<p>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 $\alpha/\beta$ (<em>see picture 1</em>) because we are so close to the center.</p>

<p><a href="https://i.sstatic.net/IeTey.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/IeTey.png" alt="Angles"></a></p>

<p><strong>Image 1</strong>: Ratio of the inbound angles</p>

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

<p><a href="https://i.sstatic.net/9gjvk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/9gjvk.png" alt="Perspective grid"></a></p>

<p><strong>Image 2</strong>: Seems about right.</p>

CC BY-SA 3.0
2015-11-29T21:15:03.770Z
How would one calculate the aspect ratio if we weren't so close to the center?
succcubbus
CC BY-SA 3.0
2015-11-29T22:20:47.103Z
@succubus there is a lengthy explanation [here](http://www.handprint.com/HP/WCL/perspect3.html) but you can do this with matrix calculation. Just didnt have time to outline the math.
joojaa
CC BY-SA 3.0
2015-11-30T10:38:01.683Z
@succcubbus please refer to [official help page](http://computergraphics.stackexchange.com/help/merging-accounts) about merging your account to regain the ownership of the question.
Andrew T.
CC BY-SA 3.0
2015-11-29T20:19:22.653Z
2015-11-29T20:30:21.200Z
2015-11-29T20:30:21.200Z
joojaa
<p>Given the 4 coordinates of a 2D shape in a 3D space I want to calculate its aspect ratio.</p>

<p>The 3D space is created with 2 vanishing points.</p>

<p>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).</p>

<p>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.</p>

<p>My exapmle:</p>

<p><a href="https://i.sstatic.net/omyRz.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/omyRz.jpg" alt="enter image description here"></a></p>

CC BY-SA 3.0
2015-11-29T18:42:42.237Z
Can we assume that the corners are 90 degree angles
joojaa
CC BY-SA 3.0
2015-12-16T11:56:41.987Z
The table's corners are, yes.
succcubbus
<transformations><geometry><projections><perspective><space>
Calculate aspect ratio from 2D shape in 3D space
succcubbus
# Calculate aspect ratio from 2D shape in 3D space

(Asked by: username_0 on 2015-11-29)

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:

[![enter image description here](https://i.sstatic.net/omyRz.jpg)](https://i.sstatic.net/omyRz.jpg)

**Tags:** transformations, geometry, projections, perspective, space

> **Comments:**
> **username_1**: Can we assume that the corners are 90 degree angles  
> **username_0**: The table's corners are, yes.  

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## 1 answers

### Answer by username_1 on 2015-11-29. Score: 5 | Accepted answer

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.

[![Angles](https://i.sstatic.net/IeTey.png)](https://i.sstatic.net/IeTey.png)

**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.

[![Perspective grid](https://i.sstatic.net/9gjvk.png)](https://i.sstatic.net/9gjvk.png)

**Image 2**: Seems about right.

> **Comments:**
> **username_0**: How would one calculate the aspect ratio if we weren't so close to the center?  
> **username_1**: @succubus there is a lengthy explanation [here](http://www.handprint.com/HP/WCL/perspect3.html) but you can do this with matrix calculation. Just didnt have time to outline the math.  
> **username_2**: @username_0 please refer to [official help page](http://computergraphics.stackexchange.com/help/merging-accounts) about merging your account to regain the ownership of the question.  

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