Formula for the location of vanishing points

[smceccarelli]

@dlarmantrout Exactly! The perfect square is the key to correct perspective in line with the chosen field of view and normally I wing it. The key is the position of the diagonal vanishing point (DVP), the vanishing point of the diagonal of the square (or the 45° lines).
Here is a scan from "Vanishing Point" - an excellent book on perspective by Jason Cheeseman-Meyer, that talks about the relation between field-of-view and DVP. It's quite obvious with one-point perspective, but not so trivial with 2-point perspective (I'm not sure I ever learnt how to do it, and if I did I forgot...)

Given that you have a formula for the second vanishing point (i.e. the 90° line to the first), it should be relatively easy to work out a formula for the vanishing point of the 45° line)...

[Eli]

@burvantill I'd be lucky to get C's in math! In my world, that actually qualifies you as a Math Whiz.

[burvantill]

My head just exploded.

Thank you for answering my question. I'm going to have to reread this many times, but I like learning new things so I'm going to try it out. I'll need to get one of those doohickies, a protractor??

[burvantill]

@eli LOL! Thanx! My son would disagree with you. He hates it when I help him with his math homework, because he always seems to know more and ends up teaching me. Lol! If I master this technique it will impress the hell out of him.

[smceccarelli]

@burvantill Don´t worry - this is a disease, not an asset. It´s called “incurable nerdyness”. It keeps your mind from just relaxing and doing great art, is a big enemy of instinct and innate skills (which it fundamentally mistrusts) and I’m pretty sure it´s responsible for the fact that I have such a hard time writing fiction...
Believe me, you don’t need maths to do great perspective drawings! It´s just the peculiar way people who have this disease go about things...

[RobertCrisp]

Thank you

[demotlj]

I'm also one of those "not so great at math but still nerdy enough to want to try this" so my question is: in your formula where w = width of paper, and the v's are the vanishing points, what is your measurement unit (metric?) or can you use any unit as long as you are consistent? Or have I so completely misunderstood the formula that my question doesn't even make sense?

[DLArmantrout]

@smceccarelli Yep, this was all due to my incurable nerdyness making me want to find the exact right answer. If I were teaching a class on drawing in perspective and someone asked how do know where to put the vanishing points, I would probably say... "There is a way to figure out the exact spot, but TRUST ME, you would rather just do it by feel." With that said, I am trying to a work out a formula for the diagonal vanishing point. And then maybe the 3rd vanishing point for 3-point perspective.

[DLArmantrout]

@demotlj You can use any units as long as you are consistent. The w is the width of the paper and v1 and v2 are the distance from the center point of the horizon line to each vanishing point (v1 on the left and v2 on the right)

[ina]

@smceccarelli Apologies for necroing this thread - but this phrasing cracked me up so hard! I'm doing the basic perspective course but my (ex)physicist brain wasn't satisfied until I figured out exactly how to draw a room if I'm standing at a specific point inside it and as a result I've spent (way waaay) too much time drawing triangles. And then this came up as I was googling, as an, ahem, gentle reminder to stop obsessing and start, you know, drawing.

[danielerossi]

Whoa this is brilliant! I was just thinking this the other day. I’ll read shortly (count me in as not so great at math).

[ina]

@danielerossi As much as it pains my nerd heart to admit it, I don't think it's worth going through the maths. Unless you want to do highly technical illustrations.

[danielerossi]

@ina No worries. It was a fun read but in the end, I agree, best to eyeball it

[NessIllustration]

@ina @danielerossi This is hilarious! Reminds me of a beginner animation class I had, first day our teacher (a hippie type) said when animating a bouncing ball (literally first exercise ever) each rebound would be about half the height of the previous rebound. A student raised his hand and started explaining the actual physics behind this and the exact formula to calculate the real height the ball would be after each rebound. You should have seen the teacher's eyes glaze over! Everyone in the class was frowning and giving each other side eye like "this is going to be a long semester". When the student was done, the teacher just said "Huuuhh, yeah.. I guess.." and resumed his lesson

[Pamela Fraley]

@NessIllustration

[Pamela Fraley]

@DLArmantrout I have to read this again when my left brain can turn on. I’m getting ready to start perspective for the second time.