22 March 1996 Method for generating fractal mountains with controllable macroscopic shapes by spectral synthesis
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Proceedings Volume 2644, Fourth International Conference on Computer-Aided Design and Computer Graphics; (1996) https://doi.org/10.1117/12.235540
Event: Fourth International Conference on Computer-Aided Design and Computer Graphics, 1995, Wuhan, China
Abstract
Let a 2D random function X(x,y) to denote fBm with exponent 0 < H < 1, then its spectral density Sx(u,v) has relation: Sx(u,v) 1/(u2 + v2)H+1. Such algorithm based on fBm has shown us beautiful pictures of fractal mountains. But the mountains (fractal surfaces) were produced naturally by random process. As a result, the macroscopic shapes and global positions of fractal mounts are not controllable. This paper presents a method that generates fractal mountains with controllable macroscopic shapes and positions using spectral synthesis. First, the discrete data of Y(x,y) on finite grids are inputted, and FFT is employed to produce discrete spectral F(u,v). Second, by InvFFT, low frequency components of F(u,v) together with high frequency components of F(u,v) are transformed to produce Z(x,y)--fractal surface. The macroscopic shapes are controlled by low frequency; meanwhile, the high frequency describes texture of fractal mountains.
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Humin Wang, "Method for generating fractal mountains with controllable macroscopic shapes by spectral synthesis", Proc. SPIE 2644, Fourth International Conference on Computer-Aided Design and Computer Graphics, (22 March 1996); doi: 10.1117/12.235540; https://doi.org/10.1117/12.235540
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