Contour Plot on a Hemisphere
This Demonstration illustrates how Mathematica's built-in function ContourPlot can be used to produce a contour plot on the surface of a hemisphere.
To make a spherical contour plot, map each point in the unit disk to a point on the northern hemisphere, and use ContourPlot on the unit disk with Cartesian coordinates. In this mapping, the distance from the origin varies linearly with the latitude . This avoids compression near the edge, which would happen if were used. The resulting 2D contour plot in the unit disk is then transformed into a 3D contour plot on a hemisphere. You can choose four different functions to plot.