Re: Spherical density visualization

*To*: mathgroup at smc.vnet.net*Subject*: [mg53312] Re: [mg53292] Spherical density visualization*From*: "David Park" <djmp at earthlink.net>*Date*: Wed, 5 Jan 2005 01:21:42 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

kj, Continuing on from my previous reply... One method for making side by side static comparisons of two functions on the sphere is to put together two one-sided sinusoidal map projections. I did this using the DrawGraphics package from my web site. Needs["DrawGraphics`DrawingMaster`"] f1[\[Theta]_, \[Phi]_] := (Sin[\[Theta]]*Sin[\[Phi]])^2 f2[\[Theta]_, \[Phi]_] := (Sin[2*\[Theta]]*Sin[\[Phi]/2])^2 Module[{func1, func2}, func1 = ContourDraw[ f1[\[Theta], \[Phi]], {\[Theta], -\[Pi]/2, \[Pi]/2}, {\[Phi], 0, 2\[Pi]}, ColorFunction -> Hue] // FineGrainPolygons[0.2, 3] // FineGrainLines[0.2, 3]; func2 = ContourDraw[ f2[\[Theta], \[Phi]], {\[Theta], -\[Pi]/2, \[Pi]/2}, {\[Phi], 0, 2\[Pi]}, ColorFunction -> Hue] // FineGrainPolygons[0.2, 3] // FineGrainLines[0.2, 3]; Draw2D[ {func1 /. DrawingTransform[-#2Cos[#1] &, #1 &], func2 /. DrawingTransform[#2Cos[#1] &, #1 &], Gray, Line[{{0, -\[Pi]/2}, {0, \[Pi]/2}}], Black, Text[f1[\[Theta], \[Phi]], {-5, 1.8}, {-1, 1}], Text[f2[\[Theta], \[Phi]], {1.5, 1.8}, {-1, 1}], Text["Comparison of Two Density Functions", {0, 2.2}]}, PlotRange -> {{-6.5, 6.5}, {-1.6, 2.5}}, Background -> Linen, ImageSize -> 550]]; David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: kj [mailto:socyl at 987jk.com.invalid] To: mathgroup at smc.vnet.net I have a family of probability density functions (actually they are empirically measured frequencies) over S^2 (the surface of a sphere). I am searching for visually effective ways to display and compare these functions. One possibility would be to use color (or grayscale density) over the surface of a sphere, and rely on software that allows simulating the rotation of the sphere in 3-D (I believe there's a Mathematica package to do this). This would work OK for single function, but for comparing more than one it is not great, unless it were possible to simultaneously control the rotation of several spheres around their respective centers through the same motion of the mouse. Even with this capability, a visualization scheme that requires the use of a computer is less than ideal, since ultimately I'll have to publish some of these distributions on a printed page. Therefore, I'm most interested in static representation schemes. Everything that I've found so far is geared towards the problem of representing distributions over the surface of the Earth, and relies on specific properties of this problem (e.g. the location of continents) that are inapplicable to my problem. Anyway, any pointers would be most welcome! kj -- NOTE: In my address everything before the first period is backwards; and the last period, and everything after it, should be discarded.