Size of a Circle (or Planet) From Curvature

Spanky The Dolphin · Post by **Spanky The Dolphin** » 2002-11-19 11:46am

Okay, I've decided to attempt the task of determining how big Lilith is in The End of Evangelion, but I need to know a few things.

How do you determine the size of a circle from it's curve? In most of the shots during Third Impact, Lilith can be seen towering over the surface of the Earth, and is so tall that you can see the world curve.

Any help, you brilliant math-a-magicians out there?

Durandal · Post by **Durandal** » 2002-11-19 12:32pm

Is Lilith some sort of skyscraper?

Utsanomiko · Post by **Utsanomiko** » 2002-11-19 12:51pm

Lilith is in my signature picture. One form of her, though. She gets big, but i don't have a pic of it online.

EDIT: Here's one: http://www.theroseking.net/animehub/eva ... hirdim.jpg

Durandal · Post by **Durandal** » 2002-11-19 02:00pm

I think a safe estimate is somewhere near a few thousand kilomters wingspan.

Zoink · Post by **Zoink** » 2002-11-19 02:03pm

This is what I'd do:

If you "complete the circle" for the earth, the diameter of that circle equals the diameter of the earth. Measure the diameter of the circle with a ruler. Divide the actual diameter of the earth by what you measured, that's the scale. Measure the size of lilith with a ruler and multiply that by the scale, that's the size of lilith.

It would be easy to do in AutoCAD (and most drafting/modeling) software because completing the circle is easy with the 3 point circle command.

Spanky The Dolphin · Post by **Spanky The Dolphin** » 2002-11-19 02:24pm

I see.

I was also refering to (I think) something that uses points on a line and angles, degrees and such, but that might be a little complicated.

Zoink · Post by **Zoink** » 2002-11-19 02:27pm

Spanky The Dolphin wrote:I see.

I was also refering to (I think) something that uses points on a line and angles, degrees and such, but that might be a little complicated.

You can do that too, but you'll have to draw and measure stuff anyway. Might as well take the measurement directly.

Durandal · Post by **Durandal** » 2002-11-19 02:39pm

Indeed. There's no sense in trying to find a purely analytical way to do it when a graphical scaling method will be faster.

Spanky The Dolphin · Post by **Spanky The Dolphin** » 2002-11-19 02:43pm

Yeah, I just sometimes like to do things the hard way fro some reason.

Durandal · Post by **Durandal** » 2002-11-19 02:49pm

Probably because you want to show off all the math on message boards.

Spanky The Dolphin · Post by **Spanky The Dolphin** » 2002-11-19 05:30pm

Know any way to "complete the circle" in Photoshop 6? Such as anything like you suggested?

Durandal · Post by **Durandal** » 2002-11-19 06:16pm

Completing the circle is done geometrically. You can estimate the angle of the visible arc by drawing it on a piece of paper and then completing the circle yourself. Once you've got the full circle drawn out, find the centerpoint, and draw two radius lines going out to either edge of the original arc. Then simply measure the angle between those two lines. Once you have that angle, set up a proportion.

(Circumference_Earth)/(360 degrees) = (Arc Length)/(Arc Angle)

You'll be solving for the Arc Length variable, so simply do a cross product, and you'll be OK.

If you want to do it in Photoshop, basically start making circles of fixed radii and doing a best-fit to the image. Once you find a circle with a radius that fits the curve, just follow the above procedure.