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I am currently trying to export out a series of points (x,y,z) that my software has identified on a 3D model into a report. The thing is, I would also like to impose these 3-dimensional points onto a 2D image of the 3D model on the report.

Is there any mathematical solution to convert 3D coordinate points into 2D coordinate points without any loss of information?

Kelvin Lim
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  • The short answer is no. You lose one dimension (not necessarily x or y or z) – Andrei Mar 03 '21 at 02:49
  • See https://en.wikipedia.org/wiki/Camera_matrix. You could project your 3D model onto a 2D plane. In spite of that, some information will be lost, i.e., the transformation is not invertible. – 1__ Mar 03 '21 at 02:54
  • Well, there is a bijection from $\mathbb{R}^{2}$ to $\mathbb{R}$ (so there would naturally be one from $\mathbb{R}^{3}$ to $\mathbb{R}^{2}$), but I doubt it would help you much. https://mathoverflow.net/questions/126069/bijection-from-mathbbr-to-mathbbr2 – Joshua Wang Mar 03 '21 at 02:59
  • A reasonably good solution is to show not one but three projections to three convenient orthogonal coordinate planes like on old technical blueprints from the era when you could not rotate the images on the computer screen by moving your mouse but had to depict a 3D object in a non-ambiguous way on a sheet of ordinary paper. As long as your model is not too complicated, it should work just fine and all necessary measurements could be made straight from your 2D pictures. – fedja Mar 03 '21 at 04:38
  • What you mean by loss of information? You are losing the depth information. – Moti Mar 03 '21 at 07:08

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