Perspective Tomfoolery

Hi there, Blogviewers! I thought I would share a few observations I've made about pespective. This post deals specifically with calculating the distance between multiple vanishing points, panned perspective and warped perspective. We start our journey with these photos my brother took with multiple lenses. The first was taken using a 24 mm and shows very little perspective warping. This kind of layout would be easy to replicate using only 1 pt perspective.

 The second is using a 10 mm. This would be a bit more difficult to replicate on paper, since the lines are now obviousley bent. Of course, it could still be fudged and look great in 1 pt perspective.

  As you can see from my third image, the perspective on the two photos are the same, one is just zoomed out more. From these two images, we can start to see a pattern of distortion develop (see the blue line I drew overtop). What would it look like if we zoomed out even more? or even panned the camera?

 This is a panorama that I rendered a long time ago in 3ds Max. This type of warped perspective is used in photography pretty much every time someone wants to do a breathtaking panorama, wether it consists of only two pictures, or you're creating a 360 degree masterpiece, like the photography of Sam Rohn ( http://www.samrohn.com/)  I say 'pretty much' because this abstraction breaks if you tried to keep all three axis ( X Y and Z) reletivley undistorted ( notice that the upper and lower areas are totally unrecognizable). computers use this type of image to create skyboxes for games, creating an undistorted 360 degree image, so long as you're looking througha virtual camera to limit the field of view to something more human. (Again, check out that Sam Rohn guy- his website does what I'm talking about)

 A crop of the above panorama, showing that a smaller field that produces normalized looking results.

 Here, I've superimposed the three images together in as accurate a perspective as I could throw together on Photoshop in 20 minutes. You can see that instead of radiating out from the vanishing points linearley, a la one and two point perspective, we have the two axis, X and Y, curving around the horizon line into their opposite poles. Facinating! This means that we can easily calculate how far apart each vanishing point is ( a 360 deg pan divided by 4 poles- 90 degrees) and also, we have a good way to estimate what FOV we would want in any given scene, as well as how distorted the perspective would have to be in that scenario. 50 degree field of view? great, just crop 50 degrees into this image, like the inset photos, and theres your perspective, wether its one or two points!

"But Chris, what does this have to do with DRAWING perspective?"
I'm glad you asked. Armed with this knowlege, you now know a bunch of new things:
> this is another checkmark to ensure that you're drawing accurate perspective. If you have two vanishing points on a page, make sure you know why you're placing them there; are you absolutley sure your layout wouldnt look more accurate if they were farther apart? 90 degrees apart? 

> This trick works horizontally, or vertically (again with the elevator shaft) no more guessing what warped perspective looks like!
>Impress your friends at parties!
>reverse engeneer photos, and match BG plates easier, if you're into matte painting
>Fool-proof panoramas and wideshots for 2d layout. some fudging required if you have to move horizontally and then vertically in the same camera move.

I hope you all find this as fascinating as I did. I want to talk about rotating objects in perspective as well as 3 pt perspective if I ever do another one of these blog posts.