New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface

New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes

With the advent of powerful 3D acquisition technology, there is a growing demand for the modeling, processing, and visualization of surfaces and volumes. The proposed methods must be efficient and robust, and they must be able to extract the essential structure of the data and to easily and quickly convey the most significant information to a human observer. Independent of the specific nature of the data, the following fundamental problems can be identified: shape reconstruction from discrete samples, data analysis, and data compression. This thesis presents several novel solutions to these problems for surfaces (Part I) and volumes (Part II). For surfaces, we adopt the well-known triangle mesh representation and develop new algorithms for discrete curvature estimation,detection of feature lines, and line-art rendering (Chapter 3), for connectivity encoding (Chapter 4), and for topology preserving compression of 2D vector fields (Chapter 5). For volumes, that are often given as discrete samples, we base our approach for reconstruction and visualization on the use of new trivariate spline spaces on a certain tetrahedral partition. We study the properties of the new spline spaces (Chapter 7) and present efficient algorithms for reconstruction and visualization by iso-surface rendering for both, regularly (Chapter 8) and irregularly (Chapter 9) distributed data samples

Trivariate C1-Splines auf gleichmäßigen Partitionen

In der vorliegenden Dissertation werden Splines auf gleichmäßigen Partitionen untersucht. Ziel der Arbeit ist die Analyse von multivariaten Splineräumen und die Entwicklung von neuen Methoden zur Lösung von Interpolations- und Approximationsproblemen mit trivariaten C1-Splines. Die entwickelten Methoden werden in Hinblick auf Lokalität, Stabilität und Approximationsordnung untersucht und die Ergebnisse dem Stand der Technik gegenübergestellt. Erstmalig kann dabei eine Quasi-Interpolationsmethode für trivariate C1-Splines vom totalen Grad zwei entwickelt werden und zur interaktiven Volumenvisualisierung mit Raycasting Techniken effizient eingesetzt werden

Lagrange interpolation and quasi-interpolation using trivariate splines on a uniform partition

We develop quasi-interpolation methods and a Lagrange interpolation method for trivariate splines on a regular tetrahedral partition, based on the Bernstein-Bézier representation of polynomials. The partition is based on the bodycentered cubic grid. Our quasi-interpolation operators use quintic C2 splines and are defined by giving explicit formulae for each coefficient. One operator satisfies a certain convexity condition, but has sub-optimal approximation order. A second operator has optimal approximation order, while a third operator interpolates the provided data values. The first two operators are defined by a small set of computation rules which can be applied independently to all tetrahedra of the underlying partition. The interpolating operator is more complex while maintaining the best-possible approximation order for the spline space. It relies on a decomposition of the partition into four classes, for each of which a set of computation rules is provided. Moreover, we develop algorithms that construct blending operators which are based on two quasi-interpolation operators defined for the same spline space, one of which is convex. The resulting blending operator satisfies the convexity condition for a given data set. The local Lagrange interpolation method is based on cubic C1 splines and focuses on low locality. Our method is 2-local, while comparable methods are at least 4-local. We provide numerical tests which confirm the results, and high-quality visualizations of both artificial and real-world data sets

Teadusarvutuse algoritmide taandamine hajusarvutuse raamistikele

Teadusarvutuses kasutatakse arvuteid ja algoritme selleks, et lahendada probleeme erinevates reaalteadustes nagu geneetika, bioloogia ja keemia. Tihti on eesmärgiks selliste loodusnähtuste modelleerimine ja simuleerimine, mida päris keskkonnas oleks väga raske uurida. Näiteks on võimalik luua päikesetormi või meteoriiditabamuse mudel ning arvutisimulatsioonide abil hinnata katastroofi mõju keskkonnale. Mida keerulisemad ja täpsemad on sellised simulatsioonid, seda rohkem arvutusvõimsust on vaja. Tihti kasutatakse selleks suurt hulka arvuteid, mis kõik samaaegselt töötavad ühe probleemi kallal. Selliseid arvutusi nimetatakse paralleel- või hajusarvutusteks. Hajusarvutuse programmide loomine on aga keeruline ning nõuab palju rohkem aega ja ressursse, kuna vaja on sünkroniseerida erinevates arvutites samaaegselt tehtavat tööd. On loodud mitmeid tarkvararaamistikke, mis lihtsustavad seda tööd automatiseerides osa hajusprogrammeerimisest. Selle teadustöö eesmärk oli uurida selliste hajusarvutusraamistike sobivust keerulisemate teadusarvutuse algoritmide jaoks. Tulemused näitasid, et olemasolevad raamistikud on üksteisest väga erinevad ning neist ükski ei ole sobiv kõigi erinevat tüüpi algoritmide jaoks. Mõni raamistik on sobiv ainult lihtsamate algoritmide jaoks; mõni ei sobi olukorras, kus andmed ei mahu arvutite mällu. Algoritmi jaoks kõige sobivama hajusarvutisraamistiku valimine võib olla väga keeruline ülesanne, kuna see nõuab olemasolevate raamistike uurimist ja rakendamist. Sellele probleemile lahendust otsides otsustati luua dünaamiline algoritmide modelleerimise rakendus (DAMR), mis oskab simuleerida algoritmi implementatsioone erinevates hajusarvutusraamistikes. DAMR aitab hinnata milline hajusraamistik on kõige sobivam ette antud algoritmi jaoks, ilma algoritmi reaalselt ühegi hajusraamistiku peale implementeerimata. Selle uurimustöö peamine panus on hajusarvutusraamistike kasutuselevõtu lihtsamaks tegemine teadlastele, kes ei ole varem nende kasutamisega kokku puutunud. See peaks märkimisväärselt aega ja ressursse kokku hoidma, kuna ei pea ükshaaval kõiki olemasolevaid hajusraamistikke tundma õppima ja rakendama.Scientific computing uses computers and algorithms to solve problems in various sciences such as genetics, biology and chemistry. Often the goal is to model and simulate different natural phenomena which would otherwise be very difficult to study in real environments. For example, it is possible to create a model of a solar storm or a meteor hit and run computer simulations to assess the impact of the disaster on the environment. The more sophisticated and accurate the simulations are the more computing power is required. It is often necessary to use a large number of computers, all working simultaneously on a single problem. These kind of computations are called parallel or distributed computing. However, creating distributed computing programs is complicated and requires a lot more time and resources, because it is necessary to synchronize different computers working at the same time. A number of software frameworks have been created to simplify this process by automating part of a distributed programming. The goal of this research was to assess the suitability of such distributed computing frameworks for complex scientific computing algorithms. The results showed that existing frameworks are very different from each other and none of them are suitable for all different types of algorithms. Some frameworks are only suitable for simple algorithms; others are not suitable when data does not fit into the computer memory. Choosing the most appropriate distributed computing framework for an algorithm can be a very complex task, because it requires studying and applying the existing frameworks. While searching for a solution to this problem, it was decided to create a Dynamic Algorithms Modelling Application (DAMA), which is able to simulate the implementation of the algorithm in different distributed computing frameworks. DAMA helps to estimate which distributed framework is the most appropriate for a given algorithm, without actually implementing it in any of the available frameworks. This main contribution of this study is simplifying the adoption of distributed computing frameworks for researchers who are not yet familiar with using them. It should save significant time and resources as it is not necessary to study each of the available distributed computing frameworks in detail

Tõhus peit- ja aktiivse ründaja vastu kaitstud turvaline ühisarvutus

Turvaline ühisarvutus on tänapäevase krüptograafia üks tähtsamaid kasutusviise, mis koondab elegantsed matemaatilised lahendused praktiliste rakenduste ehitamiseks, võimaldades mitmel erineval andmeomanikul sooritada oma andmetega suvalisi ühiseid arvutusi, ilma neid andmeid üksteisele avaldamata. Passiivse ründaja vastu turvalised protokollid eeldavad, et kõik osapooled käituvad ausalt. Aktiivse ründaja vastu turvalised protokollid ei lekita privaatseid andmeid sõltumata ründaja käitumisest. Käesolevas töös esitatakse üldine meetod, mis teisendab passiivse ründaja vastu turvalised ühisarvutusprotokollid turvaliseks aktiivse ründaja vastu. Meetod on optimeeritud kolme osapoolega arvutusteks üle algebraliste ringide; praktikas on see väga efektiivne mudel, mis teeb reaalse maailma rakendused teostatavateks. Meetod lisab esialgsele arvutusprotokollile täitmisjärgse verifitseerimisfaasi, mis muudab valesti käitunud osapooltel vahelejäämise vältimise tõenäosuse kaduvväikseks, säilitades esialgse protokolli turvagarantiid. Lisaks uurib käesolev töö rünnete uut eesmärki, mis seisneb mingi ausa osapoole vaate manipuleerimises sellisel viisil, et ta saaks midagi teada teise ausa osapoole privaatsete andmete kohta. Ründaja ise ei tarvitse seda infot üldse teada saada. Sellised ründed on olulised, sest need kohustavad ausat osapoolt tühjendama oma süsteemi teiste osapoolte andmetest, kuid see ülesanne võib olla päris mittetriviaalne. Eelnevalt pakutud verifitseerimismehhanisme täiendatakse nii, et privaatsed andmed oleksid kaitstud ka ausate osapoolte eest. Paljud ühisarvutusplatvormid on varustatud programmeerimiskeelega, mis võimaldab kirjutada privaatsust säilitavaid rakendusi ilma allolevale krüptograafiale mõtlemata. Juhul, kui programm sisaldab tingimuslauseid, kus arvutusharu valik sõltub privaatsetest andmetest, ei tohi ükski osapool haru valikust midagi teada, nii et üldjuhul peavad osapooled täitma kõik harud. Harude suure arvu kor-ral võib arvutuslik lisakulu olla ülisuur, sest enamik vahetulemustest visatakse ära. Käesolevas töös pakutakse selliseid lisakulusid vähendavat optimeerimist.Secure multiparty computation is one of the most important employments of modern cryptography, bringing together elegant mathematical solutions to build up useful practical applications. It allows several distinct data owners to perform arbitrary collaborative computation on their private data without leaking any information to each other. Passively secure protocols assume that all parties follow the protocol rules. Actively secure protocols do not leak private data regardless of the attacker’s behaviour. This thesis presents a generic method for turning passively secure multiparty protocols to actively secure ones. The method is optimized for three party computation over algebraic rings, which has proven to be quite an efficient model, making large real-world applications feasible. Our method adds to the protocol a post-execution verification phase that allows a misbehaving party to escape detection only with negligible probability. It preserves the privacy guarantees of the original protocol. In this thesis, we also study a new adversarial goal in multiparty protocols. The goal is to manipulate the view of some honest party in such a way, that this honest party learns the private data of some other honest party. The adversary itself might not learn this data at all. Such attacks are significant because they create a liability to the first honest party to clean its systems from the second honest party’s data, which may be a highly non-trivial task in practice. We check the security of our verification mechanism in this new model, and we propose some minor modifications that ensure data protection also from the honest parties. Many secure multiparty computation platforms come with a programming language that allows the developer to write privacy-preserving applications without thinking of the underlying cryptography. If a program contains conditional statements where the choice of the computational branch depends on private data, then no party should know which branch has been executed, so in general the parties need to execute all of them. If the number of branches is large, the computational overhead may be enormous, as most of the intermediate results are just discarded. In this thesis, we propose an automatic optimization that reduces this overhead

Critical Thinking Skills Profile of High School Students In Learning Science-Physics

This study aims to describe Critical Thinking Skills high school students in the city of Makassar. To achieve this goal, the researchers conducted an analysis of student test results of 200 people scattered in six schools in the city of Makassar. The results of the quantitative descriptive analysis of the data found that the average value of students doing the interpretation, analysis, and inference in a row by 1.53, 1.15, and 1.52. This value is still very low when compared with the maximum value that may be obtained by students, that is equal to 10.00. This shows that the critical thinking skills of high school students are still very low. One fact Competency Standards science subjects-Physics is demonstrating the ability to think logically, critically, and creatively with the guidance of teachers and demonstrate the ability to solve simple problems in daily life. In fact, according to Michael Scriven stated that the main task of education is to train students and or students to think critically because of the demands of work in the global economy, the survival of a democratic and personal decisions and decisions in an increasingly complex society needs people who can think well and make judgments good. Therefore, the need for teachers in the learning device scenario such as: driving question or problem, authentic Investigation: Science Processes

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement