Original title: Approximation of Terrain Data Utilizing Splines
Translated title: Approximation of Terrain Data Utilizing Splines
Authors: Tomek, Peter ; Kunovský, Jiří (referee) ; Chudý, Peter (advisor)
Document type: Master’s theses
Year: 2012
Language: eng
Publisher: Vysoké učení technické v Brně. Fakulta informačních technologií
Abstract: [eng] [cze]
Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané terenní data na určitých bodech spolu s gradientem pomocí vícerozměrných splajnů. Program by měl vyčíslit více bodů najednou a měl by pracovat v $n$-dimensionálním prostoru. For the optimization of near-of-the-earth flight trajectories the terrain data have to be taken into account very precisely. At this, a fast and efficient evaluation of terrain data is very important since within the optimization task the computational effort for one single cost function evaluation has to be as small as possible. Furthermore, the trajectory optimization is done by gradient-based optimization methods. Thus, the approximation of the terrain data has to be continuously differentiable and also the gradients of the terrain data have to be evaluated along with the terrain data itself. A very promising approach for the approximation of the terrain data are multivariate splines based on the triangulations of the approximation domain. The aim of this master thesis was to develop a MATLAB and C{}\texttt{++} function that evaluates given terrain data at certain points along with the gradients of the terrain data at these points based on multivariate splines. The function supports evaluation of multiple points at once and is not limited to the three-dimensional data but should also be capable to approximate the data of any dimension.
Keywords: barycentrické souřadnice; Bernsteinovi polynomi; lineární regrese; modelování terenních dat; podmínky spojitosti; triangulace; vícerozměrný simplex splajn; B-coefficients; B-form; barycentric coordinates; Bernstein basis polynomials; continuity conditions; equality constrained least squares estimator; linear regression; multivariate simplex splines; simplex; smoothness matrix; terrain approximation; triangulation

Institution: Brno University of Technology (web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library.
Original record: http://hdl.handle.net/11012/53631

Permalink: http://www.nusl.cz/ntk/nusl-236488


The record appears in these collections:
Universities and colleges > Public universities > Brno University of Technology
Academic theses (ETDs) > Master’s theses