       Re: discrete points in 3D polar

• To: mathgroup at smc.vnet.net
• Subject: [mg113402] Re: discrete points in 3D polar
• From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
• Date: Wed, 27 Oct 2010 05:16:04 -0400 (EDT)

Hi, Igor,

I am not quite sure that have understood you right. This is the list with your points:

lst = {{0.27, -2.17, 1.89}, {0.24, -0.92, 1.7}, {0.28, -1.61, 1.18}};

It seems that you want to visualize this (or another) list in CARTESIAN space, while the coordinates of the points
are given in spherical coordinates, right? Since if you would want to draw them in spherical axes {R,teta,phi} you
would simply use PlotPointPlot3D[lst], is not it?

If yes, try this::

g[{r_, \[CurlyPhi]_, \[Theta]_}] := {r*Sin[2 \[Pi]*\[Theta]/360]*
Cos[2 \[Pi]*\[CurlyPhi]/360],
r*Sin[2 \[Pi]*\[Theta]/360]*Sin[2 \[Pi]*\[CurlyPhi]/360],
r*Cos[2 \[Pi]*\[Theta]/360]};

ListPointPlot3D[Map[g, lst], PlotStyle ->  PointSize[Large]]

and play a bit with the PlotStyle and other options.

Have fun, Alexei

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

--
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development

IEE S.A.
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