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Van, Bloemestein Ulric Patrick. "Seasonal movement and activity patterns of the endangered geometric tortoise, Psammobates geometricus." Thesis, University of the Western Cape, 2005. http://etd.uwc.ac.za/index.php?module=etd&.
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Due to the critical status of Psammobates geometricus and the vulnerability of their habitat, there is a need to allocate areas for their protection. The aim of this study was to provide information on the space requirements and activity level of geometric tortoises to facilitate future conservation efforts.
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Centazzo, Alessandro. "Strategie di riorientamento nei bambini: uno studio in stanze grandi e piccole e in ambienti virtuali." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10069.
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2012/2013La maggior parte delle specie animali è capace di recuperare l’orientamento dopo essere stata passivamente disorientata e lo fa utilizzando le informazioni provenienti dall’ambiente, informazioni che possono essere di tipo geometrico (come per esempio la forma di una superficie contornata da margini) o di tipo non-geometrico come per esempio punti di riferimento –landmark- o, in una stanza, il colore diverso di una parete. Nel nostro lavoro abbiamo indagato la capacità di riorientamento di bambini a partire dai 6 anni. Il compito consisteva nel trovare, dopo essere stati disorientati, un oggetto che i bambini avevano visto nascondere in prossimità di un angolo di una stanza rettangolare (in prossimità di ogni angolo era presente una struttura che fingeva da nascondiglio) nella quale una parete aveva un colore diverso dalle altre. Abbiamo cercato di capire come venissero utilizzate le informazioni geometriche e non-geometriche quando queste venivano messe in conflitto tra loro (affine transformation). Per fare ciò, il colore diverso della parete veniva cambiato (passando dal lato lungo a quello corto o viceversa) tra la fase di addestramento, nella quale il soggetto vedeva dove veniva nascosto l’oggetto da cercare, e la fase di ricerca, nella quale l’oggetto doveva essere ritrovato. La nostra ricerca si è articolata in più fasi. In un primo momento abbiamo pensato di riprodurre gli esperimenti presenti in letteratura e indicativi di un utilizzo più consistente delle informazioni geometriche negli ambienti piccoli rispetto a quelli grandi. A differenza da quanto riportato in letteratura non abbiamo trovato differenze tra la stanza grande e quella piccola: in entrambe i bambini prediligono le informazioni geometriche. Successivamente abbiamo impegnato i bambini nel medesimo compito ma in stanze con caratteristiche diverse. Abbiamo utilizzato stanze nelle quali il nascondiglio aveva dimensioni dimezzate rispetto alle stanze precedenti, oppure non era presente, e stanze nelle quali abbiamo diminuito il rapporto tra le lunghezze dei lati lungo e corto (stanze che abbiamo chiamato “quasi-quadrate”). Tra le diverse tipologie di stanza è stata calcolata un’analisi della varianza che ha messo in luce che la forma (e non la dimensione) della stanza e la presenza o assenza dei nascondigli sono le due variabili che condizionano maggiormente le scelte dei soggetti. In particolare, i bambini prediligono le informazioni geometriche quando non sono presenti i nascondigli e quando le stanze sono “quasi-quadrate”. Dai nostri dati emerge che i bambini sono in grado di utilizzare tutte le informazioni a disposizione. Il prediligere un tipo piuttosto che l’altro dipende dalle caratteristiche dell’ambiente e probabilmente dalla stima di quanto una determinata informazione è affidabile per recuperare l’orientamento. La teoria della combinazione adattativa è quella che sembra spiegare meglio i risultati che abbiamo trovato.
XXV - Ciclo
1972
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MIRAGLIOTTA, ELISA. "La previsione geometrica: un modello per analizzare un processo cognitivo inerente il problem-solving in geometria." Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2020. http://hdl.handle.net/11380/1200566.
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La ricerca mira a studiare gli aspetti cognitivi coinvolti nella produzione di previsioni geometriche durante la risoluzione di problemi nell’abito della Geometria Euclidea.
Si può considerare il processo di previsione geometrica come una specifica abilità visuo-spaziale coinvolta nel pensiero geometrico. Infatti, durante il processo di risoluzione di un problema geometrico, un solutore può immaginare diverse trasformazioni della figura e i loro effetti; tali trasformazioni possono essere più o meno coerenti con i vincoli teorici dati dal problema. Inoltre, i prodotti di tali trasformazioni possono inibire o supportare il processo risolutivo.
Ricerche precedenti hanno evidenziato e posto l’attenzione sulla natura degli oggetti geometrici, considerando sia la componente concettuale che la componente figurale. Interpretando il pensiero geometrico in termini di dialettica tra questi due aspetti (Fischbein, 1993), lo studio mira a comprendere il processo di previsione geometrica, inteso come un processo attraverso il quale una figura viene manipolata, i suoi cambiamenti immaginati, mentre alcune proprietà vengono mantenute invarianti.
Il processo di previsione geometrica viene descritto attraverso un modello di generazione di previsioni elaborato ciclicamente: osservando, analizzando secondo un approccio microgenetico e analizzando nuovamente il comportamento di diversi solutori durante la risoluzione di problemi aperti di previsione proposti sia in ambiente carta e penna che in un Ambiente di Geometria Dinamica (AGD).
I problemi aperti di previsione progettati per lo studio sono stati proposti durante interviste task-based a solutori coinvolti su base volontaria. Hanno preso parte allo studio un totale di 37 solutori italiani tra studenti di scuola secondaria di secondo grado, studenti di laurea triennale e magistrale e di dottorato in Matematica. I dati constano di registrazioni video e audio, trascrizioni delle interviste, disegni dei solutori.
La versione finale del modello descrive i processi di previsione di un solutore coinvolto nella risoluzione dei problemi aperti di previsione proposti nello studio. Inoltre, il modello fornisce una lente teorica utile per analizzare le produzioni dei solutori e comprendere più profondamente i processi di previsione. In particolare, il modello chiarisce il ruolo cruciale sia degli elementi teorici introdotti dal solutore durante il processo risolutivo, sia del controllo teorico che i solutori esercitano.
Lo studio ha implicazioni didattiche, utili in particolar modo per la scuola secondaria di secondo grado, per la progettazione di attività volte a promuovere il pensiero geometrico degli studenti e il loro controllo teorico sulle figure geometriche.The purpose of the research is to study cognitive aspects of how geometric predictions are produced during problem-solving activities in Euclidean geometry. The process of geometric prediction is seen as a specific visuo-spatial ability involved in geometrical reasoning. Indeed, when solvers engage in solving a geometrical problem, they can imagine the consequences of transformations of the figure; such transformations can be more or less coherent with the theoretical constraints given by the problem, and the products of such transformations can hinder or promote the problem-solving process. Previous research has stressed the dual nature of geometrical objects, intertwining a conceptual component and a figural component. Interpreting geometrical reasoning in terms of a dialectic between these two aspects (Fischbein, 1993), this study aims at gaining insight into the cognitive process of geometric prediction, a process through which a figure is manipulated, and its change is imagined, while certain properties are maintained invariant. This process is described through a model of prediction-generation elaborated cyclically by observing, analyzing through a microgenetic approach, and re-analyzing solvers’ resolution of prediction open problems in a paper-and-pencil environment and in a Dynamic Geometry Environment (DGE). The prediction open problems designed were proposed during task-based interviews to participants selected on a voluntary basis. Participants were a total of 37 Italian high school students and undergraduate, graduate and PhD students in mathematics. Data are composed of video and audio recordings, transcriptions, solvers’ drawings. The final version of the model provides a description of the prediction processes accomplished by a solver who engages in the resolution of prediction open problems proposed in this study; it provides a lens through which solvers’ productions can be analyzed and it provides insight into prediction processes. In particular, it sheds light onto the key role played by theoretical elements that are introduced by the solvers during the resolution process and the key role played by the solver’s theoretical control. The study has implications for the design of activities, especially at the high school level, with the educational objective of fostering students’ geometrical reasoning and in particular their theoretical control over the geometrical figures.
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Caruso, Monica. "Geometrie non euclidee: dalla negazione del V postulato all'interpretazione geometrica del cosmo." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.
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La tesi è incentrata sulle geometrie non euclidee. Al di là della descrizione dei vari modelli, essa si propone di evidenziare e accertare il fatto che tutte le geometrie, euclidee e non, abbiano pari dignità, fatto oggi pienamente condiviso, ma che era messo in dubbio al momento della loro genesi.
Il primo è un capitolo introduttivo riguardo alla storia della geometria, che mira a evidenziare il cambio di prospettiva da una geometria intesa come "misura della terra" a una disciplina svincolata da ogni applicazione pratica. Si arriva poi all'opera di Euclide.
A una descrizione sommaria degli Elementi, segue un'analisi del V postulato euclideo che, a differenza dei primi quattro postulati, i quali risultavano intuitivamente evidenti, non era così immediato. Molti studiosi per secoli cercarono invano di dedurlo dagli altri quattro assiomi ma, i tentativi sempre falliti, portarono, fra la fine del XVIII e l'inizio del XIX secolo, all'idea di considerare dei modelli che contemplassero solo i primi quattro postulati e una delle due possibili negazioni del V assioma: nacquero così le geometrie non euclidee.
Nel terzo capitolo si scopre che tutte e tre le geometrie sono manifestazioni diverse di un unico concetto generale che le trascende tutte: la curvatura.
Lo studio delle geometrie non euclidee e la generalizzazione del concetto di curvatura alle dimensioni superiori, hanno consentito di intraprendere, nel quarto capitolo, un'interpretazione geometrica dell'universo, volta a capire quale geometria risulta più adatta per descriverlo, permettendoci di mostrare la naturale interdisciplinarità delle geometrie non euclidee.
Il quinto capitolo, infine, considera gli aspetti didattici attraverso un'analisi delle Indicazioni nazionali e dei libri di testo in merito all'argomento, e ai progetti volti a promuovere un approccio maturo e consapevole al moderno sistema assiomatico e alla geometria di Euclide.
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Alqahtani, Lamia Saeed M. "Geometric flows on soliton moduli spaces." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/4967/.
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It is well known that the low energy dynamics of many types of soliton can be approximated by geodesic motion on Mn, the moduli space of static n-solitons, which is usually a Kähler manifold. This thesis presents a detailed study of magnetic geodesic motion on a Kähler manifold in the case where the magnetic field 2-form is the Ricci form. This flow, which we call Ricci Magnetic Geodesic (RMG) flow, is first studied in general. A symmetry reduction result is proved which allows one to localize the flow onto the fixed point set of any group of holomorphic isometries of a Kähler manifold M. A subtlety of this reduction, which was overlooked by Krusch and Speight, is pointed out. Since RMG flow occurs at constant speed, it follows immediately that the flow is complete if M is geodesically complete. We show, by means of an explicit counterexample that, contrary to a conjecture of Krusch and Speight, the converse is false: it is possible for a geodesically incomplete manifold to be RMG complete. RMG completeness of metrically incomplete manifolds is therefore a nontrivial issue, and one which will be addressed repeatedly in later chapters. We then specialize to the case where Mn is the moduli space of abelian Higgs n-vortices, which is the context in which RMG flow was first proposed, by Collie and Tong, as a low energy model of the dynamics of a certain type of Chern-Simons n-vortices on ℝ2. The unit vortex is constructed numerically, and its asymptotics is studied. It is shown that, contrary to an assertion of Collie and Tong, RMG flow does not coincide with an earlier proposed magnetic geodesic model of vortex motion due to Kim and Lee. It is further shown that Kim and Lee’s model is ill-defined on the vortex coincidence set. An asymptotic formula for the scattering angle of well-separated vortices executing RMG flow is computed. We then change the spatial geometry, placing the vortices on the hyperbolic plane of critical curvature. An explicit formula for the two-vortex metric is derived, extending the results of Strachan, who computed the metric on a submanifold of centred 2-vortices. The RMG flow localized on this submanifold is compared with its intrinsic RMG flow, revealing strong qualitative differences. We then study the moduli space Hn,k(∑) of degree n ℂPk lumps on a compact Riemann surface ∑. It is shown that Rat1 = H1,1(S2) is RMG complete (despite being metrically incomplete). The Einstein-Hilbert action of H1,k(S2) is computed, supporting (for k > 1) a conjecture of Baptista. A natural class of topologically cylindrical submanifolds of Hn,1(∑), called dilation cylinders, is studied: their volumes are computed, and it is shown that they are all isometrically embeddable as surfaces of revolution in R3. Conditions under which they are totally geodesic, for ∑ = S2 and T2, are found, and RMG flow on some examples is studied. Finally, a new metric on Hn,1(∑), derived from the Baby-Skyrme model, is introduced. On Rat1, this metric is determined explicitly and some geometric aspects such as the volume, geodesic flow and the spectral problem with respect to this metric are studied.
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Ferro, Dennis Eduardo Zavaleta. "Some geometric aspects of non-linear sigma models /." São Paulo, 2016. http://hdl.handle.net/11449/151647.
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Orientador: Andrei MikhailovResumo: We review some relevant examples for String Theory of non-linear sigma models. These are bosonic strings propagating in curved background, the Wess-Zumino-Witten model and superstrings in flat and AdS superspace. The mathematical tools required for the study of these models (e.g. topological quantization, Cartan geometry, Lie superalgebras and geometry on coset spaces) are also described. Throughout the dissertation we have focused on classical aspects of these models such as the construction of the action and its symmetries where conditions for holomorphic symmetry of the bosonic string case were found.
Mestre
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Nandihalli, Sunil S. "A B-spline geometric modeling methodology for free surface simulation." Master's thesis, Mississippi State : Mississippi State University, 2004. http://library.msstate.edu/etd/show.asp?etd=etd-04072004-185017.
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Lundkvist, Christian. "Moduli spaces of zero-dimensional geometric objects." Doctoral thesis, Stockholm : Matematik, Kungliga Tekniska högskolan, 2009. http://www.diva-portal.org/smash/record.jsf?searchId=1&pid=diva2:223079.
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Tarasca, Nicola. "Geometric cycles on moduli spaces of curves." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://dx.doi.org/10.18452/16518.
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Ziel dieser Arbeit ist die explizite Berechnung gewisser geometrischer Zykel in Modulräumen von Kurven. In den letzten Jahren wurden Divisoren auf $\Mbar_{g,n}$ ausgiebig untersucht. Durch die Berechnung von Klassen in Kodimension 1 konnten wichtige Ergebnisse in der birationalen Geometrie der Räume $\Mbar_{g,n}$ erzielt werden. In Kapitel 1 geben wir einen Überblick über dieses Thema. Im Gegensatz dazu sind Klassen in Kodimension 2 im Großen und Ganzen unerforscht. In Kapitel 2 betrachten wir den Ort, der im Modulraum der Kurven vom Geschlecht 2k durch die Kurven mit einem Büschel vom Grad k definiert wird. Da die Brill-Noether-Zahl hier -2 ist, hat ein solcher Ort die Kodimension 2. Mittels der Methode der Testflächen berechnen wir die Klasse seines Abschlusses im Modulraum der stabilen Kurven. Das Ziel von Kapitel 3 ist es, die Klasse des Abschlusses des effektiven Divisors in $\Mbar_{6,1}$ zu berechnen, der durch punktierte Kurven [C, p] gegeben ist, für die ein ebenes Modell vom Grad 6 existiert, bei dem p auf einen Doppelpunkt abgebildet wird. Wie Jensen gezeigt hat, erzeugt dieser Divisor einen extremalen Strahl im pseudoeffektiven Kegel von $\Mbar_{6,1}$. Ein allgemeines Ergebnis über gewisse Familien von Linearsystemen mit angepasster Brill-Noether-Zahl 0 oder -1 wird eingeführt, um die Berechnung zu vervollständigen.The aim of this thesis is the explicit computation of certain geometric cycles in moduli spaces of curves. In recent years, divisors of $\Mbar_{g,n}$ have been extensively studied. Computing classes in codimension one has yielded important results on the birational geometry of the spaces $\Mbar_{g,n}$. We give an overview of the subject in Chapter 1. On the contrary, classes in codimension two are basically unexplored. In Chapter 2 we consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves. The aim of Chapter 3 is to compute the class of the closure of the effective divisor in $\M_{6,1}$ given by pointed curves [C,p] with a sextic plane model mapping p to a double point. Such a divisor generates an extremal ray in the pseudoeffective cone of $\Mbar_{6,1}$ as shown by Jensen. A general result on some families of linear series with adjusted Brill-Noether number 0 or -1 is introduced to complete the computation.
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Vieira, Erica Pinheiro. "Produção digital de maquetes arquitetonicas : um estudo exploratorio." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/257720.
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Orientador: Maria Gabriela Caffarena CelaniDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
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Resumo: Este trabalho consiste em um estudo exploratório sobre a produção digital de maquetes arquitetônicas. Inicialmente, foi realizada uma revisão bibliográfica com a finalidade de conhecer os novos métodos de produção digital de maquetes, incluindo software de modelagem e equipamentos de prototipagem rápida. Nesse estudo inicial, além de explorar os principais equipamentos, processos, aplicações e materiais, identificou-se dois arquitetos renomados que fazem uso dessa tecnologia nos seus processos de projeto: Frank Gehry e Norman Foster. Deste estudo verificou-se processos distintos de projeto e diferentes abordagens sobre a utilização dessas ferramentas, o que motivou a realização de experimentos para exemplificar como produzir digitalmente maquetes arquitetônicas. O Museu Guggenheim de Bilbao, de Frank Gehry, foi escolhido como variável fixa para realização dos experimentos de produção digital de maquetes, por ser um modelo de grande complexidade, permitindo testar os limites dos equipamentos de prototipagem rápida disponíveis no Laboratório de Prototipagem para Arquitetura e Construção (LAPAC) da FEC ¿ Unicamp e no Centro de Pesquisas Renato Archer (CenPRA). Além disso, foram testadas diferentes técnicas e materiais, inclusive materiais alternativos, com o objetivo de viabilização econômica. Os resultados comprovaram que o processo de produção digital de maquetes arquitetônicas é viável em termos de procedimentos, de custo, de materiais disponíveis no mercado, qualidade das maquetes produzidas e rapidez na execução. A partir das conclusões obtidas nos experimentos realizados foi elaborado um caderno de recomendações para a confecção de maquetes que será utilizado pelos usuários do LAPAC e que servirá como importante ferramenta de auxílio para os iniciantes na produção digital de maquetes arquitetônicas. Espera-se que os resultados desta pesquisa possam auxiliar a estabelecer diretrizes para a incorporação dessas técnicas e equipamentos em disciplinas de projeto e na prática de arquitetura
Abstract: The present work is an exploratory study about the digital fabrication of architectural models. It started with a literature review, with the aim of getting in contact with the new digital methods for making models and prototypes, from modeling software to rapid prototyping equipment, processes, materials and applications. Still in this initial study the work of two well-known architects, Frank Gehry and Norman Foster, who use rapid prototyping techniques in their design process, was analyzed. From this part of the research it was possible to conclude that the different approaches that architects have to the design process is reflected in the way they use digital techniques for making their models. The second part of the research consisted of a series of experiments with the objective of illustrating the digital production of architectural models. For these experiments, Frank Gehry's Guggenheim Museum in Bilbao was chosen as a fixed variable for the production of models, due to its geometric complexity, which allowed to push the use of the available rapid prototyping equipment to their limits. Only the equipment available at FEC-UNICAMP's (Laboratório de Prototipagem para Arquitetura e Construção - LAPAC) and CENPRA's (Laboratório de Prototipagem Rápida do Centro de Pesquisas Renato Archer) laboratories were used. They consisted of a 3d printer, a fusion deposition modeller (FDM) machine, and a laser cutter. Different techniques and materials were tested in these machines, with the objective of evaluating the quality and economic viability of the resulting models. The results showed that the digital production of architectural models is viable for use in Brazilian architecture schools, in terms of procedures, cost, availability of materials, time spent and quality of the models. Finally, a manual with recommendations and tips was produced, with the aim of helping students build their own models using rapid prototyping equipment. We hope that the results of this research will help guiding the incorporation of these techniques in architecture education and practice in Brazil
Mestrado
Arquitetura e Construção
Mestre em Engenharia Civil
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Sousa, Welington Fernandes de. "A geometria analítica como um modelo para a geometria euclidiana." reponame:Repositório Institucional da UnB, 2017. http://repositorio.unb.br/handle/10482/31974.
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Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, Programa de Mestrado Profissional em Matemática em Rede Nacional, 2017.Submitted by Raquel Almeida (raquel.df13@gmail.com) on 2017-11-07T16:23:55Z No. of bitstreams: 1 2017_VitorSoaresRabeloAdriano.pdf: 10962275 bytes, checksum: c8cb507a31646087a77dfce259e055db (MD5)
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Este trabalho mostra, com ênfase na geometria plana, o modelo dedutivo formulado por Euclides de Alexandria pelo qual ele constrói e organiza todo o conhecimento geométrico conhecido até então. Este modelo euclidiano, chamado axiomático, com o passar dos anos revelou falhas em demonstrações de algumas proposições que são citadas e comentadas neste trabalho. As tentativas para corrigir as falhas e formalizar o modelo axiomático de Euclides, levou a um novo modelo axiomático mais formal, que corrige as falhas cometidas por Euclides e traz uma linguagem mais coerente com a proposta da matemática moderna. Tal modelo foi publicado por David Hilbert em seu trabalho Grundlagen der Geometrie, e também está presente neste trabalho. Após mostrar como a geometria euclidiana plana foi formulada em função de seus axiomas, o trabalho chega ao seu ponto principal: mostrar que a geometria euclidiana plana pode ser demonstrada na geometria sobre corpos (geometria analítica). E para isso, este trabalho disponibiliza a demonstração de todos os axiomas de Hilbert, para a geometria euclidiana plana, em um plano cartesiano sobre um corpo. Veremos que não haverá necessidade de trabalharmos sobre o corpo dos números reais para que esta geometria euclidiana plana seja demonstrada pela geometria analítica. Além disso o trabalho traz um pouco das características e propriedades de corpos e suas extensões à medida que as demonstrações se aprofundam. Chegaremos à conclusão de que todos os axiomas da geometria euclidiana plana podem ser demonstrados na geometria analítica, sobre um corpo ordenado com extensão às raízes quadradas de elementos positivos.
This work shows, with emphasis on plane geometry, the deductive model formulated by Euclid of Alexandria by which he constructed and organized all known geometric knowledge until then. This Euclidean model, called axiomatic, over the years revealed aws in demonstrations of some propositions that are cited and commented on in this work. The attempts to correct the failures and formalizing the axiomatic model of Euclid led to a new more formal axiomatic model that corrects Euclid's failures which is more and uses a language more consistent to proposal of modern mathematics. Such a model was published by David Hilbert in his work Grundlagen der Geometrie, and is also present in this work. After showing how Euclidean geometry is formulated in terms of its axioms, the work reaches its main point: to show that Euclidean plane geometry can be demonstrated in geometry over elds (analytic geometry). And for this, we provide the demonstration of all axioms of Hilbert, for Euclidean plane geometry, in a Cartesian plane over a eld. We will see that there will be no need to work on the eld of real numbers for this Euclidean plane geometry to be demonstrated by analytic geometry. In addition the work brings some of the characteristics and properties of elds and their extensions as the demonstrations deepen. We will arrive at the conclusion that all the axioms of Euclidean plane geometry can be demonstrated in analytical geometry, on an ordered eld with extension to the square roots of positive elements.
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林紹健 and Siu-kin Lum. "Trimming operations for geometric modelling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31211732.
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Lum, Siu-kin. "Trimming operations for geometric modelling /." [Hong Kong : University of Hong Kong], 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13857733.
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Scasserra, Annalisa. "Un modello geometrico delle mappe di orientazioni corticali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19250/.
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L’obiettivo di questa Tesi è quello di presentare un modello geometrico costruito sul gruppo SE(2) delle rototraslazioni come soluzione al problema della modellizzazione della corteccia visiva e, in particolare, della minimizzazione delle lunghezze delle connessioni neurali.
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Gasparini, Riccardo. "Engineering Analysis in Imprecise Geometric Models." FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1793.
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Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it.
Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence
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Schwander, Olivier. "Information-geometric methods for mixture models." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/93/17/22/PDF/these.pdf.
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Cette thèse présente de nouvelles méthodes pour l'apprentissage de modèles de mélanges basées sur la géométrie de l'information. Les modèles de mélanges considérés ici sont des mélanges de familles exponentielles, permettant ainsi d'englober une large part des modèles de mélanges utilisés en pratique. Grâce à la géométrie de l'information, les problèmes statistiques peuvent être traités avec des outils géométriques. Ce cadre offre de nouvelles perspectives permettant de mettre au point des algorithmes à la fois rapides et génériques. Deux contributions principales sont proposées ici. La première est une méthode de simplification d'estimateurs par noyaux. Cette simplification est effectuée à l'aide un algorithme de partitionnement, d'abord avec la divergence de Bregman puis, pour des raisons de rapidité, avec la distance de Fisher-Rao et des barycentres modèles. La seconde contribution est une généralisation de l'algorithme k-MLE permettant de traiter des mélanges où toutes les composantes ne font pas partie de la même famille: cette méthode est appliquée au cas des mélanges de Gaussiennes généralisées et des mélanges de lois Gamma et est plus rapide que les méthodes existantes. La description de ces deux méthodes est accompagnée d'une implémentation logicielle complète et leur efficacité est évaluée grâce à des applications en bio-informatique et en classification de texturesThis thesis presents new methods for mixture model learning based on information geometry. We focus on mixtures of exponential families, which encompass a large number of mixtures used in practice. With information geometry, statistical problems can be studied with geometrical tools. This framework gives new perspectives allowing to design algorithms which are both fast and generic. Two main contributions are proposed here. The first one is a method for simplification of kernel density estimators. This simplification is made with clustering algorithms, first with the Bregman divergence and next, for speed reason, with the Fisher-Rao distance and model centroids. The second contribution is a generalization of the k-MLE algorithm which allows to deal with mixtures where all the components do not belong to the same family: this method is applied to mixtures of generalized Gaussians and of Gamma laws and is faster than existing methods. The description of this two algorithms comes with a complete software implementation and their efficiency is evaluated through applications in bio-informatics and texture classification
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Hernandez, Gabriel. "Platform design for customizable products as a problem of access in a geometric space." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/16760.
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Veelo, Bastiaan Niels. "Variations of Shape in Industrial Geometric Models." Doctoral thesis, Norwegian University of Science and Technology, Department of Product Design, 2004. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-240.
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This thesis presents an approach to free-form surface manipulations, which conceptually improves an existing CAD system that constructs surfaces by smoothly interpolating a network of intersecting curves. There are no regularity requirements on the network, which already yields superior modelling capabilities compared to systems that are based on industry-standard NURBS surfaces.
Originally, the shape of such a surface can be modified only locally by manipulating a curve in the network. In this process there is an inherent danger that the curve is being pulled away from intersections that it has with other curves. When this happens, the network is invalidated as a surface representation, and many curves may have to be adjusted to restore network consistency and surface quality. This thesis contributes a method that solves these problems by propagating changes that are made in one curve to curves in its vicinity. How and to what extent curves react to changes is controlled by two parameters that can be varied along the curve that is being manipulated. Any curve may be constrained in one or more degrees of freedom. The integrity of the curve network is implicitly conserved, as well as the geometric continuity of the surface.
The result is a tool for the modification of curve-interpolating surfaces, which can easily be applied to large areas on models with any level of detail. This allows designers to concentrate on the creative process, rather than on planning chains of actions. They can explore different design variations, optimise shapes further, and generally be more productive.
Dette doktorgradsarbeidet presenterer en fremgangsmåte for formgivning og modifisering av datamaskinbaserte, skulpturerte flater. Metoden forbedrer et eksisterende system for data-assistert konstruksjon (DAK) som bygger dobbeltkrummede flater ved å interpolere et nettverk av skjærende kurver. Nettverket trenger ikke være regelmessig, noe som allerede gir bedre modelleringsmuligheter sammenliknet med systemer som er basert på standard NURBS flater.
En slik flate kan opprinnelig bare endres lokalt ved å dra i en kurve. I denne prosessen er det fare for at kurven blir dratt fra skjæringspunkter den har med andre kurver. Hvis dette skjer, representerer ikke nettverket en flate lenger, og mange kurver må justeres for å få tilbake integriteten i nettverket og kvaliteten i formen. Denne avhandlingen bidrar med en metode som løser disse problemene ved å spre endringer som blir gjort i en kurve til andre kurver i nærheten. Hvordan og i hvilken utstrekning kurvene reagerer på endringen styres av to parametre som kan varieres langs kurven som blir endret. Enhver kurve kan låses i en eller flere frihetsgrader. Integriteten til nettverket samt glattheten i formen blir bevart automatisk.
Resultatet er et redskap for modifikasjon av kurve-interpolerende flater som med letthet kan brukes på større områder av modeller med hvilken som helst grad av detalj. Dette gir designere muligheten til å konsentrere seg om det kreative, istedenfor å planlegge handlingsrekker. De kan utforske forskjellige designvariasjoner, optimalisere former ytterligere, og i det hele tatt være mer produktive.
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Kannala, J. (Juho). "Models and methods for geometric computer vision." Doctoral thesis, University of Oulu, 2010. http://urn.fi/urn:isbn:9789514261510.
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Abstract
Automatic three-dimensional scene reconstruction from multiple images is a central problem in geometric computer vision. This thesis considers topics that are related to this problem area. New models and methods are presented for various tasks in such specific domains as camera calibration, image-based modeling and image matching. In particular, the main themes of the thesis are geometric camera calibration and quasi-dense image matching. In addition, a topic related to the estimation of two-view geometric relations is studied, namely, the computation of a planar homography from corresponding conics. Further, as an example of a reconstruction system, a structure-from-motion approach is presented for modeling sewer pipes from video sequences.
In geometric camera calibration, the thesis concentrates on central cameras. A generic camera model and a plane-based camera calibration method are presented. The experiments with various real cameras show that the proposed calibration approach is applicable for conventional perspective cameras as well as for many omnidirectional cameras, such as fish-eye lens cameras. In addition, a method is presented for the self-calibration of radially symmetric central cameras from two-view point correspondences.
In image matching, the thesis proposes a method for obtaining quasi-dense pixel matches between two wide baseline images. The method extends the match propagation algorithm to the wide baseline setting by using an affine model for the local geometric transformations between the images. Further, two adaptive propagation strategies are presented, where local texture properties are used for adjusting the local transformation estimates during the propagation. These extensions make the quasi-dense approach applicable for both rigid and non-rigid wide baseline matching.
In this thesis, quasi-dense matching is additionally applied for piecewise image registration problems which are encountered in specific object recognition and motion segmentation. The proposed object recognition approach is based on grouping the quasi-dense matches between the model and test images into geometrically consistent groups, which are supposed to represent individual objects, whereafter the number and quality of grouped matches are used as recognition criteria. Finally, the proposed approach for dense two-view motion segmentation is built on a layer-based segmentation framework which utilizes grouped quasi-dense matches for initializing the motion layers, and is applicable under wide baseline conditions.
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Cheung, Elliot. "Birational models of geometric invariant theory quotients." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/61278.
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In this thesis, we study the problem of finding birational models of projective G-varieties with tame stabilizers. This is done with linearizations, so that each birational model may be considered as a (modular) compactification of an orbit space (of properly stable points).
The main portion of the thesis is a re-working of a result in Kirwan's paper "Partial Desingularisations of Quotients of Nonsingular Varieties and their Betti Numbers", written in a purely algebro-geometric language. As such, the proofs are novel and require the Luna Slice Theorem as their primary tool.
Chapter 1 is devoted to preliminary material on Geometric Invariant Theory
and the Luna Slice Theorem.
In Chapter 2, we present and prove a version of "Kirwan's procedure". This chapter concludes with an outline of some differences between the current thesis and Kirwan's original paper.
In Chapter 3, we combine the results from Chapter 2 and a result from a paper by Reichstein and Youssin to provide another type of birational model with tame stabilizers (again, with respect to an original linearization).Science, Faculty of
Mathematics, Department of
Graduate
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Iverson, Lee A. (Lee Allan). "Toward discrete geometric models for early vision." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41630.
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Early vision is usually considered to involve the description of geometric structure in an image or sequence of images. Whether biological or artificial, the behavioural constraints on real-time visual systems typically require that this first stage of visual processing be fast, reliable, general and automatic. The design of a visual system which is general enough to handle a wide variety of tasks is thus most likely to be highly parallel, and involve distributed representations of geometric objects. In this work, we investigate some of these general principles and propose both general methodology and specific applications.We build on a general theory of distributed, local representations which we call thick traces. Thick trace descriptions of continuous graphs preserve topological properties such as connectivity, and allow for the descriptions of multi-valued mappings.
Local operators for extracting image curves have been a focus of machine vision research for twenty years. Considered in the context of thick traces, however, we can reassess the goals of these operators and provide a clear description of when they should respond positively and when they should not. In order to achieve this behaviour, we develop an algebra, the Logical/Linear algebra, which incorporates features of both Boolean and linear algebra into a set of non-linear combinators. This algebra is then used to design a family of local operators which explicitly test the logical preconditions underlying the definition of an image curve.
Relaxation labelling is a highly parallel, distributed method of extracting consistent structures from a set of labels. There is a natural match between the representations used in relaxation labelling and thick traces. We exploit this connection by developing a general method for relaxing a set of potentially noisy initial estimates of thick traces (as produced by image operators) into descriptions which are thick traces of geometric models. Furthermore we show how such a system can interpolate into gaps in the traces while simultaneously respecting legitimate discontinuities and boundaries.
Finally, we apply these methods to two problems in early vision: the description of curves and texture flow fields. For image curves, the resulting descriptions of piecewise smooth curves include both local orientation and curvature information. The entire process accurately describes end-points, corners, junctions and bifurcations by allowing many consistent traces to be incident on a single point in the image.
The term texture flow is used to describe a class of static textures with locally parallel dense orientation structure (e.g. Glass or hair patterns). We derive a geometric model of these textures from a smooth non-deforming velocity field. Initial operators and a relaxation network are then defined to interpolate dense, piecewise smooth flow from sparse inputs. The resulting system produces accurate descriptions even in the presence of discontinuities, holes, and overlapping textures.
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Salamon, Csaba. "Information hiding in boundary representation geometric models." Thesis, University of Strathclyde, 2011. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=17405.
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The increasing mobility of computer aided design (CAD) data between subcontractors and distributed manufacturing facilities is creating a need to verify providence and protect the copyright of three-dimensional CAD models. Although watermarking technologies are well established for many types of digital media (e.g. music, image and video) no viable techniques have yet emerged for the high value solid boundary representation (B-rep) models used in 3D mechanical CAD systems. This thesis reviews some of the established approaches to watermarking 3D CAD objects, before describing the particular challenges inherent in the nature and use of B-rep data. After discussing some of the possible methods for incorporating watermarks into three dimensional data structures, an approach is described that subtly alters a B-rep model's geometric representation to incorporate a "transparent" signature. Furthermore, this thesis introduces a watermark assessment scheme and adequate test objects to enable objective benchmarking of the proposed method. In addition, it demonstrates the embedding and retrieval of text information, and investigates the robustness of the embedded watermark after a variety of transformation and modifications have been carried out. Test results show that the introduced parametric orientation (PO) watermark does not change the model's shape or file size, nor has any influence on the CAD model's capabilities. Considering the overall performance, PO-watermarking has shown to be a viable method for marking 3D B-rep CAD models. It works particularly well within a single CAD environment (i.e. company network) where no data is being translated into different formats, and is robust for everyday use. III
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Arroyave-Tobón, Santiago. "Polyhedral models reduction in geometric tolerance analysis." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0720/document.
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L’analyse de tolérances par des ensembles de contraintes repose sur la détermination de l’accumulation de variations géométriques par des sommes et intersections d’ensembles opérandes 6d. Les degrés de liberté des liaisons et les degrés d’invariance des surfaces génèrent des opérandes non-bornés (polyèdres), posant des problèmes de simulation. En 2014, L. Homria proposé une méthode pour résoudre ce problème, consistant à ajouter des limites artificielles(contraintes bouchon) sur les déplacements non-bornés. Même si cette méthode permet la manipulation d’objets bornés (polytopes), les contraintes bouchon augmentent la complexité des simulations. En réponse à cette difficulté, une méthode dérivée est proposée dans cette thèse.Cette méthode consiste à tracer et simplifier les contraintes bouchon au travers des opérations.Puis une seconde stratégie basée sur la décomposition d’un polyèdre en une somme d’un polytope et de lignes droites (associées aux déplacements non-bornés). Cette stratégie consiste à simuler d’une part les sommes de droites, et d’autre part, à déterminer la somme de polytopes dans un sous-espace de dimension inférieur à 6. Ces trois stratégies sont comparées au travers d’une application industrielle. Cela montre que la traçabilité des contraintes bouchons est un aspect fondamental pour contrôler leur propagation et pour réduire le temps de calcul des simulations. Toutefois, cette méthode exige encore de déterminer les limites des déplacements non-bornés. La deuxième méthode, adaptant systématiquement la dimension de l’espace de calcul, elle permet de diminuer davantage le temps de calcul. Ce travail permet d’envisager la mise en oeuvre de cette méthode selon des formulations statistiques avec la prise en compte des défauts de forme des surfacesThe cumulative stack-up of geometric variations in mechanical systems can be modelled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The degrees of freedom (DOF) of jointsgenerate unbounded sets (i.e. polyhedra) which are difficult to deal with. L. Homri presented in 2014 a solution based on the setting of fictitious limits (called cap constraints) to each DOFto obtain bounded 6D sets (i.e. polytopes). These additional constraints, however, increase the complexity of the models, and therefore, of the computations. In response to this situation,we defined a derived strategy to control the effects of the propagation of the fictitious limits by tracing and simplifying the generated, new cap constraints. We proposed a second strategy based on the decomposition of polyhedra into the sum of a polytope and a set of straight lines.The strategy consists in isolating the straight lines (associated to the DOF) and summing the polytopes in the smallest sub-space. After solving an industrial case, we concluded that tracing caps constraints during the operations allows reducing the models complexity and,consequently, the computational time; however, it still involves working in 6d even in caseswhere this is not necessary. In contrast, the strategy based on the operands decompositionis more efficient due to the dimension reduction. This study allowed us to conclude that the management of mechanisms’ mobility is a crucial aspect in tolerance simulations. The gain on efficiency resulting from the developed strategies opens up the possibility for doing statistical treatment of tolerances and tolerance synthesis
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Meira, Gilmara Gomes. "Comunicação e resolução de problemas utilizando o modelo Van Hiele para a exploração geométrica em sala de aula." Universidade Estadual da Paraíba, 2015. http://tede.bc.uepb.edu.br/tede/jspui/handle/tede/2381.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This research analyzes limits and possibilities from problems solving that consider the level of comprehension of van Hiele Model. Therefore, we want to know how students communicate with each other when they develop activities with geometric problems solving in the referred Model perspective. The target audience for the research development was a third year class of high school from a public school in Cabaceiras city – PB. The theoretical framework emphasizes the Problem Solving, the Geometric teaching and learning relevance, van Hiele Model, the use of manipulable materials and the aspects of social interaction taking into consideration particularly the written and oral students’ communication. This research, developed together with the Program Observatório de Educação/CAPES proposal, from which we are part of, happenned in three steps – with all the class working on Duo; with all the class working individually and; with the Duo selected from its development on van Hiele tests. Such study is of qualitative nature, it happened from the class development on selected activities that after it resulted in three case studies where it is analyzed the respective development on problems solving subsidized by the use of Tangram and the manner in which the double interact and communicate. The data were collected by participant observation, audiorecordings and recordings of oral and written communication from the Duo. Some of the main references used as theoretical support were Boavida et al (2008), Nasser and Sant'Anna (2010), Rego, Rego and Vieira (2012), Van de Walle (2009), Fonseca (2009), Carvalho (2009 ), among others. The results indicate there is fragility in Geometry knowledge from the students who finish High School, reflecting in limitations to solve problems. Also it reveals the potentialities that exist in the work developed from social interaction, raising a progressive communication that leads the students on reflecting by specific development in problems solving.
A presente pesquisa analisa limites e possibilidades a partir da resolução de problemas que levam em consideração o Nível de compreensão segundo o Modelo van Hiele. Dessa forma, queremos saber como os alunos se comunicam quando desenvolvem atividades com resolução de problemas geométricos, na perspectiva do referido Modelo. O público alvo para desenvolvimento da pesquisa foi uma turma do 3º Ano do Ensino Médio de uma escola pública estadual da cidade de Cabaceiras - PB. O quadro teórico enfatiza a Resolução de Problemas, a relevância do ensino e aprendizagem da Geometria, o Modelo van Hiele, o uso de Materiais Manipuláveis e aspectos da interação social tendo em vista, particularmente, a comunicação oral e escrita dos alunos. Essa pesquisa desenvolvida em conjunto com a proposta do Programa Observatório de Educação/CAPES, do qual fazemos parte, aconteceu em três etapas - com a turma toda trabalhando em Díades; com a turma toda trabalhando individualmente e; com as Díades selecionadas a partir do seu desenvolvimento nos testes van Hiele. Esse estudo é de natureza qualitativa, aconteceu a partir do desenvolvimento da turma em atividades selecionadas que, posteriormente, resultou em três estudos de caso nos quais se analisa o respectivo desenvolvimento na resolução dos problemas subsidiados com o uso do Tangram, bem como o modo como as Díades interagem e se comunicam. Os dados foram recolhidos por meio da observação participante, áudio-gravações e registros da comunicação oral e escrita das Díades. Algumas das principais referências que utilizamos como sustentação teórica foram Boavida et al (2008), Nasser e Sant’anna (2010), Rêgo, Rêgo e Vieira (2012), Van de Walle (2009), Fonseca (2009), Carvalho (2009), entre outros. Os resultados analisados apontam para a fragilidade que há no conhecimento de Geometria por parte dos alunos que concluem o Ensino Médio, refletindo em limitações ao resolver problemas. Além disso, revela as potencialidades que há no trabalho desenvolvido a partir da interação social, suscitando em uma comunicação progressiva que leva os alunos a refletirem por meio do desenvolvimento específico na resolução dos problemas.
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Barcenas, Carolina. "Geometric tolerance verification using superquadrics." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/25603.
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Li, Yi Kapustin Anton N. "Topological sigma models and generalized geometries /." Diss., Pasadena, Calif. : California Institute of Technology, 2005. http://resolver.caltech.edu/CaltechETD:etd-05262005-154458.
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Kaltenmark, Irène. "Geometrical Growth Models for Computational Anatomy." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLN049/document.
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Dans le domaine de l'anatomie, à l'investissement massif dans la constitution de base de données collectant des données d'imagerie médicale, doit répondre le développement de techniques numériques modernes pour une quantification de la façon dont les pathologies affectent et modifie les structures biologiques. Le développement d'approches géométriques via les espaces homogènes et la géométrie riemannienne en dimension infinie, initialisé il y a une dizaine d'années par Christensen et Miller, et simultanément Trouvé et Younes, et mettant en œuvre des idées originales de d'Arcy Thompson, a permis de construire ces dernières années un cadre conceptuel extrêmement efficace pour attaquer le problème de la modélisation et de l'analyse de la variabilité de populations de formes. Néanmoins, à l'intégration de l'analyse longitudinale des données, ont émergé des phénomènes biologiques de croissance ou de dégénérescence se manifestant via des déformations spécifiques de nature non difféomorphique. On peut en effet observer lors de la croissance d'un composant organique, une apparition progressive de matière qui ne s'apparente pas à un simple étirement du tissu initial. Face à cette observation, nous proposons de garder l'esprit géométrique qui fait la puissance des approches difféomorphiques dans les espaces de formes mais en introduisant un concept assez général de déploiement où l'on modélise les phénomènes de croissance comme le déploiement optimal progressif d'un modèle préalablement replié dans une région de l'espace. Nous présentons donc une généralisation des méthodes difféomorphiques classiques pour modéliser plus fidèlement l'évolution de chaque individu d'une population et saisir l'ensemble de la dynamique de croissance. Nous nous appuyons sur l'exemple concret de la croissance des cornes animales. La considération d'un a priori sur la dynamique de croissance de la corne, nous permet de construire un chemin continu dans un espace de formes, modélisant l'évolution de la corne de sa naissance, d'un état réduit à un point (comme l'état d'embryon pour un humain ou de graine pour une plante) à un âge adulte quelconque de corne bien déployée. Au lieu d'étirer la corne, nous anticipons l'arrivée matière nouvelle en des endroits prédéfinis. Pour cela, nous définissons une forme mère indépendante du temps dans un espace virtuel, qui est progressivement plongée dans l'espace ambiant en fonction d'un marqueur temporel prédéfini sur la forme mère. Finalement, nous aboutissons à un nouveau problème de contrôle optimal pour l'assimilation de données de surfaces évoluant dans le temps, conduisant à un problème intéressant dans le domaine du calcul des variations où le choix pour la représentation des données, courant ou varifold, joue un rôle inattenduThe Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has proved to be highly efficient for addressing the problem of modelling and analysis of the variability of populations of shapes, allowing for the direct comparison and quantization of diffeomorphic morphometric changes. However, the analysis of medical imaging data also requires the processing of more complex changes, which especially appear during growth or aging phenomena. The observed organisms are subject to transformations over the time which are no longer diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material uncorrelated to the preexisting one. For this purpose, we offer to extend the LDDMM framework to address the problem of non diffeomorphic structural variations in longitudinal scenarios during a growth or degenerative process. We keep the geometric central concept of a group of deformations acting on a shape space. However, the shapes will be encoded by a new enriched mathematical object allowing through partial mappings an intrinsic evolution dissociated from external deformations. We focus on the specific case of the growth of animal horns.Ultimately, we integrate these growth priors into a new optimal control problem for assimilation of time-varying surface data, leading to an interesting problem in the field of the calculus of variations where the choice of the attachment term on the data, current or varifold, plays an unexpected role
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Liu, Yang, and 劉洋. "Optimization and differential geometry for geometric modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988077.
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Portugal, Ricardo Filipe Marques. "Modelo de Minkwoski para a Geometria de Laguerre." Master's thesis, Universidade da Beira Interior, 2010. http://hdl.handle.net/10400.6/1848.
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Este trabalho iniciou-se com um estudo prévio de pontos notáveis associados a três
circunferências ([6], ver anexo) a partir de um lema de incidência no plano projectivo
([6], Lema 1). Particularizando ao caso das três circunferências estarem ex-inscritas
a um triangulo, este lema parece estabelecer uma caracterização geométrica unificadora de muitos centros de Kimberling.
Querendo explorar mais profundamente a riqueza geométrica destas configuracões, acreditamos que, para tal, seria interessante estabelecer uma generalização
do Teorema de Ceva. Ora, a geometria de Laguerre será talvez o contexto teórico
adequado a esta generalização. De facto, nesta geometria, pontos e circunferências
são tratados como objectos matemáticos equivalentes. Por outro lado, em trabalhos recentes, tem sido colocada em evidencia a possibilidade de utilizar esta
geometria, no ˆâmbito do seu modelo de Minkowski, para o estudo de problemas
clássicos em geometria euclidiana.
Neste trabalho procurámos apresentar de forma completa e detalhada as ideias
e resultados principais que estão presentes em [2]. Em particular, começamos por
definir, de acordo com os princípios de Félix Klein e do seu Programa de Erlangen,
as geometrias de Lie, Laguerre e Mobius. De seguida, descrevemos o modelo de
Minkowski para a geometria de Laguerre. Este ´e um modelo que é fácil de manipular
e que evidencia de forma clara que o espaço subjacente `a geometria de Laguerre ´e um espaço homogéneo. Por fim, enunciamos e provamos um resultado que generaliza o
clássico Teorema de Pitágoras. Em trabalho futuro, procuraremos aplicar algumas
destas ideias na perspetiva de encontrar uma generalização adequada do Teorema
de Ceva.
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Franceschiello, Benedetta. "Cortical based mathematical models of geometric optical illusions." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066131/document.
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Cette thèse présente des modèles mathématiques pour la perception visuelle et s'occupe des phénomènes où on reconnait une brèche entre ce qui est représenté et ce qui est perçu. La complétion amodale consiste en percevoir un complètement d'un object qui est partiellement occlus, en opposition avec la complétion modale, dans laquelle on perçoit un object même si ses contours ne sont pas présents dans l'image [Gestalt, 99]. Ces contours, appelés illusoires, sont reconstruits par notre système visuelle et ils sont traités par les cortex visuels primaires (V1/V2) [93]. Des modèles géométriques de l'architecture fonctionnelle de V1 on le retrouve dans le travail de Hoffman [86]. Dans [139] Petitot propose un modèle pour le complètement de contours, équivalent neurale du modèle proposé par Mumford [125]. Dans cet environnement Citti et Sarti introduisent un modèle basé sur l'architecture fonctionnelle de la cortex visuel [28], qui justifie les illusions à un niveau neurale et envisage un modèle neuro-géometrique pour V1. Une autre classe sont les illusions d'optique géométriques (GOI), découvertes dans le XIX siècle [83, 190], qui apparaissent en présence d'une incompatibilité entre ce qui est présent dans l'espace object et le percept. L'idée fondamentale développée ici est que les GOIs se produisent suite à une polarisation de la connectivité de V1/V2, responsable de l'illusion. A partir de [28], où la connectivité qui construit les contours en V1 est modelée avec une métrique sub-Riemannian, on étend cela en disant que pour le GOIs la réponse corticale du stimule initial module la connectivité, en devenant un coefficient pour la métrique. GOIs seront testés avec ce modèleThis thesis presents mathematical models for visual perception and deals with such phenomena in which there is a visible gap between what is represented and what we perceive. A phenomenon which drew the interest most is amodal completion, consisting in perceiving a completion of a partially occluded object, in contrast with the modal completion, where we perceive an object even though its boundaries are not present [Gestalt theory, 99]. Such boundaries reconstructed by our visual system are called illusory contours, and their neural processing is performed by the primary visual cortices (V1/V2), [93]. Geometric models of the functional architecture of primary visual areas date back to Hoffman [86]. In [139] Petitot proposed a model of single boundaries completion through constraint minimization, neural counterpart of the model of Mumford [125]. In this setting Citti and Sarti introduced a cortical based model [28], which justifies the illusions at a neural level and provides a neurogeometrical model for V1. Another class of phenomena are Geometric optical illusions (GOIs), discovered in the XIX century [83, 190], arising in presence of a mismatch of geometrical properties between an item in object space and its associated percept. The fundamental idea developed here is these phenomena arise due to a polarization of the connectivity of V1/V2, responsible for the misperception. Starting from [28] in which the connectivity building contours in V1 is modeled as a sub-Riemannian metric, we extend it claiming that in GOIs the cortical response to the stimulus modulates the connectivity of the cortex, becoming a coefficient for the metric. GOIs will be tested through this model
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Smith, Robert Frederick. "Geometric models of the stenosed human carotid bifurcation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ32510.pdf.
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Jarnagin, Andrew B. "Effective digital exchange of three dimensional geometric models." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/16442.
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El-Berry, S. E. M. "Some geometric and negative binomial time series models." Thesis, University of Strathclyde, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381119.
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Nill, Scott T. (Scott Thomas). "Aerospace composite manufacturing cost models as geometric programs." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/118731.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 108-110).
The introduction of large, composite transport aircraft, such as the Airbus A350 and the Boeing 787, has been fraught with billions of dollars of production cost overruns. This research develops a novel approach to manufacturing cost modeling during the conceptual design phase using Geometric Programming (GP). A new formulation of a closed queuing network as a GP is presented to capture the crucial cost trade-offs between capacity and inventory. Additionally, GP models are presented for modeling unit processes in composite manufacturing and for modeling cost accounting metrics. Applied to the challenges of conceptual design for composite aircraft, the cost models can be used as a tool to help inform decisions about which manufacturing process to use and what type of supply chain should be deployed. The special sensitivity-analysis properties of the GP solutions can be exploited to explain how different aspects of the design drive manufacturing costs and to find highly sensitive areas of the trade-space that would have a large impact on cost if the design needed to be altered. The framework is demonstrated for fast but informative analyses of process trade-offs in composite fuselage fabrication.
by Scott T. Nill.
Ph. D.
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Robertson, Duncan Paul. "Recovering geometric models from photographs of architectural scenes." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616042.
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Yang, Baofen. "Geometric deformable models using the level set method." Mémoire, Université de Sherbrooke, 2005. http://savoirs.usherbrooke.ca/handle/11143/4664.
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Geometric deformable models for active contours have brought tremendous impact to classical problems in image processing such as providing ways to devise efficient computational algorithms for automatic segmentation. This is achieved by using the level set method, which allows handling automatic changes in topology while providing a framework for very fast numerical schemes. However, topological flexibility is not desired when an object with known topology is sought. It is natural to capture the target in a way that gives the correct topology. A geometric deformable model with topology preserving is developed that can guarantee the topology will be preserved while all the computational advantages of the level set approach are maintained. A key issue in object detection using the shape of the object’s boundary and surface reconstruction using slice contours is the ability to identify the complete boundaries of the segmented objects in the scene. The segmentation results provided by geometric deformable models are usually dependent on the contour initialization, and in most cases, the results of the segmentation will only provide partial objects boundaries. A new method based on digital topology is proposed to detect the complete boundary information of the segmented objects. By carrying out a topological analysis of the objects, this method can provide the right initialization that can capture all the boundaries of the objects in certain cases.
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Ferro, Dennis Eduardo Zavaleta [UNESP]. "Some geometric aspects of non-linear sigma models." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/151647.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
We review some relevant examples for String Theory of non-linear sigma models. These are bosonic strings propagating in curved background, the Wess-Zumino-Witten model and superstrings in flat and AdS superspace. The mathematical tools required for the study of these models (e.g. topological quantization, Cartan geometry, Lie superalgebras and geometry on coset spaces) are also described. Throughout the dissertation we have focused on classical aspects of these models such as the construction of the action and its symmetries where conditions for holomorphic symmetry of the bosonic string case were found.
Nesta dissertação estudamos alguns exemplos de modelos sigma não lineares em Teoria de cordas. Estes são a corda bosónica se propagando em espaços curvos, o modelo Wess-Zumino-Witten e supercordas em superespaço plano e AdS. As ferramentas matemáticas que se precisam para o estudo destes modelos (e.g. quantização topológica, geometria de Cartan, super-álgebras de Lie e geometria em espaços coset) também são descritas. Ao longo desta dissertação focamos os aspectos clássicos destes modelos tais como a construção da ação e suas simetrias onde condições para serem estas holomorficas no caso da corda bosónica foram achadas.
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Couvreur, Romain. "Geometric lattice models and irrational conformal field theories." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS062.
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Dans cette thèse nous étudions différents aspects des modèles critiques non-unitaires de physique statistique en deux dimensions. Notre approche, partant de modèles discrets sur le réseau, permet d'en apprendre plus sur les théories conformes associées. Celles-ci sont non-unitaires et souvent irrationnelles, logarithmiques ou encore non-compactes. Pour commencer, le problème de l'entropie d'intrication dans des chaînes de spin non-unitaires et son interprétation dans les modèles de boucles sont considérés. Le rôle de la charge centrale effective, une quantité pertinente pour étudier aussi d'autres problèmes de ce manuscrit, y est discuté. Ensuite, nous regardons deux problèmes liés au modèle de Chalker-Coddington, une chaîne de spin supersymétrique de dimension infinie, importante pour l'étude de la transition entre plateaux dans l'effet Hall quantique entier. Puisque ce modèle a un nombre infini de degrés de liberté, il a été proposé de considérer une série de troncations. Nous présentons de nouveaux résultats basés sur cette approche et développons cette méthode dans le cadre du mouvement Brownien dans sa formulation supersymétrique. Ensuite, un nouveau modèle est proposé pour interpoler la classe A et la classe C de l'effet Hall quantique. Le modèle de Chalker-Coddington est une réalisation particulière de la classe A tandis que la classe C, qui décrit la physique de l'effet Hall quantique de spin, est relié à un modèle de percolation. Ce modèle donne un exemple de flot sous l'action du groupe de renormalisation entre une théorie conforme compacte et non-compacte. La dernière partie de cette thèse discute la classification des observables sur réseau avec une symétrie discrète. Le processus est illustré sur le modèle de Potts avec sa symétrie sous l'action du groupe des permutations et des résultats déjà connus sont étendus au cas des opérateurs non-scalaires. Cette approche est importante dans l'étude de l'indécomposabilité des modèles non-unitaires et peut être utilisée pour étudier la percolation en dimension supérieureIn this thesis we study several aspects of two-dimensional lattice models of statistical physics with non-unitary features. This bottom-up approach, starting from discrete lattice models, is helpful to understand the features of the associated conformal field theories. They are non-unitary and often irrational, logarithmic or even non-compact. First, we study the problem of the entanglement entropy in non-unitary spin chains and its interpretation in loop models. We discuss the role of the effective central charge, a relevant quantity to study the next problems in this thesis. We then address two problems related to the Chalker-Coddington model, an infinite-dimensional supersymmetric chain important for the study of the plateau transition in the integer quantum Hall effect. Since the model has an infinite number of degrees of freedom, it has been proposed to study it with a series of truncations. We present new results based on this approach and extend this methodology to the case of Brownian motion in its supersymmetric formulation. Next, a new model is proposed to interpolate between class A and class C. The Chalker-Coddington model is a particular realisation of class A whereas class C, describing the physics of the spin quantum Hall effect, can be related to a model of percolation. This interpolating model provides an example of a RG-flow between a non-compact CFT and compact one. The last part of this thesis deals with the problem of classifying observables in lattice models with discrete symmetries. The process is illustrated on the Potts model and its symmetry under the group of permutations and previous results are extended for non-scalar operators. This approach is important to study indecomposability of non-unitary models and can be used to study models such as percolation in higher dimensions
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Mackie, Ewan Thomas Braid. "Rational term-structure models and geometric Levy martingales." Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/9483.
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One of the most important problems in modern finance is to understand how best to model the occurrence of jumps in asset pricing models. With this issue in mind, the main topic of this thesis is the development of a set of asset pricing models, driven by Levy uncertainty, applicable across a wide range of asset classes. In particular, we model the term structure of interest rates in a Levy setting, by use of the so-called positive interest models of Flesaker and Hughston. We begin with a brief review of the term-structure literature. We then introduce elements of the theory of Levy processes and develop a rather general theory of geometric Levy models (GLMs) for dynamic asset pricing, paying attention in particular to issues concerning the relation between risk and return for the models under consideration. The special case of a GLM with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion used in the Black-Scholes theory. General conditions are established under which assets show a positive risk premium in such a setting. The Flesaker-Hughston approach has the advantage that positive nominal interest rates are built in from the beginning. The resulting models are rational in the sense that the price of a discount bond is given by a ratio of integrals of families of positive martingales. We develop a class of models of this type, where the martingale families are modelled by parametric families of geometric Levy processes. Closed-form expressions are provided for the prices of discount bonds, the short rate of interest, and the prices of options on discount bonds, for various specific cases of Levy uncertainty. In the example of the geometric Brownian motion family we include a rather detailed discussion of the behaviour of the risk premium, and establish conditions under which it is positive. We put forward a proposal for a two-stage calibration of the rational Levy models to the market prices of options. Empirical studies are carried out on the calibration performance of (a) the rational Brownian model, and (b) the rational variance gamma model. We then develop a novel hedging strategy for a portfolio of options on discount bonds. The hedging strategy takes the form of a functional derivative of the option price with respect to the price of the underlying discount bond.
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Klíma, Ondřej. "Rekonstrukce tvaru polygonálních modelů." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-412883.
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The thesis is focussed on the reconstruction of a damaged skull represented by a polygonal model. The reconstruction is based on a statistical shape model of the skull. The thesis covers the registration of skulls by using a thin-plate spline method, aligning polygonal models by generalized procrustes analysis, the identification of missing parts of a skull by means of statistical shape models outliers analysis. Finally, missing parts of the skull are reconstructed and the accuracy of the reconstruction is estimated.
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Baldwin, Elizabeth. "A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487135.
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We construct the moduli spaces of stable maps, Mg,n(pr, d), via geometric invariant theory (GIT). This construction is only valid over Spec C, but a special case is a GIT presentation of Mg,n, which is valid over any algebraically closed field. Our method follows that of Gieseker in [G] and Swinarski in [Sw2], though our proof that the semistable set is nonempty is different.
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Wimelaratna, Ramasinghege. "Multi dimensional geometric moduli and exterior algebra of a Banach space /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759830383865.
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Roper, Steven Michael. "Theoretical models for dyke geometries and trajectories." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614961.
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Leão, Rafael de Freitas 1979. "Geometria não-comutativa e o modelo de Connes-Lott." [s.n.], 2003. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307239.
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Orientador: Jayme Vaz JrDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Nesta dissertação estudamos uma forma de generalizar, algebricamente, alguns conceitos de geometria deferencial clássica (como por exemplo os conceitos de variedade e de fibrados vetoriais sobre variedades). Além disso, construímos para estas estruturas algébricas as ferramentas usuais do cálculo integro-diferencial. Estes conceitos são a base da geometria não-comutativa, que nos permite estudar alguns espaços excluídos do tratamento geométrico usual, como por exemplo o espaço com apenas dois pontos. Em particular usamos a geometria do espaço de dois pontos juntamente com a geometria usual do espaço-tempo para estudar uma versão geométrica do conhecido modelo padrão de partículas elementares (em particular o modelo de Weinberg-Salam). Um dos grandes ganhos obtidos com essa formulação geométrica é que o boson de Higgs aparece de uma forma natural dentro do modelo como parte de uma conexão nesse espaço mais geral
Abstract: In this dissertation we studied how to generalize in an algebraic way some of the concepts of classical differential geometry (like the concepts of manifolds and vector bundles). Moreover, we developed the integral and differential calculus over these algebraic structures. These concepts are the basis of the noncom mutative geometry, which enabled us to study from a geometrical point of view some spaces (like the two point space) that are excluded from usual treatments. In particular we used the geometry of the two point space with the usual space-time geometry in order to formulate a geometrical version of the standard model of elementary particles (in particular the Weinberg-Salam model). One of the great advantages of this geometric formulation is that the Higgs boson appears in a natural way as part of a conection in this more general space
Mestrado
Mestre em Matemática
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Rocha, André Rodrigues de la. "Geometria e heterogeneidade na dinâmica no modelo de Potts." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/83661.
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O conceito de heterogeneidade de tamanhos de domínios (Heq), definido como o número de tamanhos distintos de domínios existentes em determinada configuração de um sistema, foi recentemente introduzido no contexto do modelo de percolação explosiva. Além de introduzir um novo expoente de escala, o mesmo se mostrou útil em outros problemas da mecânica estatística de equilíbrio, como o de percolação aleatória, bem como nos modelos de Ising e Potts. Neste trabalho, aplicamos e medimos esta quantidade em situações fora do equilíbrio. Em particular, após submetermos os modelos de Ising e Potts a um súbito resfriamento, a partir de um estado de equilíbrio de alta temperatura, para uma temperatura crítica ou subcrítica, T > Tc, medimos a evolução temporal de H(t). Mostramos que o comportamento para tempos grandes é uma lei de potência com expoentes diferentes para os casos crítico e subcrítico. Adicionalmente, o comportamento para tempos pequenos apresenta ainda um máximo no valor de H(t), quando a temperatura inicial é T0 → Ѡ. Apresentamos um extenso conjunto de dados de simulação que apoiam essas conclusões e discutimos perspectivas futuras, com o objetivo de tentar compreender melhor o comportamento de H(t).The concept of domain size heterogeneity (Heq), the number of distinct domain sizes occurring in a given con guration, was recently introduced in the context of explosive percolation. Besides introducing a new scaling exponent, it was shown to be useful in other classical equilibrium statistical mechanics problems, like random percolation, and the Ising and Potts models. Here we apply and measure this quantity for out of equilibrium situations. In particular, after quenching the Ising and Potts models from a high temperature equilibrium state, T > Tc, to a critical or subcritical temperature, T Tc, we measure the time evolution of H(t). We show that the long time behavior is power law with di erent exponents for critical and subcritical coarsening. Moreover, the short time behavior also presents a surprising maximum of H(t) when the initial temperature is T0 → Ѡ. We present extensive simulation data supporting these conclusions and discuss future perspectives, in order to help understand the overall behavior of H(t).
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SOUZA, Carlos Bino de. "Geometria hiperbólica : consistência do modelo de disco de Poincaré." Universidade Federal Rural de Pernambuco, 2015. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6695.
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Euclid wrote a book in 13 volumes called Elements where systematized all the mathematical knowledge of his time. In this work, the 5 postulates of Euclidean geometry were presented. For several years, the 5th Postulate was frequently asked, this inquiries it was discovered that there are several other possible geometries, including hyperbolic geometry. Beltrimi proved that hyperbolic geometry is consistent if Euclidean geometry is consistent. Hilbert showed that Euclidean geometry is consistent if the arithmetic is consistent and presented an axiomatic system that capped the gaps in Euclid’s axiomatic system. Poincaré created a model, called the Poincaré disk, to represent the plan of hyperbolic geometry. The objective of this work is to show that the Poincaré disk model is consistent with reference Axioms Hilbert, replacing only the Axioms of Parallel to "On a point outside a line passes through the two parallel straight lines given", by constructions of Euclidean geometry.
Euclides escreveu uma obra em 13 volumes chamada de Elementos onde sistematizava todo o conhecimento matemático do seu tempo. Nesta obra, foram apresentados os 5 postulados da Geometria Euclidiana. Durante vários anos, o 5o Postulado foi muito questionado, desses questionamentos descobriu-se a existência de várias outras Geometrias possíveis, entre elas a Geometria Hiperbólica. Beltrimi provou que a Geometria Hiperbólica é consistente se a Geometria Euclidiana é consistente. Hilbert mostrou que a Geometria Euclidiana é consistente se a Aritmética é consistente e apresentou um sistema axiomático que preencheu as lacunas do sistema axiomático de Euclides. Poincaré criou um Modelo, chamado de Disco de Poincaré, para representar o plano da Geometria Hiperbólica. O objetivo deste trabalho é mostrar que o Modelo de Disco de poincaré é consistente, tomando como referência os Axiomas de Hilbert, substituindo apenas os Axiomas das Paralelas para "Por um ponto fora de uma reta passam duas retas paralelas à reta dada", através de construções da Geometria Euclidiana.
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Cooper, Robert John. "Geometric parameterisation in finite element models of femoroacetabular impingement." Thesis, University of Leeds, 2017. http://etheses.whiterose.ac.uk/19210/.
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Abnormal bony morphology is a factor implicated in hip joint soft tissue damage and an increased lifetime risk of osteoarthritis. One geometric feature causing impingement and thus resulting in such damage is a bony lump on the femoral neck, known as a cam deformity. A three-dimensional geometric parameterisation system was developed to capture key variations in the femur and acetabulum of subjects with clinically diagnosed cam deformity. Novel quantitative measures of the size and position of cams were taken and used to assess differences in morphological deformities between males and females. The precision of the measures was sufficient to identify differences between subjects that could not be seen using two-dimensional imaging; cams were found to be more superiorly located in males than in females. As well as providing a means to distinguish between subjects more clearly, the geometric hip parameterisation facilitated flexible and rapid automated generation of a range of hip geometries including cams. These were used to develop finite element models. Patient-specific parametric finite element models of hips under impingement conditions were verified with comparison to their patient-specific segmentation-based equivalents. The parameterisation system was then used to generate further models to investigate the effects of bone morphology on tissue strains. This demonstrated that a combination of cam location and extent affect impingement severity, highlighting the importance of reporting the full three-dimensional geometry used for parametric models.
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Muradali, Amirmohamed. "Geometric models to model acoustic barriers including atmospheric conditions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/mq22643.pdf.
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Vestweber, Johanna [Verfasser]. "Geometric ergodicity of multivariate stochastic volatility models / Johanna Vestweber." Ulm : Universität Ulm, 2018. http://d-nb.info/1151938378/34.
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Branda, Ewan E. (Ewan Edward) 1964. "Drawing interfaces : building geometric models with hand-drawn sketches." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/64901.
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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1998.Includes bibliographical references (p. 49-51).
Architects work on drawings and models, not buildings. Today, in many architectural practices, drawings and models are produced in digital format using Computer-aided Design (CAD) tools. Unquestionably, digital media have changed the way in which many architects perform their day to day activities. But these changes have been limited to the more prosaic aspects of practice. To be sure, CAD systems have made the daily operations of many design offices more efficient; nevertheless, they have been of little use - and indeed are often a hindrance - in situations where the task at hand is more conjectural and speculative in nature, as it is during the early stages of a project. Well-intentioned efforts to insinuate CAD into these aspects of practice have only served to reveal the incongruities between the demands of designer and the configuration of the available tools. One of the chief attributes of design practice is that it is action performed at a distance through the agency of representations. This fundamental trait implies that we have to understand how computers help architects describe buildings if we are to understand how they might help architects design buildings. As obvious as this claim might seem, CAD programs can be almost universally characterized by a tacit denigration of visual representation. In this thesis, I examine properties of design drawings that make them useful to architects. I go on to describe a computer program that I have written that allows a designer to build geometric models using freehand sketches. This program illustrates that it is possible to design a software tool in a way that profits from, rather than negates, the power of visual representations.
by Ewan E. Branda.
M.S.