Imagine you can walk on a blue hemisphere line marked with clock hour positions from 9 AM to 3 PM. It should make sense to you that on that hemisphere, the walking distance between any two adjacent hours is the same.
Now imagine that that those points are put on a red line over the hemisphere. For this mapping the “x” position of the blue point becomes the location for the corresponding point on the red line.
For now, it is enough for you to see how the difference between the blue curve and the red line is responsible for the “curvature”, the lack of a linear relation between the two.
Vectoreverything 