Building perspective from plane projection and height

Hi! This post is less of a technical question, and more of a riddle for people who are interested descriptive geometry. A while ago I made this algorithm, just as a proof of concept, with a lot of hardcoded stuff in it:


detarminant.3dm (62.7 KB)
detarminant.gh (29.6 KB)
Now I am trying to make the approach more parametric, and so it works with many shapes. I am struggling to find a coefficient that would represent lens length for each given point at the same time, without looping based on one determined point.
Basic principal looks like this:

We can represent a line in a 2p perspective view, based on its height and plane view.

Here’s a demonstration for 2 lines.

The problem starts when i try to make more lines, or just points. I need some kind of coefficient value, that i struggle to find.
Here is an example where i use such coefficient, but i violate some of the rules of perspective, and get this strange result:

determinant2.3dm (54.1 KB)
determinant2.gh (42.7 KB)

I do it for fun, but i think it can be useful. Please share your thoughts on the matter.
Imagine using this approach being able to build isometry, 2 or 3 point perspective drawings for complex breps in a matter of milliseconds

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My interpretation.
determinant2 a.gh (18.4 KB)

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Nice attempt! 1Point perspective method. Looks similar to so called “Architects method”

Second track.
Two points.

determinant2 b.gh (18.5 KB)


determinant2 c.gh (17.1 KB)

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Looks great! Thank you for input.
While i was looking for a coefficient for determinant method, I made this Radial method (Durer 1471-1528). I am not sure about 3pt though. Still want to find a solution for a determinant method


durer.gh (23.6 KB)

I don’t quite understand what you mean by determining method.
I’ve tweaked your definition a bit.
The accuracy of my three-point axonometry remains to be verified.
durer a.gh (49.5 KB)

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