Introduction of loose ribbons in geographic information system

Abstract

In a geographic information system, we use principally many models, such as points, polylines and regions to represent spatial objects. But, usually, lines represent linear objects that have a width, whereas from a mathematical point of view, lines have no width. To solve this paradox, in previous papers, the notion of rectilinear lines was replaced by rectangular ribbons. The rectangular ribbon was used to represent longish objects such as streets, roads and rivers. However, the problems come from their mathematical modeling because in reality, rivers and roads can have irregular widths and measurement errors must be taken into account. So, not all longish objects have rectangular shapes, but they can have loose ones. To solve this problem, the concept of a loose ribbon need be developed. In this paper, we address the eventual mutation of the topological relations between loose ribbons into other topological relations, according to certain criteria, when downscaling.