Fractal-based modeling of 3D terrain surfaces

Fractal-based methods have been developed and implemented for analyzing a 3D mesh of terrain sample points and using then to approximate the terrain surface at points between the known sample points. Fractal features such as fractal dimension and distribution function are extracted from a coarsely sampled 3D surface, and then interpolated in order to estimate the intervening surface. The sample mesh is generated using random midpoint displacement. For comparison, a reference 2 meter mesh is sampled at 4 meters, and the random midpoint displacement method is used to predict 2 meter grid points. The reference mesh and the interpolated mesh are found to give a reasonable match. Software algorithms implement the fractal-based analysis and interpolation techniques. Fractional Brownian functions are used in random displacements.