Topological Relations using Two Models of Uncertainty for Lines

This paper presents two models for determining the uncertainty in the topological relations between two lines. One model considers the uncertainty associated with the position of the line, while the other model captures the uncertainty associated with the position of the nodes. The first case considers a region of uncertainty surrounding the entire line and is called a broad line, whereas the second case considers two regions of uncertainty at the end points of the line and is called a line with a broad boundary. The 9-intersection as a generic model for binary topological relations identifies 33 different relations for lines without uncertainty. We found that for broad lines the number of distinguishable cases reduces to 5, while for lines with broad boundaries is extends to 77.