Contour Plot on a Hemisphere

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This Demonstration illustrates how Mathematica's built-in function ContourPlot can be used to produce a contour plot on the surface of a hemisphere.

Contributed by: Tom Verhoeff (August 2016)
(Eindhoven University of Technology, 2016)
Open content licensed under CC BY-NC-SA



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.

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