The deconstruction of teragons into decogons

摘要

This paper focuses on the process of deconstruction, which is different from the complementary processes of approximation and generalisation, for deriving representations of curves at different levels of detail. The aim of deconstruction is to discover geometric pattern sequences whose pre-existence cannot easily be predicted to study the invariant properties of different deconstructors. Meaningless patterns, abstracted by deconstruction, a re called decogons. The decogons abstracted from teragons (generations of fractal curves) are especially useful for studying the geometric properties of specific deconstructors. In this paper, two filtering algorithms, commonly used for approximation and generalisation of curves in cartography, are studied by scrutinising the decogons they abstract from the triadic and quadric Koch curves. The rectangular Koch curve was particularly useful for noting the types of symmetric elements which are preserved by specific deconstructors. It suggests that 2D lines are best represented by Visvalingam's algorithm used with the area metric.