Calculating correct line length in perspective drawing?

Question

I have no formal technical drawing background, and I was just wondering if there was a mathematical way of determining the correct length of lines in 3D perspective, e.g., if I want to draw a cube in relation to a vanishing point, how can I get the receding lines to be the correct length? Judging by eye gets me close but I need to learn this precisely. I assume this is fairly straightforward (for architecture, etc) but have been unable to find the answer anywhere.

Answer 1

This is visual scale, as you said you can eyeball it but of course it will never be exact. The best option for getting a closer to scale size for this is that you can use relative size from other objects around it to demonstrate the precise size. If this isn't accurate enough to your liking there is a measuring tool for life drawing called a proportional divider. It is sorta like two sticks fixed together at a certain point. You close one eye and compare the dividers side to say one side of this cube, the opposite side of the proportional divider can translate this to fixed size relations like 1/4th, 1/2, 1:1, 1:1.5, 1:2, ect... This is a much more accurate way of getting the right size to translate to a drawing. A strong tool that will train your brain and help as a cheat for fast mapping proportions for an artwork.