trigonometric calculations

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 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.

Thanks in advance for any pointers
Ron Gibbs
Gibbs Associates

"Ron Gibbs" wrote in message
. ..
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 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.

Thanks in advance for any pointers
Ron Gibbs
Gibbs Associates

I now think I can do this, using 3D rotation matrices, and transforms
between spherical polar and cartesian coordinates.
Ron

"Ron Gibbs" wrote in message
. ..
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 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.

Thanks in advance for any pointers
Ron Gibbs
Gibbs Associates

I now think I can do this, using 3D rotation matrices, and transforms
between spherical polar and cartesian coordinates.
Ron




Not the sole method, but look to Calculus. Specifically Translation of
Axis, usually calc II level. Not particularly demanding, but can be
tedious.

"Ron Gibbs" wrote in message
. ..

"Ron Gibbs" wrote in message
. ..
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 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.

Thanks in advance for any pointers
Ron Gibbs
Gibbs Associates

I now think I can do this, using 3D rotation matrices, and transforms
between spherical polar and cartesian coordinates.
Ron

You might try posting on one of the maths newsgroups; there are some people
out there who love to show off!

"newshound" wrote in message
...

"Ron Gibbs" wrote in message
. ..

"Ron Gibbs" wrote in message
. ..
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 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.

Thanks in advance for any pointers
Ron Gibbs
Gibbs Associates

I now think I can do this, using 3D rotation matrices, and transforms
between spherical polar and cartesian coordinates.
Ron

You might try posting on one of the maths newsgroups; there are some
people out there who love to show off!

Yes, I did that, and got some very esoteric suggestions! I also posted to
sci.optics, who as always were very helpful, and got confirmation that I was
working on the right lines. I have now completed and tested my model, using
rotation matrices. Thanks, all.

Ron

"Ron Gibbs" wrote in
:

snip

Yes, I did that, and got some very esoteric suggestions! I also posted
to sci.optics, who as always were very helpful, and got confirmation
that I was working on the right lines. I have now completed and tested
my model, using rotation matrices. Thanks, all.
Ron

Peter Duffet-Smith. (1988 3rd ed.) Practical Astronomy with your
Calculator. Cambridge Press.

and, I believe -

Oliver Montenbruck and Thomas Pfleger. (2000 4th ed). Astronomy on the
Personal Computer. Springer.

- both contain examples of using matrices to quickly transform between
the major coordinate systems used in astronomy, e.g. - from the local
horizon (alt,az) to the celestial coordinate system (ra, dec), the
ecliptic (e-lat,e-long) or the galactic coordinate system.

http://www.amazon.com/Practical-Astr...Peter-Duffett-
Smith/dp/0521356997

http://www.amazon.com/Astronomy-Pers...mputer-Oliver-
Montenbruck/dp/3540672214/ref=pd_sim_b_img_2

You might also want to take a look at some of the titles at Willman-
Bell:

http://www.willbell.com/math/index.htm

Duffet-Smith and Montenbruck are usually carried at any nearby
university library. Duffet-Smith is in many community public libraries.

Duffet-Smith should get you close to the final rotation transform matrix
between the local horizon and the plane of the solar collector.

- Canopus56

P.S. - Personally, I use linear equation code and have not implemented
code for the faster and much cooler matrix computation method.


--
Posted via a free Usenet account from http://www.teranews.com

"Ron Gibbs" wrote in
:


"newshound" wrote in message
...
snip

You might try posting on one of the maths newsgroups; there are some
people out there who love to show off!

Yes, I did that, and got some very esoteric suggestions! I also posted
to sci.optics, snip Ron

Also try:

http://tech.groups.yahoo.com/group/alpocs/

The computational section of the Association of Lunar and Planetary
Observers. - Canopus56

--
Posted via a free Usenet account from http://www.teranews.com

In uk.sci.astronomy message
5.47, Fri, 29 Feb 2008 23:10:58, canopus56
posted:

Peter Duffet-Smith. (1988 3rd ed.) Practical Astronomy with your
Calculator. Cambridge Press.

Amazon and CUP do not recognise that name.

Without dissenting from the other suggestions, I'd be tempted to assign
an arbitrary distance, such as 1, to go with the angular co-ordinates
known, convert to Cartesian, and use that to work out the results
needed. At least it would be a check on a result more elegantly
obtained; if both agree, they might well be right.

--
(c) John Stockton, nr London UK.
Web URL:http://www.merlyn.demon.co.uk/ - FAQish topics, acronyms, & links.
Correct = 4-line sig. separator as above, a line precisely "-- " (SoRFC1036)
Do not Mail News to me. Before a reply, quote with "" or " " (SoRFC1036)

Dr J R Stockton wrote:
In uk.sci.astronomy message
5.47, Fri, 29 Feb 2008 23:10:58, canopus56
posted:
Peter Duffet-Smith. (1988 3rd ed.) Practical Astronomy with your
Calculator. Cambridge Press.

Amazon and CUP do not recognise that name.

I do... I read that book 15 years ago to help complete my honours year
computer science project

In message , Calum
writes
Amazon and CUP do not recognise that name.

I do... I read that book 15 years ago to help complete my honours year
computer science project

Slight correction... Peter Duffett-Smith

http://www.mrao.cam.ac.uk/~pjds/ascript/author.html

--
David Entwistle