# Calculate aspect ratio from 2D shape in 3D space

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 Nov 29, 2015 at 18:42
• The table's corners are, yes. Dec 16, 2015 at 11:56

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.