Calculate aspect ratio from 2D shape in 3D space

Question

Given the 4 coordinates of a 2D shape in a 3D space I want to calculate its aspect ratio.

The 3D space is created with 2 vanishing points.

The 4 coordinates - marked blue - are the 2D coordinates on the display. in the example they should be roughly (14, 5.5), (19, 5), (20.3, 7.3), (25.3, 6).

I'm not sure if this is possible at all, if someone could find proof that for 2 different aspect ratios the 2D coordinates are the same this problem would be unsolvable.

My exapmle:

Can we assume that the corners are 90 degree angles – joojaa Nov 29 '15 at 18:42 — joojaa, Nov 29 '15 at 18:42
The table's corners are, yes. – succcubbus Dec 16 '15 at 11:56 — succcubbus, Dec 16 '15 at 11:56

joojaa · Accepted Answer · 2015-11-29T20:30:21.200

5

The ratio is with a quick and dirty visual measurement $665:501$ which is approximately $5:4$. You can measure it by taking the ratio of the vanishing angles $\alpha/\beta$ (see picture 1) because we are so close to the center.

Image 1: Ratio of the inbound angles

We can check the situation visually by drawing a 2 point perspective grid. For this we need the center line between the vanishing points.

Image 2: Seems about right.

edited Nov 29 '15 at 20:30

answered Nov 29 '15 at 20:19

joojaa

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How would one calculate the aspect ratio if we weren't so close to the center? – succcubbus Nov 29 '15 at 21:15
@succubus there is a lengthy explanation here but you can do this with matrix calculation. Just didnt have time to outline the math. – joojaa Nov 29 '15 at 22:20
@succcubbus please refer to official help page about merging your account to regain the ownership of the question. – Andrew T. Nov 30 '15 at 10:38

Calculate aspect ratio from 2D shape in 3D space

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