3D representation of spherical coordinates

[Christophe Jorssen-2]

Hello all,

For my machanics lecture, I'd like to be able to draw some 3D figures
and particularly something that looks like the figure shown here

http://mathworld.wolfram.com/SphericalCoordinates.html

In addition, I'd like to have arcs with arrows that show clearly the
angles: those portions of circle must look like a portion of ellipse in
3D, I think.

Of course, I can use some tricks to achieve this goal (by tricks, I mean
trying some values, see the result, correct the values, etc), but I'd
like to know if a cleaner way already exists in tikz (like the
undocumented 3D library and/or with coordinate transformations?). In
particular, I like to specify the points in a figure not by their
coordinates: I most likely define them by their "nature", ie middle of
AB, projection of M on AB, etc.

And a final question: extending the partway modifiers to 3D, is it a
huge task? I'd like to be able to
- project a point on a plane,
- draw a parallel line to an other,
- rotate in 3D
- etc.
Did anybody already think about that? Since this part of the tikz code
isn't much documented, extending it sounds a bit hard for me.

Thanks in advance

PS: I'm aware of the wonderful work done by Tomasz M. Trzeciak
(http://www.texample.net/tikz/examples/map-projections/). In his code, I
don't understand the syntax of the coordinate matrix (line 118)

\tikzset{xyplane/.estyle={cm={cos(\angAz),sin(\angAz)*sin(\angEl),-sin(\angAz),

                               cos(\angAz)*sin(\angEl),(0,-\H)}}}

Would it be possible to extend it to a (theta,phi) plane (in spherical
coordinates)?

Thanks again.
--
Christophe

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