Yes / Bezier curves and surfaces are two very useful tools in Geometric Modeling, with many applications. In this paper, we will offer a new method to provide approximations of regular curves and surfaces by Bezier ones, with the corresponding examples.

Determinar curvas a partir de uma série da pontos é uma tarefa importante e muito utilizada em CAD. Este trabalho propõe um algoritmo para determinar uma curva aproximadora representada por diversas curvas de Bézier em sequência a partir de uma sequência de pontos. É utilizada uma abordagem de curvas de Bézier por trechos, onde cada trecho possui continuidade C1-fraca. A otimização é feita pelo recozimento simulado com vizinhança adaptativa que minimiza a soma das distâncias de cada ponto da sequência à curva aproximadora e utiliza o comprimento da curva aproximadora como um fator de regularização. Adicionalmente, é utilizado o recozimento simulado multi-objetivo que avalia a influência da soma das distâncias de cada ponto à curva e do comprimento da curva separadamente. Também é feita uma comparação entre a técnica de ajuste de curvas e a técnica de interpolação de curvas. / The task of determining a curve from a set of points is very important in CAD. This work proposes an algorithm to determine a sequence of Bézier curves that approximate a sequence of points. The piecewise Bézier curve is used, where each curve has C1- weak continuity. The optimization is done using the simulated annealing with adaptive neighborhood aiming at minimizing the sum of the distances from each point of the sequence to the generated curve. The length of this curve is used as a regularization factor. In addition, it is used a multi-objective simulated annealing that evaluates the influence of the sum of the distances from each point to the generated curve, and the curves length. It is also done a comparison between curve fitting and curve interpolation techniques.

Determinar curvas a partir de uma série da pontos é uma tarefa importante e muito utilizada em CAD. Este trabalho propõe um algoritmo para determinar uma curva aproximadora representada por diversas curvas de Bézier em sequência a partir de uma sequência de pontos. É utilizada uma abordagem de curvas de Bézier por trechos, onde cada trecho possui continuidade C1-fraca. A otimização é feita pelo recozimento simulado com vizinhança adaptativa que minimiza a soma das distâncias de cada ponto da sequência à curva aproximadora e utiliza o comprimento da curva aproximadora como um fator de regularização. Adicionalmente, é utilizado o recozimento simulado multi-objetivo que avalia a influência da soma das distâncias de cada ponto à curva e do comprimento da curva separadamente. Também é feita uma comparação entre a técnica de ajuste de curvas e a técnica de interpolação de curvas. / The task of determining a curve from a set of points is very important in CAD. This work proposes an algorithm to determine a sequence of Bézier curves that approximate a sequence of points. The piecewise Bézier curve is used, where each curve has C1- weak continuity. The optimization is done using the simulated annealing with adaptive neighborhood aiming at minimizing the sum of the distances from each point of the sequence to the generated curve. The length of this curve is used as a regularization factor. In addition, it is used a multi-objective simulated annealing that evaluates the influence of the sum of the distances from each point to the generated curve, and the curves length. It is also done a comparison between curve fitting and curve interpolation techniques.

One of the most important design issues for phase change materials is to engineer the phase transition process. The challenge of accurately predicting a phase transition is estimating the true value of transition rate, which is determined by the saddle point with the minimum energy barrier between stable states on the potential energy surface (PES). In this thesis, a new algorithm for searching the minimum energy path (MEP) is presented. The new algorithm is able to locate both the saddle point and local minima simultaneously. Therefore no prior knowledge of the precise positions for the reactant and product on the PES is needed. Unlike existing pathway search methods, the algorithm is able to search multiple transition paths on the PES simultaneously, which gives us a more comprehensive view of the energy landscape than searching individual ones. In this method, a Bézier curve is used to represent each transition path. During the searching process, the reactant and product states are located by minimizing the two end control points of the curve, while the shape of the transition pathway is refined by moving the intermediate control points of the curve in the conjugate directions. A curve subdivision scheme is developed so that multiple transitions paths can be located. The algorithm is demonstrated by examples of LEPS potential, LEPS plus harmonic oscillator potential, and PESs defined by Rastrigin function and Schwefel function.

A nuclear waste stream is the complete flow of waste material from origin to treatment facility to final disposal. The objective of this study was to design and develop a Geographic Information Systems (GIS) module using Google Application Programming Interface (API) for better visualization of nuclear waste streams that will identify and display various nuclear waste stream parameters. A proper display of parameters would enable managers at Department of Energy waste sites to visualize information for proper planning of waste transport. The study also developed an algorithm using quadratic Bézier curve to make the map more understandable and usable. Microsoft Visual Studio 2012 and Microsoft SQL Server 2012 were used for the implementation of the project. The study has shown that the combination of several technologies can successfully provide dynamic mapping functionality. Future work should explore various Google Maps API functionalities to further enhance the visualization of nuclear waste streams.

Diploma thesis deals with calculations of a steam turbine with two uncontrolled extraction points according to the assignment, aerodynamics of the last two stages and operating range with respect to ventilation, range of performance and straining of the last blading under the large condensation pressure deviations. For the first three stages the calculation of prismatic action blades is executed. The fourth and the fifth stages are designed with inconstant reaction over the blades length and their calculation is executed with constant circulation method. For these stages, aerofoil design with respect to their aerodynamic qualities is carried out using Bézier curves. During the whole time verification process of aerofoils qualities, their energy losses and isoentropic Mach number distribution is executed in MISES program in cooperation with Doosan Škoda Power.

This thesis introduces new algorithms for solving curve/curve and ray/surface intersections. These algorithms introduce the concept of a geometric interval to extend the technique of Bézier clipping. A geometric interval is used to tightly bound a curve or surface or to contain a point on a curve or surface. Our algorithms retain the desirable characteristics of the Bézier clipping technique such as ease of implementation and the guarantee that all intersections over a given interval will be found. However, these new algorithms generally exhibit cubic convergence, improving on the observed quadratic convergence rate of Bézier clipping. This is achieved without significantly increasing computational complexity at each iteration. Timing tests show that the geometric interval algorithm is generally about 40-60% faster than Bézier clipping for curve/curve intersections. Ray tracing tests suggest that the geometric interval method is faster than the Bézier clipping technique by at least 25% when finding ray/surface intersections.

I denna uppsats presenteras ett verktyg för att assistera skapandet av spelbanor i dungeon-miljö. Skapandet av sådana banor är ofta resurskrävande under produktionen och har fokus på design. För att behålla designaspekten men underlätta arbetet är verktyget framtaget för att med tillgängliga parametrar producera grottgångar för sådana banor. Vi undersöker med användartester hur verktyget kan användas för att effektivisera en känd metod för att skapa spelbanor, men samtidigt skapa den kvalité som eftertraktas. Med detta avser vi inte bara att ta fram ett effektivt verktyg, utan även att demonstrera en metod för att använda procedurell generering av spelinnehåll för ett nytt ändamål inom speldesign. / In this article a tool for assisting the creation of game levels in a dungeon environment is presented. Creating such game levels often requires a large amount of resources during a game production and has focus on design. To keep the aspect of design but ease work, the tool is created to produce caverns for such game levels with accessible parameters. We examine with user tests how the tool can be used to make an existing method for creation of game levels more effective. But at the same time producing the quality that is coveted. With this we do not only hope to produce an effective tool, but also to demonstrate a method for using procedural generation for a new purpose in game design.

This thesis deals with basic methods of root mean square and peak value measurement of a digital acoustic signal, algotithms to measure audio programme loudness and true-peak audio level according to recommendation ITU-R BS.1770-1 and digital systems for control of signal dynamic range. It shows achieved results of root mean square and peak value measurement and results of implementation of dynamic processor with general piecewise linear non-decreasing static curve and algorithms according to recommendation ITU-R BS.1770-1.

This thesis focuses on the increasingly popular shareware Blender which has growing application possibilities in various branches. The thesis aims at a general description of basic modelling techniques working with mesh objects as well as curves used for creating models and computer graphics. Part of the thesis is dedicated to a description of animation abilities of the programme, an outline of dierent methods and a more detailed description of correspondent modules. The central point of the thesis is to introduce the reader to the basic and advanced modelling techniques and their use in Blender, in the form of a tutorial.