2012 arXiv   pre-print
Also known as spring embedders, such algorithms calculate the layout of a graph using only information contained within the structure of the graph itself, rather than relying on domain-specific knowledge  ...  Then we obtain pseudo-code for a traditional Euclidean spring embedder and its corresponding Riemannian counterpart; see Algorithm 8.  ...  Non-Euclidean Approaches Much of the work on non-Euclidean graph drawing has been done in hyperbolic space which offers certain advantages over Euclidean space; see Munzner [52, 54] .  ... 
arXiv:1201.3011v1 fatcat:ndxz6xgx7fdkthtloaty5en2fq

On graphical representations of similarity in geo-temporal frequency data

Daniel Weidele, Mereke van Garderen, Mark Golitko, Gary M. Feinman, Ulrik Brandes
2016 Journal of Archaeological Science  
Distance scaling (Gansner et al., 2005) , on the other hand, is the use of non-metric MDS (Kruskal, 1964) for graph layout and can be viewed as a special type of spring-embedder with springs of various  ...  We also note that common spring-embedder algorithms do not result in layouts that can be interpreted reliably.  ... 
doi:10.1016/j.jas.2016.05.013 fatcat:sn2ifoxjivbvrfhdakfzyumxgu

Self-Referential Noise and the Synthesis of Three-Dimensional Space

Reginald T. Cahill, Christopher M. Klinger
2000 General Relativity and Gravitation  
We argue that this is relevant to modelling the universe and show how three-dimensional space may arise from a non-geometric order-disorder model driven by self-referential noise.  ...  The measure V corresponds to a spring embedding model in which the spring between monad i and j has spring constant κ = B 2 ij , and natural length 1/|B ij |.  ...  embeddability.  ... 
doi:10.1023/a:1001984518976 fatcat:bnewekbt5zb5pd3arb5q6ul4gu

The spring bounces back: Introducing the Strain Elevation Tension Spring embedding algorithm for network representation [article]

Jonathan Bourne
2020 arXiv   pre-print
This paper introduces the Strain Elevation Tension Spring embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks  ...  These algorithms are sometimes called 'spring embedders' [17] due to using springs or spring-like methods to place nodes and typically attempt to optimise an ideal distance between nodes, minimising  ...  SETSe space is a non-Euclidean metric space of n + 1 dimensions where n is the number of attributes the network has. The n + 1th dimension is the graph space, representing the graph adjacency matrix.  ... 
arXiv:2007.09437v1 fatcat:lesyl7zjwbhqrczl633njb5nzy

A Characterization of bi-Lipschitz embeddable metric spaces in terms of local bi-Lipschitz embeddability

Jeehyeon Seo
2011 Mathematical Research Letters  
We characterize uniformly perfect, complete, doubling metric spaces, which embed bi-Lipschitzly into Euclidean space.  ...  We prove that if the Whitney cubes embed uniformly bi-Lipschitzly into a fixed Euclidean space, and if the complement of Ω also embeds, then so does the full space. Received by the editors xxx.  ...  Mackay when I took reading courses in Fall 2009 and in Spring 2010. I also want to thank Jang-Mei Wu, John P. D'Angelo, and Sergiy Merenkov for their careful reading and comments.  ... 
doi:10.4310/mrl.2011.v18.n6.a9 fatcat:nearlydovjccpeq6q3d4qodjve

A Characterization of Bi-Lipschitz Embeddable Metric Spaces in Terms of Local Bi-Lipschitz Embeddability [article]

Jeehyeon Seo
2011 arXiv   pre-print
We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into Euclidean space.  ...  We prove that if the Whitney cubes embed uniformly bi-Lipschitzly into a fixed Euclidean space, and if the complement of Ω also embeds, then so does the full space.  ...  is not bi-Lipschitzly embeddable into any Euclidean space.  ... 
arXiv:1105.2529v1 fatcat:coe7ltprevfevegxoze6fpzhim

Drawing graphs using modular decomposition

Charis Papadopoulos, Costas Voglis
2007 Journal of Graph Algorithms and Applications  
In order to achieve aesthetically pleasing results, we use grid and circular placement techniques, and utilize an appropriate modification of a well-known spring embedder algorithm.  ...  It turns out, that for some classes of graphs, our algorithm runs in O(n + m) time, while in general, the running time is bounded in terms of the processing time of the spring embedder algorithm.  ...  Modified Spring Embedder In this section we describe in detail a spring embedder algorithm for the implementation of function Draw Prime. Recall that this function is applied on an N-node t ∈ T (G).  ... 
doi:10.7155/jgaa.00155 fatcat:dxobmywkdzbv7eqtpcszpxyz5u

Drawing Graphs Using Modular Decomposition [chapter]

Charis Papadopoulos, Constantinos Voglis
2006 Lecture Notes in Computer Science  
In order to achieve aesthetically pleasing results, we use grid and circular placement techniques, and utilize an appropriate modification of a well-known spring embedder algorithm.  ...  It turns out, that for some classes of graphs, our algorithm runs in O(n + m) time, while in general, the running time is bounded in terms of the processing time of the spring embedder algorithm.  ...  Modified Spring Embedder In this section we describe in detail a spring embedder algorithm for the implementation of function Draw Prime. Recall that this function is applied on an N-node t ∈ T (G).  ... 
doi:10.1007/11618058_31 fatcat:jtektwfdn5dl5evytclh7zgw6i

eulerForce: Force-directed layout for Euler diagrams

Luana Micallef, Peter Rodgers
2014 Journal of Visual Languages and Computing  
However, current automatic methods often produce diagrams with irregular, non-smooth curves that are not easily distinguishable.  ...  One of the simplest forcedirected methods is the spring embedder [6] .  ...  Our repulsive forces are the same as those used in Eades' spring embedder [6] .  ... 
doi:10.1016/j.jvlc.2014.09.002 fatcat:32nnhvt7gzcudjtefpvlcswwsy
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