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Let's say I know two persons are standing at GPS location A and B. A is looking at B.

I would like to know B's (x, y, z) coordinates based on A, where the +y axis is the direction to B (since A is looking at B), +z is the vertically to the sky. (therefore +x is right-hand side of A)

I know how to convert a GPS coordinate to UTM, but in this case, a coordinate system rotation and translation seem needed. I am going to come up with a calculation, but before that, will there be some codes to look at?

I think this must be handled by many applications, but I could not find so far.

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YW P Kwon
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1 Answers1

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  1. Convert booth points to 3D Cartesian

    GPS suggest WGS84 so see How to convert a spherical velocity coordinates into cartesian

  2. Construct transform matrix with your desired axises

    see Understanding 4x4 homogenous transform matrices. So you need 3 perpendicular unit vectors. The Y is view direction so

    Y = normalize(B-A);

    one of the axises will be most likely up vector so you can use approximation

    Z = normalize(A);

    and as origin you can use point A directly. Now just exploit cross product to create X perpendicular to both and make also Y perpendicular to X and Z (so up stays up). For more info see Representing Points on a Circular Radar Math approach

  3. Transfrom B to B' by that matrix

    Again in the QA linked in #1 is how to do it. It is simple matrix/vector multiplication.

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