First, my question is how does the x value get devided by element[1, 1] of the projection matrix. If you can answer that please just write your response now. Otherwise, please read on to figure out what I mean. The projection matrix is set up with a call to gluPerspective(fovy, aspect, zNear, zFar) f = cotangent(fovy/2) f/aspect, 0, 0, 0 0, f, 0, 0 0, 0, (zFar+zNear)/(zNear-zFar), (2*zFar*zNear)/(zNear-zFar) 0, 0, -1, 0 Sorry if I can't write the matrix that clearly but I can't scan in a picture or anything to make it look better. When you multiply this by your coordinates [x, y, z, w] transposed, you get the fallowing: [x*f/aspect, y*f, z*(zFar+zNear)/(zNear-zFar) + w*(2zFar*zNear)/(zNear-zFar), -z] transposed. The z*(zFar+zNear)/(zNear-zFar) + w*(2zFar*zNear)/(zNear-zFar) is used for clipping out objects too far away. The projection matrix is multiplied with this orthagonal matrix: 1, 0, 0, 0 0, 1, 0, 0 0, 0, 0, 0 0, 0, 1, 0 The result looks like this [x*f/aspect, y*f, 0, -z]. Finally, perspective division yields what we're used to seeing [x/z*f/aspect, y/z*f, 0, 1]. Here's what is strange set f equal to cottan(45/2) and the aspect to .75. This means that f/aspect is approximatly .55228 which is what x is multiplied by. If x is equal to 1 and z is equal to -1, our rastorized x coordinate comes out to .55228. If the right side of the screen represents 1 and the left side -1 this puts us at about 3/4 of the way across the screen, but it doesn't. Instead, x = .55228 is the very edge of the screen when z = -1. This means that instead of being multiplied by .55228 it is being devided by it. The y coordinate has a simular thing happening. I cannot figure out why. Anyone know why?

I got the projection matrix information off of a man page in a quick internet search. Here's the site www.hmug.org/man/3/gluPerspective.html. Of course, the page could always be wrong. There's an easy way to find out though. I'm gonna grab the matrix and print each value. Hehe.

Your projection matrix is correct. nts's is just transposed (but if written like that as a C-style array it would be correct due to the memory layout used by OpenGL).

Enigma

Thanks guys. I still haven't figured it out yet and I'm still looking. I made a little mistake though perspective division yields [-x/z*f/aspect, -y/z*f, 0, 1], but that doesn't change anything.

Quote:Original post by binarybob0001
First, my question is how does the x value get devided by element[1, 1] of the projection matrix. If you can answer that please just write your response now. Otherwise, please read on to figure out what I mean.
The projection matrix is set up with a call to gluPerspective(fovy, aspect, zNear, zFar)
f = cotangent(fovy/2)
f/aspect, 0, 0, 0
0, f, 0, 0
0, 0, (zFar+zNear)/(zNear-zFar), (2*zFar*zNear)/(zNear-zFar)
0, 0, -1, 0
Sorry if I can't write the matrix that clearly but I can't scan in a picture or anything to make it look better.
When you multiply this by your coordinates [x, y, z, w] transposed, you get the fallowing: [x*f/aspect, y*f, z*(zFar+zNear)/(zNear-zFar) + w*(2zFar*zNear)/(zNear-zFar), -z] transposed. The z*(zFar+zNear)/(zNear-zFar) + w*(2zFar*zNear)/(zNear-zFar) is used for clipping out objects too far away. The projection matrix is multiplied with this orthagonal matrix:
1, 0, 0, 0
0, 1, 0, 0
0, 0, 0, 0
0, 0, 1, 0
The result looks like this [x*f/aspect, y*f, 0, -z]. Finally, perspective division yields what we're used to seeing [x/z*f/aspect, y/z*f, 0, 1].
Here's what is strange set f equal to cottan(45/2) and the aspect to .75. This means that f/aspect is approximatly .55228 which is what x is multiplied by. If x is equal to 1 and z is equal to -1, our rastorized x coordinate comes out to .55228. If the right side of the screen represents 1 and the left side -1 this puts us at about 3/4 of the way across the screen, but it doesn't. Instead, x = .55228 is the very edge of the screen when z = -1. This means that instead of being multiplied by .55228 it is being devided by it.
The y coordinate has a simular thing happening. I cannot figure out why. Anyone know why?

I do not know much about this stuff - but I do see a few math problems that might be messing you up.

: f = cotangent(fovy/2) ==> f = cotangent(fovy/2.0f)
: f/aspect, 0, 0, 0 ==? (float)f/(float)aspect, 0, 0, 0 // just in case!

I'd just make sure all the operations are using floats, just to be sure.

Yes, when I'm programming I should indicate that I'm dealing with floats. I'm just trying to figure out exactly what happens mathematically, and in math we usually assume an infinite precision real or complex number system. My math is probably wrong, and I really, really want to know why. So if anyone has a book that explains everything or knows the name of a book then please post or cite it here. Thanks.

Surely someone here knows. A book anything please.

I looked at that site, but it didn't explain the numbers. It only explained what happens with the numbers. It's a start though. Any other suggestions?