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

  1. May 3, 2009 #1
    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?
  2. jcsd
  3. May 3, 2009 #2


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    You say "an arc between points #1 and #2, with a center point #3." What do you mean by "center point" here?
  4. May 4, 2009 #3
    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.
  5. May 4, 2009 #4
    Re: Turning point of aircraft on the left or right of travel direction.

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