The deconstruction of teragons into decogons

This paper focuses on the process of deconstruction, which is different fro m the complementary processes of approximation and generalisation, for deri ving representations of curves at different levels of detail. The aim of de construction 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, are cal led decogons. The decogons abstracted from teragons (generations of fractal curves) are especially useful For studying the geometric properties of spe cific deconstructors. In this paper, two filtering algorithms, commonly use d for approximation and generalisation of curves in cartography, are studie d by scrutinising the decogons they abstract from the triadic and quadric K och curves. The rectangular Koch curve was particularly useful for noting t he types of symmetric elements which are preserved by specific deconstructo rs. It suggests that 2D lines are best represented by Visvalingam's algorit hm used with the area metric. (C) 1999 Published by Elsevier Science Ltd. A ll rights reserved.