Linearlized Terrain: Languages for Silhouette Representation

Lars Kulik and Max Egenhofer
Conference on Spatial Information Theory (COSIT '03), Kartause Ittingen, Switzerland, Lecture Notes in Computer Science, Vol. 2825, Springer, pp. 118-135, September 2003.

Abstract

The scope of this paper is a qualitative description of terrain features that can be characterized using the silhouette of a terrain. The silhouette is a profile of a landform seen from a particular observerŐs perspective. We develop a terrain lan-guage as a formal framework to capture terrain features. The terrain silhouette is represented as a string. The alphabet of the terrain language comprises straight-line segments. These line primitives are classified by three criteria: (1) the alignment of their slope, (2) their relative lengths, character-ized by orders of magnitude, and (3) their differ-ences in elevation, described by an order relation. We employ term rewriting rules to identify terrain features at differ-ent granularity levels. There are three kinds of rules: aggregation, generalization, and simplification rules. The aggregation rules generate a description of the terrain features at a given granularity level. For a terrain description the generalization and simplification rules define the transition from a finer granularity level to a coarser one. Finally, we provide a grammar for the terrain language that allows us to decide, whether or not a string of line segments belongs to the language and describes a terrain.

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