This thesis describes a novel terrain synthesis method based on distances in a weighted graph. The method begins with a regular lattice with arbitrary edge weights; heights are determined by path cost from a set of generator nodes. The shapes of individual terrain features, such as mountains, hills, and craters, are specified by a monotonically decreasing profile describing the cross-sectional shape of a feature, while the locations of features in the terrain are specified by placing the generators. Pathing places ridges whose initial location have a dendritic shape. The method is robust and easy to control, making it possible to create pareidolia effects. It can produce a wide range of realistic synthetic terrains such as mountain ranges, craters, faults, cinder cones, and hills. The algorithm incorporates random graph edge weights, permits the inclusion of multiple topography profiles, and allows precise control over placement of terrain features and their heights. These properties all allow the artist to create highly heterogeneous terrains that compare quite favorably to existing methods.

This thesis describes a novel terrain synthesis method based on distances in a weighted graph. The method begins with a regular lattice with arbitrary edge weights; heights are determined by path cost from a set of generator nodes. The shapes of individual terrain features, such as mountains, hills, and craters, are specified by a monotonically decreasing profile describing the cross-sectional shape of a feature, while the locations of features in the terrain are specified by placing the generators. Pathing places ridges whose initial location have a dendritic shape. The method is robust and easy to control, making it possible to create pareidolia effects. It can produce a wide range of realistic synthetic terrains such as mountain ranges, craters, faults, cinder cones, and hills. The algorithm incorporates random graph edge weights, permits the inclusion of multiple topography profiles, and allows precise control over placement of terrain features and their heights. These properties all allow the artist to create highly heterogeneous terrains that compare quite favorably to existing methods.

Synthetically generated terrain models are useful across a broad range of applications, including computer generated art & animation, virtual reality and gaming, and architecture. Existing algorithms for terrain generation suffer from a number of problems, especially that of being limited in the types of terrain that they can produce and of being difficult for the user to control. Typical applications of synthetic terrain have several factors in common: first, they require the generation of large regions of believable (though not necessarily physically correct) terrain features; and second, while real-time performance is often needed when visualizing the terrain, this is generally not the case when generating the terrain. In this thesis, I present a new, design-by-example method for synthesizing terrain height fields. In this approach, the user designs the layout of the terrain by sketching out simple regions using a CAD-style interface, and specifies the desired terrain characteristics of each region by providing example height fields displaying these characteristics (these height fields will typically come from real-world GIS data sources). A height field matching the user's design is generated at several levels of detail, using a genetic algorithm to blend together chunks of elevation data from the example height fields in a visually plausible manner. This method has the advantage of producing an unlimited diversity of reasonably realistic results, while requiring relatively little user effort and expertise. The guided randomization inherent in the genetic algorithm allows the algorithm to come up with novel arrangements of features, while still approximating user-specified constraints.