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### Computing the optimal bridge between two convex polygons

Cai Leizhen, Xu Yinfeng, Zhu Binhai
1999 Information Processing Letters
Given 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 .  ...

### Computing the Optimal Bridge between Two Polygons

Sung Kwon Kim, Chan-Su Shin
2001 Theory of Computing Systems
These problems are motivated from 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.  ...

### EXACT AND APPROXIMATION ALGORITHMS FOR FINDING AN OPTIMAL BRIDGE CONNECTING TWO SIMPLE POLYGONS

AMIT M. BHOSLE, TEOFILO F. GONZALEZ
2005 International journal of computational geometry and applications
We show that an 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.  ...

### Optimal tetrahedralization of the 3D-region "between" a convex polyhedron and a convex polygon

Leonidas Palios
1996 Computational geometry
Our result also implies a simple and 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   ...

### Dual-Space Decomposition of 2D Complex Shapes

Guilin Liu, Zhonghua Xi, Jyh-Ming Lien
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition
Our method creates a nearly 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.  ...

### On separating two simple polygons by a single translation

G. Toussaint
1989 Discrete & Computational Geometry
Let P and Q be 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  ...

### Editorial

Jin Akiyama, Tetsuo Asano, Mikio Kano
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  ...

### Triangulation of Branching Contours Using Area Minimization

Mu Hong, Thomas W. Sederberg, Krzysztof S. Klimaszewski, Kazufumi Kaneda
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  ...

### Optimal positioning of irregular shapes in stamping die strip

Roberto Licari, E. Lo Valvo
2010 The International Journal of Advanced Manufacturing Technology
In particular, most of 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.  ...

### Hybrid method for automating generation of reticulated structures (lattice structures) in complex conception domains

Zineb Biallaten, Raddouane Chiheb, Abdellatif El Afia
2019 International Journal of Electrical and Computer Engineering (IJECE)
So they can be 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.  ...

### Approximate convex decomposition of polygons

Jyh-Ming Lien, Nancy M. Amato
2004 Proceedings of the twentieth annual symposium on Computational geometry - SCG '04
We propose a simple algorithm that 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.  ...

### Approximate convex decomposition of polygons

Jyh-Ming Lien, Nancy M. Amato
2006 Computational geometry
We propose a simple algorithm that 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.  ...

### 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

Jyh-Ming Lien, Nancy M. Amato
2008 Computer Aided Geometric Design
In this work, we have developed an approximate technique, called Approximate 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.  ...

### Ear-Clipping Based Algorithms of Generating High-Quality Polygon Triangulation [chapter]

Gang Mei, John C. Tipper, Nengxiong Xu
2012 Lecture Notes in Electrical Engineering
To apply 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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