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Geometric GPS

  1. Feb 14, 2016 #1
    Hi, I have an interesting problem.

    I have three GPS coordinates, creating two lines across the surface of a sphere (assuming the earth is spherical). I want to be able to create a new line (across the surface of a sphere) with a gradient that is in between the gradient of the two existing lines, and intersects with one of the coordinates.

    On this new line, I want to find a new coordinate, which I can use to represent the new curve. The result should be the new coordinate, not the equation of the new curve.

    I've created a simple diagram, not representing the curved nature of the sphere. All lines are to be crossing the surface of the globe, and maintaining the GPS structure.

    Thanks in advance for any help! :)
  2. jcsd
  3. Feb 15, 2016 #2


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    I am curious: three GPS coodinates will create three lines, not two - one for each pair of points.
    Of the three, what makes the upper right point special?

    I'm going to label your points, clockwise from upper right.
    x0y0, x1y1, x2y2.

    To bisect lines x0y0, - x2y2 and x1y1 - x0y0,
    simply create a point x3y3 midway between x1y1 and x2y2.
    Now draw your new line from x0y0 - x3y3
    Last edited: Feb 15, 2016
  4. Feb 15, 2016 #3
    This is exactly what I was looking for, thanks for such a simple but effective answer.
  5. Feb 18, 2016 #4


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    I suggest you to consider the problem of generate appropriate triangulations on the sphere ...
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