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Computing the optimal bridge between two convex polygons

1999
*
Information Processing Letters
*

Given

doi:10.1016/s0020-0190(99)00003-4
fatcat:gow4keukbbefzmbxeoxkg7qweu
*two*disjoint*convex**polygonal*regions P, Q in*the*plane, add a line segment to connect them so as to minimize*the*maximum of*the*distances*between*points in one region and points in*the*other region ... An O(n2 logn) time algorithm is presented to lind such a line segment (*optimal**bridge*) (p, q), where n is*the*maximal cardinality of P. Q. ...*The*above algorithm certainly runs in O(n) time as*the**computation*of*the*separation*between**two**convex**polygons*can easily be*computed*in O(n) time with*the*hierarchical representations of P, Q [6]. ...##
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Computing the Optimal Bridge between Two Polygons

2001
*
Theory of Computing Systems
*

These problems are motivated from

doi:10.1007/s00224-001-1018-2
fatcat:ankd6mkr4fayfb7kyqj7stvj6m
*the**bridge*construction*between**two*islands (or*the*canal construction*between**two*lakes). ... Let P and Q be disjoint*polygons*in*the*plane. ...*compute**the**optimal**bridge**between*P and Q in O(n + m) time. ...##
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EXACT AND APPROXIMATION ALGORITHMS FOR FINDING AN OPTIMAL BRIDGE CONNECTING TWO SIMPLE POLYGONS

2005
*
International journal of computational geometry and applications
*

We show that an

doi:10.1142/s0218195905001889
fatcat:wds3w2xbjbflbm2n4nhzigxx5m
*optimal**bridge*always exists such that*the*endpoints of*the**bridge*lie on*the*boundaries of*the**two**polygons*. ... Mitchell) Given*two*simple*polygons*P and Q we define*the*weight of a*bridge*(p, q), with p ∈ ρ(P ) and q ∈ ρ(Q), where ρ() denotes*the*compact region enclosed by*the*boundary of*the**polygon*,*between**the*... Their algorithm takes O(n 2 log n) time to construct an*optimal**bridge**between*any*two*given disjoint*convex**polygons*. ...##
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Optimal tetrahedralization of the 3D-region "between" a convex polyhedron and a convex polygon

1996
*
Computational geometry
*

Our result also implies a simple and

doi:10.1016/0925-7721(95)00011-9
fatcat:zjs6b5simjadjlnfbxj66xobii
*optimal*algorithm for*the*side-by-side case (Bern, 1993) when Steiner points are allowed:*the*region "*between*"*two*non-intersecting*convex*polyhedra of total size n ... P, and can be*computed*in*optimal*O(n) time. ... We*compute**the**bridges*of*the**convex*hull of P tO Q; this can be done by using*the*lineartime merging procedure of*the*divide-and-conquer algorithm to*compute**the**convex*hull of a point set in ~3 [8] ...##
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Dual-Space Decomposition of 2D Complex Shapes

2014
*
2014 IEEE Conference on Computer Vision and Pattern Recognition
*

Our method creates a nearly

doi:10.1109/cvpr.2014.529
dblp:conf/cvpr/LiuXL14
fatcat:zjwrygmgyjhdpewjwhdtldit4e
*convex*decomposition of a given shape by segmenting both*the**polygon*itself and its complementary. ... Based on*two*evaluation methods, we show that this new decomposition method creates statistically similar to those produced by human subjects. ...*The*simplified polygonP is composed of intolerable concave features and*the*vertices*between**two*consecutive*bridges*. ...##
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On separating two simple polygons by a single translation

1989
*
Discrete & Computational Geometry
*

Let P and Q be

doi:10.1007/bf02187729
fatcat:kmnpoma7gjbplfcjbzxanvqleu
*two*disjoint simple*polygons*having n sides each. ...*The*algorithm runs in time O(t(n)) where t(n) is*the*time needed to triangulate an n-sided*polygon*. ... Acknowledgment*The*author is grateful to David Avis and Hossam ElGindy for discussions on this topic and to Binay Bhattacharya for*the*suggestion that*the*region Z(P, Q) might help in reducing*the*complexity ...##
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Editorial

2003
*
Computational geometry
*

*The*second paper by Takeshi Tokuyama gives efficient algorithms for constructing a

*bridge*

*between*

*two*

*convex*regions in a fixed dimensional space so that

*the*diameter of

*the*

*bridged*region is minimized ... Finally,

*the*fifth paper by Hiro Ito discusses

*the*sum of edge lengths of a multigraph drawn on a

*convex*

*polygon*and notes that three different partial orders on local transformations are equivalent. ...

*The*second paper by Takeshi Tokuyama gives efficient algorithms for constructing a

*bridge*

*between*

*two*

*convex*regions in a fixed dimensional space so that

*the*diameter of

*the*

*bridged*region is minimized ...

##
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Triangulation of Branching Contours Using Area Minimization

1998
*
International journal of computational geometry and applications
*

*The*current algorithm extends this idea by searching for

*the*surface of minimal area which connects

*two*contours comprised of more than one

*polygon*. ... This paper presents a new method for reconstructing piecewise linear surfaces from planar

*polygonal*contours that branch. ...

*The*views and conclusions contained herein are those of

*the*authors and should not be interpreted as necessarily representing

*the*o cial policies or endorsements, either expressed or implied, of

*the*Air ...

##
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Optimal positioning of irregular shapes in stamping die strip

2010
*
The International Journal of Advanced Manufacturing Technology
*

In particular, most of

doi:10.1007/s00170-010-2772-6
fatcat:oi4smb5cerfefhfvaq7vonvev4
*the*different proposed procedures are based on*the*No Fit*Polygon*(NFP)*computation*of non-*convex**polygons*, which often generates holes. ... This procedure firstly obtains*the*"No Fit Path" (NFPh); secondly,*between*all*the*existing positions on*the*NFPh,*the*algorithm searches*the**optimal*one, minimizing*the*global waste. ... Acknowledgments This work was performed with*the*financial support of*the*Italian Ministry of University and Research. ...##
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Hybrid method for automating generation of reticulated structures (lattice structures) in complex conception domains

2019
*
International Journal of Electrical and Computer Engineering (IJECE)
*

So they can be

doi:10.11591/ijece.v9i2.pp1327-1334
fatcat:v5iukacg5vepblpqqpzknmo2ze
*the*best choice when material gain is an*optimization*purpose. Generating a reticulated structure automatically is a feature helping industrial players in*the*design phase. ... Our new algorithm uses a method of*computational*geometry. ...*The*solution we propose is hybridization*between**two*solutions. First we take advantage of*the*simplicity of*the*principle of generating reticulated structures in a*convex*domain. ...##
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Approximate convex decomposition of polygons

2004
*
Proceedings of the twentieth annual symposium on Computational geometry - SCG '04
*

We propose a simple algorithm that

doi:10.1145/997817.997823
dblp:conf/compgeom/LienA04
fatcat:v3uw4fhnqvbx3fu2nohxmc5heq
*computes*an ACD of a*polygon*by iteratively removing (resolving)*the*most significant non-*convex*feature (notch). ... Our algorithm*computes*an ACD of a simple*polygon*with n vertices and r notches in O(nr) time. In contrast, exact*convex*decomposition is NP-hard or, if*the**polygon*has no holes, takes O(nr 2 ) time. ... Given a simple*polygon*P . Notches can only be found in pockets. Each*bridge*has an associated pocket,*the*chain of ∂P 0*between**the**two**bridge*vertices. ...##
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Approximate convex decomposition of polygons

2006
*
Computational geometry
*

We propose a simple algorithm that

doi:10.1016/j.comgeo.2005.10.005
fatcat:uaoejsgl7zfdfol5wtvc2mvgeq
*computes*an ACD of a*polygon*by iteratively removing (resolving)*the*most significant non-*convex*feature (notch). ... Our algorithm*computes*an ACD of a simple*polygon*with n vertices and r notches in O(nr) time. In contrast, exact*convex*decomposition is NP-hard or, if*the**polygon*has no holes, takes O(nr 2 ) time. ... Given a simple*polygon*P . Notches can only be found in pockets. Each*bridge*has an associated pocket,*the*chain of ∂P 0*between**the**two**bridge*vertices. ...##
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Page 3565 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
*
Mathematical Reviews
*

2002e:68131 68U05
Bhattacharya, Binay (3-SFR-SC; Burnaby, BC);
Benkoczi, Robert (3-SFR-SC; Burnaby, BC)
On

*computing**the**optimal**bridge**between**two**convex**polygons*. ... An*optimal*algorithm for constructing an*optimal**bridge**between**two*simple rectilinear*polygons*. (English summary) Inform. Process. Lett. 79 (2001), no. 5, 229-236. ...##
###
Approximate convex decomposition of polyhedra and its applications

2008
*
Computer Aided Geometric Design
*

In this work, we have developed an approximate technique, called Approximate

doi:10.1016/j.cagd.2008.05.003
fatcat:eus3f3libvcrvgmv2qjgzpuwta
*Convex*Decomposition (ACD), which decomposes a given*polygon*or polyhedron into "approximately*convex*" pieces that may provide ... similar benefits as*convex*components, while*the*resulting decomposition is both significantly smaller (typically by orders of magnitude) and can be*computed*more efficiently. ...*Bridges*and Pockets Our concavity measures use*the*concepts of notches,*bridges*and pockets; see Each*bridge*has an associated pocket,*the*chain of ∂P 0*between**the**two**bridge*vertices. ...##
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Ear-Clipping Based Algorithms of Generating High-Quality Polygon Triangulation
[chapter]

2012
*
Lecture Notes in Electrical Engineering
*

To apply

doi:10.1007/978-3-642-34531-9_105
fatcat:pski2vstiffojnsuy42i2ezfnq
*the**two*algorithms on*polygons*with holes, "*Bridge*" edges are created to transform a*polygon*with holes to a degenerate*polygon*which can be triangulated by*the**two*algorithms. ... A basic and an improved ear clipping based algorithm for triangulating simple*polygons*and*polygons*with holes are presented. ... Because*the**two*vertices of*the*'*Bridge*' edge are added twice,*the*new*polygon*P new has (m+n+2) vertices. ...
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