Turning point of car on the left or right of travel direction.

Main Question or Discussion Point

I've got an interesting problem that I can solve sometimes, but not always. Say I've got a 3 sets of lat/long positions on the earth, relatively close to each other. The idea is your in a car/airplane driving along and arc between points #1 and #2, with a center point #3. The question to be answered, is is point #3 on my left, or on my right.

My initial solution was to convert from spherical to cartesian, then calculate the vector from #1 to #2 and cross that with the vector from #1 to #3. Then a positive/negative z value would give me left/right.

However this doesn't see to work in the southern hemisphere, nor very well at the poles. Someone thought it would help to dot-product the resulting cross-product with the initial vector to point #1, but that hasn't seemed to produce a consistant result at various problem points on a sphere.

Any ideas, I'm I chasing the wrong concepts, should I be focusing more on a full 3d matrix solution instead of simple vectors?

HallsofIvy
Homework Helper
You say "an arc between points #1 and #2, with a center point #3." What do you mean by "center point" here?

In this particular case, Points #1 and #2 both lay on a circle with center point #3.

I assuming that it really doesn't help in solving the problem though, since my solution should of worked for any point reasonably close (couple miles) to the vector formed between 1 and 2.

Please note, this is a real world problem I'm having translating data between two separate aircraft systems.