Linearized terrain: Languages for silhouette representations

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 observer's perspective. We develop a terrain language as a formal framework to capture terrain features. The horizon of a terrain silhouette is represented as a string. The alphabet of the terrain language comprises straight-line segments. These line primitives are classified according to three criteria: (1) the alignment of their slope, (2) their relative lengths, characterized by orders of magnitude, and (3) their differences in elevation, described by an order relation. We employ term rewriting rules to identify terrain features at different 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 specify the transition from a finer granularity level to a coarser one. An example shows how the three kinds of rules lead to a terrain description at different granularity levels. © Springer-Verlag Berlin Heidelberg 2003.