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I have co-ordinates (x,y,z) for three markers placed on the leg, and I need to calculate the position of a 'fourth' marker which appears in the first frame of my recording and then disappears. Together the four markers make up a rectangle shape, and the markers are fixed (one marker is on the inside of the ankle, a second is on the outside of the ankle, the third is on the outside of the knee, and the one I need to find is on the inside of the knee). I wonder if there is a way to calculate the co-ordinates of the 'fourth' point based on the co-ordinates of the others. I think this should be relativley simple but I don't know where to start!


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inside of knee equals inside of ankle plus outside of knee minus outside of ankle.

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+1 what a nice equation! – draks ... Feb 28 '12 at 12:14

Based on Gerry Myerson's answer:

$$x_{ik} = x_{ia} + x_{ok} - x_{oa}$$ $$y_{ik} = y_{ia} + y_{ok} - y_{oa}$$ $$z_{ik} = z_{ia} + z_{ok} - z_{oa}$$

This works even if the rectangle becomes a parallelogram.

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