Re: finding great circle connecting two points on a line of latitude
- From: Ken Quirici <ken.quirici@xxxxxxxxxx>
- Date: Sat, 22 Dec 2007 18:44:34 -0800 (PST)
On Dec 22, 8:07 pm, Adam <n...@xxxxxxxx> wrote:
On Sat, 22 Dec 2007 14:08:52 -0800 (PST), Ken Quirici wrote:
Given a line of latitude l1 at ld1 degrees from the
origin line of latitude (equator);
given two points on l1, p1 and p2, with point p1
at d1 degrees from the origin line of longitude and
p2 at d2 degrees from the origin line of longitude.
In the following a '-' means negative - that is,
multiply the number to the right by -1.
The great circle thru p1 and p2
The points p1 and p2 are constrained by the first paragraph to lie on
a parallel of latitude: "given two points on l1, p1 and p2 ..."
A circle through them is a great circle only if they are on the
equator.
I didn't notice this my first read, but any two points
regardless of where they lie relative to a circle of
latitude are connected by a great circle - the great
circles define a hyperbolic geometry on the
sphere don't they? I'm probably missing something.
intersects
a line of latitude l2 at -ld1 degrees.
The points at which it intersects l2
are points p3 at -d1 degrees longitude and
p4 at -d2 degrees longitude.
Why are p3 and p4 important if the procedure above could produce them?
For what purpose are you trying to find a great circle through two
points?
Adam
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