Representation and Generation of Terrain Using Mathematical Modeling
نویسنده
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1. The Mathematics of Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Modeling Terrain Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Modeling Levee Failure . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Data Manipulation and Exploration . . . . . . . . . . . . . . . . . . . 9 1.4 Contributions and Outline of Thesis . . . . . . . . . . . . . . . . . . . 9 2. Prior Art in Terrain Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 Surface Representations of Terrain . . . . . . . . . . . . . . . . . . . 12 2.1.1 Height Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.2 Triangulated Irregular Networks . . . . . . . . . . . . . . . . . 15 2.1.3 Fourier Series, Splines, and Other Mathematical Models . . . 16 2.2 Volumetric Representations of Terrain . . . . . . . . . . . . . . . . . 18 2.3 Hydrography Network . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Terrain Data Compression . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 Compressing Terrain Features . . . . . . . . . . . . . . . . . . 22 2.4.2 Image Compression . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Summary of Prior Art in Terrain Modeling . . . . . . . . . . . . . . . 25 3. The Drill Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1 Terrain Hydrography . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1.1 Extracting the Channel Network . . . . . . . . . . . . . . . . 27 3.1.2 Choosing a Flow Threshold . . . . . . . . . . . . . . . . . . . 30 3.2 The Drill Representation . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2.1 Representing Terrain as a Series of Drills . . . . . . . . . . . . 33 3.2.2 Terrain Regeneration . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Measuring Terrain Distances . . . . . . . . . . . . . . . . . . . . . . . 38
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