This animated visualisation gives insight into properties of scales in normal cylindrical map projections.
There are three curves, one for each scale: meridian scale (red curve), parallel scale (dashed black curve) and area scale (green curve). Curves are drawn in its own coordinate system overlapped over map. Latitute of points on curves is equal to latitute on map. Value of scales, as functions of latitude, is indicated on horizontal axis. Vertical black lines indicate the scales value, scale of 1 is at center of map, i.e. central meridian, and value of 0 and 2 are added to the left and right. Scale at some points is larger then 2 and curves extend outside of map.
Visibility of curves is controled by clicking rectangles (green = visible, gray = hidden) in the legend placed to the left (Fig 1).
Fig 1. Changing visibility of scale curves by clicking rectangles in the legend
By draging two sliders on the side of the map user controls the parameters of cylindrical projection.
Left slider changes the type of deformations in projection. Special cases are conformal, equidistant and equiareal projections, and all steps in between are interpolated by linear interpolation (Fig 2).
Fig 2. Changing type of deformations of projection
Right slider is used to change standard parallel. For practical reasons max. and min. values are constrained to 80°. Standard parallel defined by slider is drawn with thicker line, and the parallel with the same properties and negative value is drawn with thicker dashed line (Fig 3).
Fig 3. Changing standard parallel of projection
Meridian scale equals 1 for whole map. Parallel scale is larger then 1 if absolute value of latitude is greated then absolute value of standard parallel, and smaller then 1 if absolute value of latitute is less then absolute value of standard parallel. Area scale is multiplication of meridian and parallel scale, which in this special case equals parallel scale.
Changing standard parallel affects width of map (if map scale is constant), and map height is constant due to constant meridian scale. Map width is equal to the length of standard parallel.
Pole is mapped to a line, which means that parallel scale (and area scale) for poles is infinite.
Meridian scale and parallel scale are equal. Each scale is larger then 1 if absolute value of latitude is greated then absolute value of standard parallel, and smaller then 1 if absolute value of latitute is less then absolute value of standard parallel. Area scale is multiplication of meridian and parallel scale, which in this special case equals square of meridian or parallel scale.
Changing standard parallel affects equaly width and height of map (if map scale is constant) and proportions are kept. There are no angular deformations at points.
Area scale equals 1 for whole map. Parallel scale is larger then 1 if absolute value of latitude is greated then absolute value of standard parallel, and smaller then 1 if absolute value of latitute is less then absolute value of standard parallel. Meridian scale equals 1/parallel scale and equals 0 at the poles.
Changing standard parallel affects equaly width and height of map (if map scale is constant) while multiplication of map width and height is constant.