Editing Scale (map) (section)

===Visualisation of point scale: the Tissot indicatrix===
{{main|Tissot indicatrix}}

 [[File:Tissot indicatrix world map Winkel Tripel proj.svg|thumb|right|350px|The Winkel tripel projection with [[Tissot's indicatrix]] of deformation]]

Consider a small circle on the surface of the Earth centred at a point P at latitude <math>\varphi</math> and longitude <math>\lambda</math>. Since the point scale varies with position and direction the projection of the circle on the projection will be distorted. [[Nicolas Auguste Tissot|Tissot]] proved that, as long as the distortion is not too great, the circle will become an ellipse on the projection. In general the dimension, shape and orientation of the ellipse will change over the projection. Superimposing these distortion ellipses on the map projection conveys the way in which the point scale is changing over the map. The distortion ellipse is known as [[Tissot's indicatrix]]. The example shown here is the [[Winkel tripel projection]], the standard projection for world maps made by the [[National Geographic Society]]. The minimum distortion is on the central meridian at latitudes of 30 degrees (North and South). (Other examples<ref>[http://www.progonos.com/furuti/MapProj/Normal/CartProp/Distort/distort.html Examples of Tissot's indicatrix.] Some illustrations of the Tissot Indicatrix applied to a variety of projections other than normal cylindrical.</ref><ref>[http://commons.wikimedia.org/wiki/Category:Map_projections_with_Tissot%27s_indicatrix Further examples of Tissot's indicatrix] at Wikimedia Commons.</ref>).