Contour line positioned at a contour line (when they are, this indicates a measurement precisely equal to the value of the contour). Instead, lines are drawn to best approximate the locations of exact values, based on the scattered information points available. Meteorological contour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure over a period of time, or forecast data such as predicted air pressure at some point in the future Thermodynamic diagrams use multiple overlapping contour sets (including isobars and isotherms) to present a picture of the major thermodynamic
Alignments of random points examined the mathematics of alignment of random points on the plane. In all of these, the width of the line - the allowed displacement of the positions of the points from a perfect straight line - is important. It allows the fact that real-world features are not mathematical points, and that their positions need not line up exactly for them to be considered in alignment. Alfred Watkins, in his classic work on ley lines "The Old Straight Track", used the width of a pencil line on a map as the threshold for the tolerance of what might be regarded as