QUADRILATERAL MESHING BY CIRCLE PACKING

We use circle-packing methods to generate quadrilateral meshes for polygonal domains, with guaranteed bounds both on the quality and the number of elements. We show that these methods can generate meshes of several types: (1) the elements form the cells of a Voronoï diagram, (2) all elements have two opposite 90° angles, (3) all elements are kites, or (4) all angles are at most 120°. In each case the total number of elements is O(n), where n is the number of input vertices.

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Voronoi diagram for multiply-connected polygonal domains II: Implementation and application

IBM Journal of Research and Development ◽

10.1147/rd.313.0373 ◽

1987 ◽

Vol 31 (3) ◽

pp. 373-381 ◽

Cited By ~ 18

Author(s):

Siavash N. Meshkat ◽

Constantine M. Sakkas

Keyword(s):

Voronoi Diagram ◽

Polygonal Domains ◽

Multiply Connected

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Voronoi diagram for multiply-connected polygonal domains I: Algorithm

IBM Journal of Research and Development ◽

10.1147/rd.313.0361 ◽

1987 ◽

Vol 31 (3) ◽

pp. 361-372 ◽

Cited By ~ 64

Author(s):

Vijay Srinivasan ◽

Lee R. Nackman

Keyword(s):

Voronoi Diagram ◽

Polygonal Domains ◽

Multiply Connected

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Diamond-Kite Meshes: Adaptive Quadrilateral Meshing and Orthogonal Circle Packing

Proceedings of the 21st International Meshing Roundtable ◽

10.1007/978-3-642-33573-0_16 ◽

2013 ◽

pp. 261-277

Author(s):

David Eppstein

Keyword(s):

Circle Packing ◽

Quadrilateral Meshing ◽

Orthogonal Circle

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A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains

Algorithmica ◽

10.1007/pl00009199 ◽

1998 ◽

Vol 20 (4) ◽

pp. 319-352 ◽

Cited By ~ 24

Author(s):

E. Papadopoulou ◽

D. T. Lee

Keyword(s):

Voronoi Diagram ◽

Simple Polygon ◽

New Approach ◽

Polygonal Domains

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Model and algorithm for searching for victims in emergency situations and fires using the Voronoi diagram

Technology of technosphere safety ◽

10.25257/tts.2019.4.86.53-61 ◽

2019 ◽

Vol 86 ◽

pp. 53-61

Author(s):

N. G. Topolskiy ◽

◽

A. V. Mokshantsev ◽

To Hoang Thanh ◽

◽

...

Keyword(s):

Voronoi Diagram ◽

Emergency Situations

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A Bottom-Up Approach to Solution-Processed, Atomically Precise Graphitic Cylinders on Surfaces

10.26434/chemrxiv.7158959 ◽

2018 ◽

Author(s):

Erik Leonhardt ◽

Jeff M. Van Raden ◽

David Miller ◽

Lev N. Zakharov ◽

Benjamin Aleman ◽

...

Keyword(s):

Self Assembly ◽

Carbon Nanostructures ◽

Carbon Nanomaterials ◽

Circle Packing ◽

Pyrolytic Graphite ◽

Building Blocks ◽

Bottom Up ◽

Casting Technique ◽

New Class ◽

Solution Casting Technique

Extended carbon nanostructures, such as carbon nanotubes (CNTs), exhibit remarkable properties but are difficult to synthesize uniformly. Herein, we present a new class of carbon nanomaterials constructed via the bottom-up self-assembly of cylindrical, atomically-precise small molecules. Guided by supramolecular design principles and circle packing theory, we have designed and synthesized a fluorinated nanohoop that, in the solid-state, self-assembles into nanotube-like arrays with channel diameters of precisely 1.63 nm. A mild solution-casting technique is then used to construct vertical “forests” of these arrays on a highly-ordered pyrolytic graphite (HOPG) surface through epitaxial growth. Furthermore, we show that a basic property of nanohoops, fluorescence, is readily transferred to the bulk phase, implying that the properties of these materials can be directly altered via precise functionalization of their nanohoop building blocks. The strategy presented is expected to have broader applications in the development of new graphitic nanomaterials with π-rich cavities reminiscent of CNTs.

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