# Thread: Is 2 point perspective inherently distorted?

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## Is 2 point perspective inherently distorted?

Recently I've been doing some experimentation, trying to figure out where to put my Vanishing Points(VPs) in order not to make my perspective appear distorted. By distorted I mean a linear perspective with a field of view different than 60* (degrees) , which is considered the natural FoV for the human eyes. I actually did some maths, trying to create some simple formula to solve this problem, or to create a quick rule of thumb (Im kinda like da Vinci, a true renaissance man ).

The formula I arrived at for a two point perspective with horizontal horizon line is as follows (Maths is scary i know, you can skip this bit if you want):
d = |(tg(alpha) + ctg(alpha)) * (a * sqrt(3))/2|
where :
d - distance between the VPs (as measured on the picture plane)
tg/ctg - tangent/cotangent
alpha - the angle between the horizon line and the line between the station point (the place the observer is standing at) and the first VP
a - the width of the picture plane
sqrt - square root

Welp, so what I got is some mathematical nonsense, what does it all mean?
You see, the minimum value of |(tg(alpha) + ctg(alpha))| is 2. This means that the minimum value of this entire expression is about 1.7 * a (so 1.7 times the width of the entire picture). This means that the minimum distance between the VPs is about 1.7 * a. This distance is longer than the width of the entire picture, hence you can NEVER have 2 VPs in the field of view at once. What this seems to suggest is that 2 point perspective is a lie. Having two VPs visible at once inevitably leads to distorting the image, because it requires a FoV greater than 60*, which is not how we see things in reality. You can get away with it most of the time and noone will notice (unless you push your VPs wayyy to close) but I think it is important to know that any perspective higher than 1-point causes some degree of distortion to your image.

What do you think?

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3. Just because one ofyour VPs isnt in the picture doesnt make the picture 1-point. It's about how manympoints you use in construction, not how many are actually located in the picture itself.

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Hmm well I'm sorry then this is how it was explained to me or at least how I understood it. I'm self tought you know. I guess it's good to know. Still, I've seen examples with 2 or more VPs visible and that must cause some degree of distortion

6. Originally Posted by AlanKalane
Hmm well I'm sorry then this is how it was explained to me or at least how I understood it. I'm self tought you know. I guess it's good to know. Still, I've seen examples with 2 or more VPs visible and that must cause some degree of distortion
I suggest you study the meaning of the distance of the stationary point to the horizon, aka the intended viewing distance.

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Originally Posted by eezacque
I suggest you study the meaning of the distance of the stationary point to the horizon, aka the intended viewing distance.
What exactly is wrong with my SP? It's kind of vague.
I understand the intended viewing distance as the distance at which the observer has the intended FoV.

8. Originally Posted by AlanKalane
What exactly is wrong with my SP? It's kind of vague.
Your SP is not wrong, but my suggestion helps you to understand when vanishing points are too close.

9. Does every 2pp image look distorted to you? I seem to have seen 2pp images that didn't look distorted, don't know if I'm the only one.

10. I think technically 2pp is inherently distorted because it's a simplified construction of how we see. True perspective being curvilinear. But the point is really does it look good? is it convincing? Is it characteristic of how we perceive real space?

I would answer yes to all those questions. Art is not an exact science. Speaking of da vinci, in the renaissance they used all sorts of cheats with perspective to make their composition better. Breakin' the rules all over. 2pp is an invention, which you can choose to use.

I think it looks good. Key word is looks because it's already known that it's not 100% true to reality. So the mathematical proof of the distortion doesn't really matter in my opinion. I mean we already know it's a lie.

Sorry I'm not great at math so I can't comment on the formula. But it seems that as long as the vanishing points are far apart there shouldn't be an issue. Usually at least on vanishing point is off the page anyway so you're rarely going to break the perspective.

But by the way if you wanna talk about distortion. 1 point perspective is the worst! The further you go from the vanishing point the more crazy distorted it is.

11. Originally Posted by JoeCowan
I think technically 2pp is inherently distorted because it's a simplified construction of how we see. True perspective being curvilinear.
Wrong.
https://www.handprint.com/HP/WCL/perspect5.html