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Given the two green lines and the real distance between them (blue lines), is it possible to calculate where in the picture would be placed a point 4.5m away from a certain initial point (red line)?

perspective

I've been reading other posts about this and it is not clear to me if I need more data to compute this, but I think I do.

EDIT

As said in the comments, I know the line equation of the green lines and the angle they form between them. I also know the length of the blue lines (in the picture and the real one) and the distance between them in the picture, but I don't know their distance in real life.

The conclusions I've arrived so far are:

  • Since the four points aren't collinear and I don't have any real distances along lines converging to vanishing point, I can't use the cross ratio.
  • Given that I don't have the real distance between the blue lines I can't scale along green lines.
  • The only thing I've found that might be helpful is projective transformation, but since my lack of knowledge in the subject I don't know how to apply it to my problem.
ltg
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  • You'll need more information, for example, the distance (either actual or based on the drawing) between the two blue lines, or the lengths of the drawings of the two blue lines, or the angle in between the green lines. – JRN Sep 13 '18 at 06:41
  • I can know the distance between the blue lines (based on the drawing), their length and the angle between the green lines since I have all the information of the lines. – ltg Sep 13 '18 at 07:12
  • @JoelReyesNoche: Excuse my ignorance, but I don't see how this question is a duplicate. The question "How to calculate true lengths from perspective projection?" has nothing to do with mine, since I don't have information about distances along the green lines. – ltg Sep 18 '18 at 09:22
  • @JoelReyesNoche: In the other question marked as a duplicate (A formula for Perspective measurement), the only thing I could compute would be the projective transformation but I don't see how it would be useful for my problem (I need the coordinates of the red line in the original image, not in a transformed one). So, I'm really sorry for bothering, but I still haven't found a solution to my problem and I would appreciate any help. – ltg Sep 18 '18 at 09:27
  • You are correct that the questions that were suggested as duplicates are not exact duplicates of your post. I'm voting to reopen your post. – JRN Sep 18 '18 at 09:40
  • Your question is an interesting one, but unfortunately I don't have time right now to answer it. Your recent edit has bumped your post on the main page, so maybe someone else will answer sooner. – JRN Sep 18 '18 at 09:42
  • @JoelReyesNoche: Thank you, I appreciate it. – ltg Sep 18 '18 at 10:25

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