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Dissertations / Theses on the topic 'Polygonal'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Chipatala, Overtone. "Polygonal numbers." Kansas State University, 2016. http://hdl.handle.net/2097/32923.

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Master of Science<br>Department of Mathematics<br>Todd Cochrane<br>Polygonal numbers are nonnegative integers constructed and represented by geometrical arrangements of equally spaced points that form regular polygons. These numbers were originally studied by Pythagoras, with their long history dating from 570 B.C, and are often referred to by the Greek mathematicians. During the ancient period, polygonal numbers were described by units which were expressed by dots or pebbles arranged to form geometrical polygons. In his "Introductio Arithmetica", Nicomachus of Gerasa (c. 100 A.D), thoroughly

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2

Eu, David. "Polygonal curve approximation." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56992.

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Given a polygonal curve $P = lbrack p sb1,p sb2 ... p sb{n} rbrack$, the polygonal approximation problem considered in this thesis calls for determining a new curve $P sp prime = lbrack p sbsp{1}{ prime}, p sbsp{2}{ prime}, ..., p sbsp{m}{ prime} rbrack$ such that (i) m is significantly smaller than n, (ii) the vertices of $P sp prime$ are a subset of the vertices of P and (iii) any line segment $ lbrack p sbsp{A}{ prime}, p sbsp{A+1}{ prime} rbrack$ of $P sp prime$ that substitutes a chain $ lbrack p sb B, ...,p sb C rbrack$ in P is such that for all i where $B le i le C$, the approximation e

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3

陳健華 and Kin-wah Chan. "Multiresolution polygonal approximation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B30257402.

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4

Chan, Kin-wah. "Multiresolution polygonal approximation /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1985965X.

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5

Boczko, Erik M. "Polygonal approximation for flows." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/27306.

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6

Aloupis, Greg. "Reconfigurations of polygonal structures." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85114.

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This thesis contains new results on the subject of polygonal structure reconfiguration. Specifically, the types of structures considered here are polygons, polygonal chains, triangulations, and polyhedral surfaces. A sequence of vertices (points), successively joined by straight edges, is a polygonal chain. If the sequence is cyclic, then the object is a polygon. A planar triangulation is a set of vertices with a, maximal number of non-crossing straight edges joining them. A polyhedral surface is a three-dimensional structure consisting of flat polygonal faces that are joined by common

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7

陳穎韶 and Wing-shiu Chan. "Approximation of polygonal curves." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31211240.

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8

Chan, Wing-shiu. "Approximation of polygonal curves /." [Hong Kong : University of Hong Kong], 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1378710X.

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9

Žák, Pavel. "Modelování postav - Polygonal wrapper." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2007. http://www.nusl.cz/ntk/nusl-236897.

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This project is engaged in optimalization of 3D polygonal models. Main automatic and also manual principles and methods used in the area of character model optimalization are introduced and discussed. Next the approach named geometry mapping, which was created as a part of the project and enables the creation of models with desired topology, is described.

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10

Bonin, Arnaud Stephane. "Wrinkling in polygonal membranes." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/246094.

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Larger telescopes are required by astronomers to see further into the depths of our Universe, in order to understand its origins and the origins of life. A solution is to replace conventional primary mirrors in space-telescopes by membrane reflectors, that can be folded and fitted into a spacecraft before launch. Once deployed, the membrane would provide a large reflective surface necessary to obtain images of faraway celestial objects. Whilst the primary mirror of a space-telescope needs to have a very precise shape, membranes can have an uncertain shape for they are prone to wrinkling. For t

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11

BUI, XUAN-NAM. "Planification de trajectoire pour un robot polygonal non holonome dans un environnement polygonal." Paris, ENMP, 1994. http://www.theses.fr/1994ENMP0443.

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Nous etudions les robots non holonomes de type voiture et leurs trajectoires optimales en longueur. Ces robots sont soumis a deux contraintes cinematiques : son orientation est toujours tangente a la trajectoire, qui a une courbure majoree par une constante strictement positive. Dans un premier temps, nous partons des resultats de dubins limitant les formes des trajectoires optimales pour un robot se deplacant en marche avant dans un environnement plan sans obstacle. Nous calculons la synthese de ce probleme d'optimisation. Nous obtenons alors une partition de l'espace des configurations du ro

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12

Dietrich, Christof Peter. "Cavity effects in polygonal resonators." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-104393.

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In der vorliegenden Arbeit werden ZnO-Mikronadeln bezüglich ihrer Anwendbarkeit als Mikroresonatoren untersucht. Dabei stehen Kavitätsmoden im Fokus der Untersuchungen, die sich nur senkrecht zur Nadelachse ausbreiten, sprich innerhalb der hexagonalen Nadelquerschnittsfläche. Folglich wird der Einfluss der Gestalt der Querschnittsfläche auf Resonatoreigenschaften wie Propagation, Form, Direktionalität und Qualität der Kavitätsmoden sowohl theoretisch simuliert als auch experimentell nachgewiesen. Die dabei beobachteten hohen Qualitätsfaktoren von Flüstergalerie-Moden ermöglichen es darüberhina

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13

Garland, Michael. "Quadric-Based Polygonal Surface Simplification." Research Showcase @ CMU, 1999. http://repository.cmu.edu/dissertations/282.

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Many applications in computer graphics and related fields can benefit fromautomatic simplification of complex polygonal surface models. Applications areoften confronted with either very densely over-sampled surfaces or models toocomplex for the limited available hardware capacity. An effective algorithmfor rapidly producing high-quality approximations of the original model is avaluable tool for managing data complexity. In this dissertation, I present my simplification algorithm, based on iterativevertex pair contraction. This technique provides an effective compromisebetween the fastest algor

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14

Valle, Raciel. "Polygonal Complexes with Octahedral Links." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306345474.

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15

Qiu, Li. "Polygonal models from range scanned trees." Thesis, Linköping University, Visual Information Technology and Applications (VITA), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-50704.

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<p>3D Models of botanical trees are very important in video games, simulation, virtual reality, digital city modeling and other fields of computer graphics. However, since the early days of computer graphics, the modeling of trees has been challenging, because of the huge dynamical range between its smallest and largest structures and their geometrical complexity. Trees are also ubiquitous which makes it even hard to model them in a realistic way, Current techniques are limited in that they model a tree either in a rule-based way or in an approximated way. These methods emphasize appearance wh

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16

Mehrotra, Rajat. "Monodispersed polygonal water droplets in microchannel." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2726.

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17

Chien, Yu-Yen. "On the Platonicity of polygonal complexes." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/377150/.

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18

Backer, Jonathan. "Bounded-curvature motion planning amid polygonal obstacles." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/5153.

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We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known

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19

Larsen, Leif Christian. "Framework for Polygonal Structures Computations on Clusters." Thesis, Norwegian University of Science and Technology, Department of Computer and Information Science, 2007. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-8787.

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<p>Seismological applications use a 3D grid to represent the subsea rock structure. Many computations, such as detecting layers of rock in the seismic, can be done using the 3D grid exclusively. However, some algorithms for detecting vertical dislocations in the seismic require computations over a discretized polygon surface imposed over the 3D grid to assist geophysicists in interpreting the seismic data. When using seismological applications on clusters, the 3D grid data is distributed between several cluster nodes. This thesis considers how algorithms involving discretized polygon surfaces

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20

Handayani, Surya. "Polygonal reconstruction of free-form engineering components." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.417081.

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21

Sze, Chuen-kan, and 施泉根. "S-normality and polygonal s-numerical ranges." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B29815630.

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22

DeHaemer, Michael Joseph. "Simplification of objects rendered by polygonal approximation." Thesis, Monterey, California. Naval Postgraduate School, 1989. http://hdl.handle.net/10945/27265.

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Sze, Chuen-kan. "S-normality and polygonal s-numerical ranges /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19616223.

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24

HOSHINA, THOMÁS YOITI SASAKI. "TOPOLOGY OPTIMIZATION WITH ADAPTIVE POLYGONAL MESH REFINEMENT." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=27874@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>A otimização topológica tem como objetivo encontrar a distribuição mais eficiente de material (ótima topologia) em uma determinada região, satisfazendo as restrições de projeto estabelecidas pelo usuário. Na abordagem tradicional atribui-se uma variável de projeto, constante, denominada densidade, para cada elemento finito da malha. Dessa forma, a qualidade da representação dos novos contornos da estrutura depende do nível de discretização da malha: quanto maior a quantidade de elementos, mais bem definida será a topologia da estrutura otim

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25

Hiemer, Philipp Robert. "Topics in polygonal billiards and oriented percolation." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620413.

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26

Yirci, Murat. "A Comparative Study On Polygonal Mesh Simplification Algorithms." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12610074/index.pdf.

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Polygonal meshes are a common way of representing 3D surface models in many different areas of computer graphics and geometry processing. However, these models are becoming more and more complex which increases the cost of processing these models. In order to reduce this cost, mesh simplification algorithms are developed. Another important property of a polygonal mesh model is that whether it is regular or not. Regular meshes have many advantages over the irregular ones in terms of memory requirements, efficient processing, rendering etc. In this thesis work, both mesh simplification and regul

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27

Isenberg, Tobias. "Capturing the essence of shape of polygonal meshes." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971682089.

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28

Carruthers, Thomas. "Interaction of polygonal fault systems with salt diapirs." Thesis, Cardiff University, 2012. http://orca.cf.ac.uk/42375/.

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Salt diapirs are some of the most dynamic geological structures in sedimentary basins and vertical rise through their overburdens leads to the development of complex fault systems. Polygonal fault systems constitute a major structural element of fine-grained sediments in sedimentary basins, forming without the requirement of tectonic extension during the early burial phase of sediment compaction and dewatering. These same fine-grained sedimentary overburdens are also deformed by salt diapirs and their associated fault systems in basins such as the Gulf of Mexico, the South Atlantic margins and

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29

TELLES, PABLO VINICIUS FERREIRA. "MULTI-CLASS BLUE NOISE SAMPLING ON POLYGONAL SURFACES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=24793@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>A amostragem de pontos por discos de Poisson preserva a uniformidade espacial e as propriedades de ruído azul do seu espectro de Fourier. Esse padrão de amostragem é bem popular por ser visualmente agradável o que favorece algumas aplicações. Diversos estudos se dedicam à amostragem de um único conjunto de pontos distribuídos por discos de Poisson, caracterizando uma única classe de pontos sobre domínios planares ou sob

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30

Durso, Catherine. "On the inverse spectral problem for polygonal domains." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/84196.

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31

Hännestrand, Filip. "Real-time generation of nature from polygonal data." Thesis, Luleå tekniska universitet, Datavetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-70125.

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Lantmäteriet is developing an application that can show a three-dimensional representation of Sweden based on the data that Lantmäteriet has. The purpose of this application is to be able to crowdsource improvements and changes to the map data that Lantmäteriet has, it will also be able to be used to improve a case's information for easier and faster turnaround at Lantmäteriet. In this Project, I examine how best to use this map data to generate nature such as vegetation in this application to improve usability, and make it easier for the user to know where they are in the application. During

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Rivière, Stéphane. "Calculs de visibilité dans un environnement polygonal 2D." Université Joseph Fourier (Grenoble), 1997. http://tel.archives-ouvertes.fr/tel-00528854.

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Beaucoup de programmes de visualisation, de planification de trajectoire, etc. , utilisent intensivement des calculs de visibilité. Si ces calculs de visibilité ne constituent qu'une petite partie de ces programmes, ils sont en revanche responsables d'une grande partie du temps d'exécution de ces programmes: leur efficacité est donc cruciale. Les algorithmes traditionnels de calculs de visibilité ont deux défauts: ils effectuent - inutilement - des calculs sur des objets non visibles et refont tous ces calculs à chaque nouvelle requête, même si les changements avec la requête précédente sont m

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Morgan, Daniel Ashley. "The growth and evolution of polygonal fault tiers." Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/88909/.

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Polygonal faults are layer-bound arrays of normal faults confined to specific stratigraphic intervals called tiers. Typically hosted in fine-grained sediments, polygonal faults are thought to have the potential for fluid leakage and represent a potential seal bypass mechanism. Intergral to understanding the impact of polygonal faults on regional top seal is timing and evolution of polygonal fault tiers. Whilst there are numerous studies imaging and describing polygonal faults in numerous basins around the world, very few specifically consider the growth of polygonal faults. Additionally, very

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34

Backenhof, Albert. "Automatic Generation of Collision Hulls for Polygonal Objects." Thesis, Linköpings universitet, Medie- och Informationsteknik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-69259.

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Physics in interactive environments, such as computer games, and simulations require well madeand accurate bounding volumes in order to act both realistically and fast. Today it is common to useeither inaccurate boxes or spheres as bounding volumes or to model the volume by hand. Thesemethods are either too inaccurate or require too much time to ever be able to be used in real-time,accurate virtual environments.This thesis presents a method to automatically generate collision hulls for both manifolds and nonmanifolds.This allows meshes to be used in a physical environment in just a few seconds

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SUAREZ, MIGUEL ANGEL AMPUERO. "TOPOLOGY OPTIMIZATION FOR EIGENVALUE PROBLEMS USING POLYGONAL FINITE ELEMENTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=28017@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>Neste trabalho, são apresentadas algumas aplicações da otimização topológica para problemas de autovalor onde o principal objetivo é maximizar um determinado autovalor, como por exemplo uma frequência natural de vibração ou uma carga crítica linearizada, usando elementos finitos poligonais em domínios bidimensionais arbitrários. A otimização topológica tem sido comumente utilizada para minimizar a flexibilidade de estruturas sujeitas a restri

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Jia, Bicen. "Resistance of Polygonal Cross Sections of Lattice Wind Tower." Thesis, Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-63487.

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Wind energy is one of the most efficient renewable energies. The most used wind towers are tubularand lattice wind towers. Parts of lattice are easier to transfer, especially in the inland areas. Also, it is easier to build higher lattice tower in order to have more efficient energy conversion in inland areas.However, most of the cross sections for lattice tower are tubular cross sections.This thesis represents the parametric study of polygonal cross section of lattice tower. It consists ofthe numerical analysis based on finite element method (ABAQUS) and analysis based on EN 1993-1-3. The obj

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Castelló, Boscá Pascual. "Viewpoint-driven Simplification of Polygonal Models using Information Theoretic measures." Doctoral thesis, Universitat Jaume I, 2007. http://hdl.handle.net/10803/10484.

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Los modelos poligonales actualmente dominan el campo de los gráficos interactivos. Esto es debido a su simplicidad matemática que permite que los más comunes algoritmos de visualización se implementen directamente en el hardware. Sin embargo la complejidad de estos modelos (medidos por el número de polígonos) crece más rápido que la capacidad del hardware grafico para visualizarlos interactivamente. Las técnicas de simplificación de polígonos ofrecen una solución para tratar estos modelos complejos. Estos métodos simplifican la geometría poligonal reduciendo el coste de visualización del model

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Wei, Xiangzhi. "Monotone path queries and monotone subdivision problems in polygonal domains /." View abstract or full-text, 2010. http://library.ust.hk/cgi/db/thesis.pl?IELM%202010%20WEI.

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Jones, Nathaniel Earl. "Real-time geometric motion blur for a deforming polygonal mesh." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/468.

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Motion blur is one important method for increasing the visual quality of real-time applications. This is increasingly true in the area of interactive applications, where designers often seek to add graphical flair or realism to their programs. These applications often have animated characters with a polygonal mesh wrapped around an animated skeleton; and as the skeleton moves the mesh deforms with it. This thesis presents a method for adding a geometric motion blur to a deforming polygonal mesh. The scheme presented tracks an object's motion silhouette, and uses this to create a polygonal mesh

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Yang, Ying. "Information analysis for steganography and steganalysis in 3D polygonal meshes." Thesis, Durham University, 2013. http://etheses.dur.ac.uk/8492/.

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Information hiding, which embeds a watermark/message over a cover signal, has recently found extensive applications in, for example, copyright protection, content authentication and covert communication. It has been widely considered as an appealing technology to complement conventional cryptographic processes in the field of multimedia security by embedding information into the signal being protected. Generally, information hiding can be classified into two categories: steganography and watermarking. While steganography attempts to embed as much information as possible into a cover signal, wa

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Cox, John Stephen. "Simplification of Animated Polygonal Meshes: A localised tolerance volume approach." Thesis, Staffordshire University, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.536451.

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Muche, Tilahun Abay. "Hamiltonian Sets of Polygonal Paths in 4-Valent Spatial Graphs." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4177.

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Spatial graphs with 4–valent rigid vertices and two single valent endpoints, called assembly graphs, model DNA recombination processes that appear in certain species of ciliates. Recombined genes are modeled by certain types of paths in an assembly graph that make a ”oper pendicular ” turn at each 4–valent vertex of the graph called polygonal paths. The assembly number of an assembly graph is the minimum number of polygonal paths that visit each vertex exactly once. In particular, an assembly graph is called realizable if the graph has a Hamiltonian polygonal path. An assembly graph ɣ^ obtaine

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Srisatkunarajah, Sivakolundu. "On the asymptotics of the heat equation for polygonal domains." Thesis, Heriot-Watt University, 1988. http://hdl.handle.net/10399/1001.

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Judish, Nathan P. "Polygonal random fields and the reconstruction of piecewise continuous functions." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12593.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1993.<br>Includes bibliographical references (leaves 77-78).<br>by Nathan P. Judish.<br>M.S.

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Nayakanti, Nigamaa. "Flexigami : folded polygonal unit cells for deployable metamaterials and mechanisms." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104281.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 83-85).<br>Deployable and transformable structures are of broad interest for applications including satellites and space exploration, temporary shelters, packaging, transportation, robotics and medical devices. One emerging approach to scalable fabrication of such structures involves the general concept of Origami-inspired design along with cutting, folding, and fastening of sheet materials. However, contrasting

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Swartz, Eric Allen. "2-arc transitive polygonal graphs of large girth and valency." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1243923530.

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Taylor, Brian. "The design of a lathe attachment for grinding non-circular cross- section shafts suitable for torque transmission." Thesis, University of Newcastle Upon Tyne, 1987. http://hdl.handle.net/10443/769.

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The principle concern of this work is the design of a lathe attachment for grinding non-circular 'polygonal' shaped workpieces suitable for use as torque transmitting machine elements. In the course of the work substantial attention is also given to the general theory and development of computer aided error analysis procedures for planar linkage mechanisms. A further smaller part of the work investigates the torsion of polygonal shafts. The non-circular shapes considered here may be loosely defined as polygonal profiles. Their application is in torque transmitting couplings for which they repr

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Lo, Hsing-Yuan, and 羅興源. "Fixing 3D Polygonal Models." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/88472335664850398134.

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碩士<br>國立交通大學<br>資訊工程系所<br>93<br>Mesh representation is a common choice for representing 3-D geometric models. However, due to the original design problems of mesh structure, many existing algorithms devised for creating mesh structures are facing challenges when processing these mesh models. In this work, we make use of cutting algorithm to remove topological singularities and then apply triangulation algorithm to generate patches to fill the holes. We find the existing cutting algorithms fused with a hole-filling algorithm with generate new topological problems. Therefore, we propose a new me

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Chen, Chi-Feng, and 陳啟峰. "Evaluation of the Polygonal Mesh Layout Techniques for Cached-Based Polygonal Mesh Simplification Acceleration." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/68775975015073917491.

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碩士<br>國立勤益科技大學<br>電子工程系<br>98<br>Concurrent 3D model files mostly adapt traditional indexed faced format such as ply and obj. With the improvements of model scanning technology, the file size becoming larger and larger as the resolution of the resulted 3D meshes increases. To process these kinds of meshes, it is usually not possible to process the entire mesh in the main memory. If an in-core algorithm is used, the operating system usually has use virtual memory blocks in the disk space. If the locality-of-reference of the data accesses is low, the algorithm will has extremely low efficiency.

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Ward, Clayton Collin. "Fuchsian groups and polygonal billiards." Thesis, 1996. http://hdl.handle.net/1911/16978.

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Let P be a simple, closed polygon in the plane, all interior angles of which are rational multiples of $\pi$. We consider the possible paths of a point, rebounding in the interior of P with constant speed and elastic reflections. Such a dynamical system is known as "billiards in P". By means of a well-known construction, "billiard" trajectories in such a polygon P are identified with geodesic paths on a closed Riemann surface $X\sp{P}$, where the Riemannian metric is one of zero curvature with isolated singularities, and is given by a holomorphic one-form $\omega$ on the surface. To this holom

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