Figure 3: Solutions to the Poisson equation (4) obtained using a metric-unaware solver with various spherical parameterizations, compared to the expected harmonic solutions (degree 1,2,3) in the top row, and our metric-aware solver in the bottom row. (Functions are visualized by scaling points on the unit sphere in proportion to the absolute function value and coloring the points with positive value in red and negative value in blue.) The table shows the RMS errors for the degree-3 harmonic at solution convergence.
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