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The Dude
07-23-2005, 06:50 AM
Consider the image below. The green screen in the center that the man is watching is a rectangle with an aspect ration of 1:1.73.


We can calculate the coordinates relative to the origin of the entire image (ie, the image's upper left corner = (0,0)) of the three visible coordinates of the green screen: lower-left, upper-left, upper-right. The lower-right is being blocked by the man's head.

The question is: Given ONLY the coordinates of the three visible corners of the green screen, how can we calculate the coordinates of the lower right corner?

EDIT: I realize the coords listed in the picture may not be exactly consistent with the lines they need to fall on, since they were taken from photoshop and I had to eyeball what defined the corner in each particular case. Nevertheless, they should be close enough and I am only interested in the method anyway.
http://www.geocities.com/gaming_mouse/entity.jpg

This is a cross-post from the probability forum from a couple weeks back. Here's the original post by gaming_mouse. (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=2739831 &Forum=f11&Words=&Searchpage=0&Limit=25&Main=27398 31&Search=true&where=bodysub&Name=20330&daterange= 1&newerval=1&newertype=m&olderval=&oldertype=&body prev=#Post2739831) Those suckers were unable to decide if was solvable or not.

Dov
07-23-2005, 04:55 PM
[ QUOTE ]
Those suckers were unable to decide if was solvable or not.

[/ QUOTE ]

Since it does not seem to be readily solvable, maybe you could try to eyeball the last corner in Photoshop as well, and then try to derive a method from all of the data which would work in other cases as well.

pzhon
07-23-2005, 05:55 PM
[ QUOTE ]
Those suckers were unable to decide if was solvable or not.

[/ QUOTE ]
Did you not read the whole thread?

PairTheBoard
07-23-2005, 06:08 PM
"The green screen in the center that the man is watching is a rectangle with an aspect ration of 1:1.73. "

What does the "aspect ratio" mean?

PairTheBoard

jason_t
07-23-2005, 06:51 PM
[ QUOTE ]
"The green screen in the center that the man is watching is a rectangle with an aspect ration of 1:1.73. "

What does the "aspect ratio" mean?

PairTheBoard

[/ QUOTE ]

The ratio of the two sides.

The Dude
07-23-2005, 07:18 PM
[ QUOTE ]
Did you not read the whole thread?

[/ QUOTE ]
Not in careful detail, although not everybody was convinced it was unsolvable. Also, those who were claiming it was unsolvable managed only to convince me that they didn't know how to solve it, not that it was inherently unsolvable.

07-24-2005, 02:00 AM
Without the z coordinate for at least two of those points it's unsolveable. You can narrow it down to a finite number of possibilities (four I think, but only two make sense based on the picture) but you can't solve it.

YourFoxyGrandma
07-24-2005, 03:30 AM
I feel like it's possible as a geometry problem looking at the 3d space as a 2d shape; The left and right sides would be paralell, according to perspective. Given the coordinates, find the angles of the three visible corners and then the angle of the fourth corner, then calculate the side lengths and come up with the coordinates for the fourth point.

I'm not actually sure any of that is possible, nor am I going to try because I'm bad at math, but it seems reasonable.

EDIT: I'm wrong. Can't assume lines paralell. Meh.