High frequency surface estimation
Abstract
Mountain generation can be considered a part of the general theory of surface estimation; In this thesis, two methods have been presented to generate fractals--fast Fourier method and a new generalized stochastic subdivision method. Also, a new surface estimation method has been introduced that deals with points of unequal powers. The uniqueness of this method is the usage of splines to calculate the arc lengths between the points, as opposed to Euclidean distances used in Kriging. The fast Fourier technique has been used to generate mountains in particular; also, some extensions have been suggested, whereby different sets of mountains can be obtained by modifying some parameters. This method is global and has the advantages of simplicity and efficiency; it also provides exact spectral control. The search for a more localized method resulted in the new generalized stochastic subdivision technique. The choice of an autocorrelation function is pivotal here. The only significant differences between the fractal subdivision method and this new technique are the increased neighborhood size, boundary conditions and the need to solve a system of equations for each subdivision level; The source code for these techniques was implemented on SGI machines, using C with GL as a graphics standard.