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Interactive Planarization and Optimization of 3D Meshes

2013
*
Computer graphics forum (Print)
*

Specifically, polyhedral meshes -those having

doi:10.1111/cgf.12005
fatcat:32sugisk5zbuxehkouho4hhgjq
*planar*faces -are very important, but also notoriously difficult to generate*and*manipulate efficiently. ... We describe an interactive method for computing, optimizing*and*editing polyhedral meshes. ... We would also like to thank Philippe Block*and*Lorenz Lachauer for introducing us to the optimal lifting*problem**and*the meshes in Fig. 4. C. Gotsman's work was partially supported by the B.*and*G. ...##
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Strip Planarity Testing
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show that the

doi:10.1007/978-3-319-03841-4_4
fatcat:tcn2wccmvfefblzuevhebnqnp4
*problem*is polynomial-*time*solvable if G has a fixed*planar*embedding. ... In this paper we introduce*and*study the strip*planarity*testing*problem*, which takes as an input a*planar*graph G(V, E)*and*a function γ : V → {1, 2, . . . , k}*and*asks whether a*planar*drawing of G ... A celebrated result of Hopcroft*and*Tarjan [20] states that the*planarity*testing*problem*is solvable in*linear**time*. ...##
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The complexity of the locally connected spanning tree problem

2003
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Discrete Applied Mathematics
*

On the other hand, we obtain a

doi:10.1016/s0166-218x(02)00417-1
fatcat:sfncnok4ozdc5pkddvkrt5omsm
*linear*-*time*algorithm for ÿnding a*locally*connected spanning tree in a directed path graph,*and*a*linear*-*time*algorithm for adding fewest edges to a graph to make a given ... We prove that the*problem*of determining whether a graph contains a*locally*connected spanning tree is NP-complete, even when input graphs are restricted to*planar*graphs or split graphs. ... On the other hand, we will give a*linear*-*time*algorithm for ÿnding a*locally*connected spanning tree in a directed path graph,*and*a*linear*-*time*algorithm for adding fewest edges to a graph to make a given ...##
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A Decoupled and Linear Framework for Global Outlier Rejection over Planar Pose Graph
[article]

2022
*
arXiv
*
pre-print

It turns out that it runs significantly (sometimes up to over 30

arXiv:2209.08543v1
fatcat:6haz6dogl5gbdniza6jnfkm6ni
*times*) faster than the standard*and*general-purpose GNC while resulting in high-quality estimates. ... Thanks to the*linearity*properties of both the subproblems, our framework requires only*linear*solvers to optimally solve the optimization*problems*encountered in GNC. ... Decoupling the TLS-based robust PGO*problem**and*introducing a*linear*representation for*planar*rotation are the keys to the proposed framework. ...##
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Predecessor existence problems for finite discrete dynamical systems

2007
*
Theoretical Computer Science
*

*problem*-deciding whether there is a unique predecessor

*and*the AMBIGUOUS-PREDECESSOR EXISTENCE (or APRE)

*problem*-given a configuration C

*and*a predecessor C of C, deciding whether there is a different ... Our results extend the earlier results of Green, Sutner

*and*Orponen on the complexity of the predecessor existence

*problem*

*and*its variants. ... UPRE is D P -complete for (BOOL, S,

*PLANAR*)-SDSs (SyDSs). ...

##
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Designing Practical PTASes for Minimum Feedback Vertex Set in Planar Graphs
[article]

2018
*
arXiv
*
pre-print

We present two algorithms for the minimum feedback vertex set

arXiv:1804.07869v1
fatcat:nrvw3s55f5emxmtgkfywlwwp7e
*problem*in*planar*graphs: an O(n n) PTAS using a*linear*kernel*and*balanced separator,*and*a heuristic algorithm using kernelization*and**local*...*And*our heuristic algorithm can outperform the 2-approximation algorithm on most large*planar*graphs*and*provide a trade-off between running*time**and*solution quality, i.e. a "PTAS behavior". ... If the function h(k) is*linear*in k, then we say the*problem*admits a*linear*kernel. Bonamy*and*Kowalik's*linear*kernel for*planar*FVS [9] consists of a sequence of 17 reduction rules. ...##
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Analysis situs and image processing
[chapter]

1997
*
Lecture Notes in Computer Science
*

Furthermore, a new

doi:10.1007/3-540-63507-6_201
fatcat:lmadhfzupfgndk62cyv3igrdf4
*linear**time*algorithm for the shortest path*problem*solution is described,*and*the approximation of the most important characteristic set in image processing is shown. ... In the paper a topological approach to approximation of*planar*Jordan curves*and*arcs is described. ... In view of Theorem 5, Step (4) has*linear**time*complexity which implies that Algorithm has also*linear**time*complexity. ...##
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Stability of self-similar solutions for van der Waals driven thin film rupture

1999
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Physics of Fluids
*

Of these, the dynamically stable similarity solutions produce observable rupture behavior as

doi:10.1063/1.870138
fatcat:jeew5bh4bfgg3e444kzatpxhna
*localized*, finite-*time*singularities in the models of the flow. ... In this letter we describe a systematic technique for calculating such solutions*and*determining their*linear*stability. ... ACKNOWLEDGMENTS We are indebted to Wendy Zhang*and*John Lister for sharing a preprint 2 of their work with us,*and*to Andrea Bertozzi for enlightening conversations about thin films*and*self-similarity ...##
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EEG source localization by multi-planar analytic sensing

2008
*
2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro
*

The estimation of the projection on each plane of the dipoles' positions, which is a non-

doi:10.1109/isbi.2008.4541186
dblp:conf/isbi/KandaswamyBSMV08
fatcat:5dyqvqdhcbbsvgcvaaytoykw54
*linear**problem*, is reduced to polynomial root finding. ... Source*localization*from EEG surface measurements is an important*problem*in neuro-imaging. We propose a new mathematical framework to estimate the parameters of a multidipole source model. ... Each 2-D*localization*provides us with the projection of the dipoles' positions*and*moments onto the respective plane. The paper is organized as follows. In Sect. 2, we introduce the*problem*setting. ...##
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Subject Index

2006
*
Journal of Discrete Algorithms
*

algorithms for weighted

doi:10.1016/s1570-8667(06)00094-3
fatcat:e5in7ez4svbdlcjyzzev4xkzhm
*problems*in sparse graphs, 588 Minimum-weight independent set Distributed algorithms for weighted*problems*in sparse graphs, 588 Monotonic*Linear**time*isotonic*and*unimodal ... The strength of weak proximity, 384 VLSI design Delay optimization of*linear*depth boolean cir- cuits with prescribed input arrival*times*, 526 Weighted flow*time*Online weighted flow*time**and*deadline ...##
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Checking the convexity of polytopes and the planarity of subdivisions

1998
*
Computational geometry
*

In particular, we design simple optimal checkers for convex polytopes in two

doi:10.1016/s0925-7721(98)00039-x
fatcat:y3eox33r2rfolf4qeri63hrire
*and*higher dimensions,*and*for various types of*planar*subdivisions, such as triangulations, Delaunay triangulations,*and*convex ... This paper considers the*problem*of verifying the correctness of geometric structures. ... Acknowledgements We would like to thank Giuseppe Di Battista, Michael Goodrich, David Kirkpatrick*and*Luca Vismara for useful discussions. ...##
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Checking the convexity of polytopes and the planarity of subdivisions (extended abstract)
[chapter]

1997
*
Lecture Notes in Computer Science
*

In particular, we design simple optimal checkers for convex polytopes in two

doi:10.1007/3-540-63307-3_59
fatcat:lbpnbl3qbjefbgq7uyuvwx2wai
*and*higher dimensions,*and*for various types of*planar*subdivisions, such as triangulations, Delaunay triangulations,*and*convex ... This paper considers the*problem*of verifying the correctness of geometric structures. ... Acknowledgments We w ould like to thank Giuseppe Di Battista, Michael Goodrich, David Kirkpatrick,*and*Luca Vismara for useful discussions. ...##
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Connectivity check in 3-connected planar graphs with obstacles

2008
*
Electronic Notes in Discrete Mathematics
*

Such embeddings can be constructed in

doi:10.1016/j.endm.2008.06.030
fatcat:iwpmuccqobfkjcmqqyyimavhcy
*linear**time*by Schnyder's algorithm [9] (see also [6, 7] ). ... A connectivity query asks whether there exists in the given graph a path linking u*and*v that avoids a set F of edges*and*a set X of vertices. ... Thorup [10] shows that a*planar*digraph can be preprocessed in near-*linear**time*, producing a near-*linear*space oracle that can answer reachability queries in constant*time*. ...##
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Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems
[article]

2008
*
arXiv
*
pre-print

The following dichotomy theorems are shown: (1) If F contains the self-dual functions

arXiv:0801.3802v2
fatcat:c4o6mzrkojdahhz3pp6hlmtkii
*and*G contains the*planar*graphs then the fixed-point existence*problem*for (F, G)-systems with*local*transition function ... existence*problem*for (F, G)-systems with*local*transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial*time*. ... Mayr (TU München) for careful proofreading*and*pointing out an error in earlier versions of this paper. ...##
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Page 5635 of Mathematical Reviews Vol. , Issue 96i
[page]

1996
*
Mathematical Reviews
*

“Variational principles are applied to generate numerical solu- tions to the full non-

*linear**problems*. ... This is another interesting paper by the author in which he proves the blow-up*and*asymptotics of thermal runaway in the non-*local**problem*u; = uxx +Af(u)/(f', f(u)dx)? ...
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