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I have the following problem:

I have several (23) 3D coordinates of points (points on a human head) and need to know the corresponding coordinates of three points lying on x-, +y-, and -y-axes, i.e., (x, 0, 0), (0, -y, 0) and (0, +y, 0). Those points are necessary because they are needed as reference points in a coregistration problem (brain research).

In the coordinate system the origin is defined as the midpoint between -y and y, and of course x- and z-axes are perpendicular to the y-axis.

(1) Is there any way to calculate these points based on the 23 3D coordinates I have?

Furthermore, for that same person I have another set of the same head locations plus the x, -y and +y coordinates I am looking for. However, the coordinates of the positions slightly differ (collected on different days by different persons...) and I am sure that also the x, -y, and +y differ so that I can not simply take the second version of these coordinates.

If the first question is answered with 'no', is there a way to use a combination of the first and the second measurement to calculate those positions (x, -y, +y) for the first measurement where they are missing?

Thanks!

PeterPetersilie
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    "I have", how? Text input? Content of variables? What type? What structure? Please show. Also please give examples of input and desired output. Remember that this a community for programming questions. How this is programming realted is currently unclear. Tagging your programming language might help. – Yunnosch May 29 '20 at 10:31
  • Please clarfiy what kind of calculcation you are thinking of. What confuses me is that you seem to have the basics (just zero approriate parts of the coordinates) clear already. So what got you stuck? – Yunnosch May 29 '20 at 10:33
  • What do you mean by: `need to know the corresponding coordinates of three points lying on x-, +y-, and -y-axes` You got 23 points and want just one as a result but which one? center of AABB ?, avg point ? , or what ... Your axises are axis aligned or not? if not you need to know how to describe them the usual is `Origin position + 3*Basis vector ` or `4x4 transform matrix` ... Your next part of question is more about aligning 2 pointclouds together ... for that you need to lock onto features. Without sample input we can only guess... see https://stackoverflow.com/a/52163563/2521214 – Spektre May 29 '20 at 15:08

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