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MathGroup Archive 2010

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discrete points in 3D polar

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113353] discrete points in 3D polar
  • From: Igor Barani <ibarani at gmail.com>
  • Date: Mon, 25 Oct 2010 06:39:35 -0400 (EDT)

Hi,

I am trying to plot a list of discrete points in 3D polar (spherical)
space.  The data is in the format (r, phi, psi) where the r value
represents a normalized radial distance, phi (in degrees) is the
inclination (polar angle), and psi (in degrees) is the azimuth
(azimuthal angle).  For this specific problem, we have a spherical
object that was divided in half by a plane.  From the center of the
sphere (the origin), a line was drawn to the sphere edge on this plane
such that a vector (1,0,0) represents the main axis.  All the
coordinates are reported with respect to this axis and the radial
distance is normalized to this vector.  For example, if I have two
spheres of different size and specify the main axis in the same manner
in both cases, the spherical coordinates for a "relative" location in
one sphere would correspond to the same "relative" location in the
other sphere.  Some sample data is shown below (CSV file is also
attached):

Structure, R, Phi (degrees), Psi (degrees)
Target 1, 0.27, -2.17, 1.89
Target 2, 0.24, -0.92, 1.7
Target 3, 0.28, -1.61, 1.18

I am unfortunately a novice in mathematica (a physician) and despite
spending some time playing with the program, I could not create a nice
3D graph to display this information.  I would very much appreciate
your help and suggestions to solve this display problem.  I believe
that another system has a function called "3D polar plot" (based on my
websearch) but I could not find an equivalent function in Mathematica.
 I don't think that RevolutionPlot3D works here because it only
accepts a function and not discrete points for input.  Please advise.

Thank you in advance for your help and suggestions.

- Igor


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