Re: trigonometric calculations

In article <91cyj.7466$v47.4009@trnddc08>,
Patrick White <none@xxxxxxxxx> wrote:
Ron Gibbs wrote:
"David L. Wilson" <dwilson314@xxxxxxxxxxx> wrote in message
news:D6Txj.21271$Hd.6799@xxxxxxxxxxx
"Ron Gibbs" <ron.gibbs@xxxxxxxxxxx> wrote in message
news:47c7d797$0$520$c5fe31e7@xxxxxxxxxxxxxxxxxxxxxxx
Hi everyone:

I'm new to this group, and looking for assistance. I've been struggling
to
get to grips with 3D spherical geometry, and I could use some good
references to useful books and/or online resources.

My problem is to transform astromonical azimuth/elevation coordinates to
the relative azimuth/elevation as measured from a tilted observation
plane. I have been trying to work through the compound angle calculations
from first
principles, but it occurs to me that this must have been done before.
This
is not student homework; I am a professional optical engineer working on
solar collection systems.

Googling has found me many resources for celestial sphere calculations,
and
some stuff on spherical geometry, which is great, but I haven't yet
turned
up anything that seems to directly help with my coordinate transformation
problem.
A similar problem is rouutinely addressed in modeling and simulation of
military and remote sensing so you may want to research such literature.
Often the approach uses quaterions to do these coordinate transmformations
so you may want to research qaternions also.
http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

In any case, you will have to adapt things to your particular problem.
Thanks David, but at first sight quaternions look a bit scary! I now think I
can do what I want with 3D rotation matrices, and transformations between
spherical polar and cartesian coordinates.
3D rotation matrices are the standard way to do these transformations
now-a-days. Especially because they lead to super-easy and efficient
computer code.

The standard text on this is the Explanatory Supplement to the
Astronomical Almanac. It will tell you everything you need to know. In a
good library; hard to find online.

For spherical trig, the standard text there is W.M. Smart, Spherical
Trig, 1960. Also hard to find, but thorough.

Finally, for a recipe-book style approach, Jean Meeus' "Astronomial
Algorithms" gives lots of useful code, with minimal mathematical
derivation. It may have exactly what you're looking for. And it may not!
Check out the page at http://en.wikipedia.org/wiki/Jean_Meeus for links
to libraries that implement his code in various languages.

I thought I recognized W.M. Smart, Spherical Trig, 1960, but when I
went to grab my copy, I found out what I have is W.M. Smart, Spherical
Astronomy, 1956. Its first chapter is "Spherical Trigonometry", but
I imagine the book Spherical Trigonometry is a more complete coverage
of the subject. I have been working on a spherical trig primer, but
it is still under construction. I will put a note on sci.math when
it is finished.

Rob Johnson <rob@xxxxxxxxxxxxxx>
take out the trash before replying
to view any ASCII art, display article in a monospaced font
.