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Approximation of Terrain Data Utilizing Splines
 Tomek, Peter ; Kunovský, Jiří (oponent) ; Chudý, Peter (vedoucí práce)
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.
Úplný záznam
Approximation of Terrain Data Utilizing Splines
 Tomek, Peter ; Kunovský, Jiří (oponent) ; Chudý, Peter (vedoucí práce)
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.
Úplný záznam

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