OpenGL LookAt function: is the up vector arbitrary?

Question

I am trying to understand the glLookAt function.

It takes 3 triplets. The first is the eye position, the second is the point at which the eye stares. That point will appear in the center of my viewport, right? The third is the 'up' vector. I understand the meaning of the 'up' vector if it is perpendicular to the vector from eye to starepoint. The question is, is it allowed to specify other vectors for up, and, if yes, what's the meaning then?

A link to a graphical detailed explanation of gluPerstpective, glLookAt and glFrustum would be also much appreciated. The official OpenGL documentation appears not to be intended for newbies.

Please note that I understand the meaning of up vector when it is perpendicular to eye->object vector. The question is what is the meaning (if any), if it is not. I can't figure that out with playing with parameters.

Answer 1

It works as long as it is "sufficiently perpendicular" to the up vector. What matters is the plane between the up-vector and the look-at vector.

If these two become aligned the up-direction will be more or less random (based on the very small bits in your values), as a small adjustment of it will leave it pointing above/left/right of the look-at vector.

If they have a sufficiently large separating angle (in 32-bit floating point math) it will work well. This angle needs usually not be more than a degree or so, so they can be very close. But if the difference is down to a few bits, each changed bit will yield a huge direcitonal change.

It comes down to numerical precision.

(I'm sure there are more mathematical terms & definitions for this, but it's been a few years since college.. :)

final word: If the vectors are parallel, then the up-direction is completely undefined and you'll get a degenerate view matrix.

Answer 2

The up vector lets openGL know what way your have your camera.

Think in the really world, if you have to points in space, you can draw a line from one to the other. You can then align an object, such as a camera so that it points from one to the other. But you have no way of knowing how you object should be rotated around this axis that the line makes. The up vector dictates which direction the camera should be standing.

most of the time, your up vector will be (0,1,0) which means that the camera will be rotated just like you would normally hold a camera, or if you held your head up straight. if you set your up vector (1,0,0) it would be like holding your head on its side, so from the base of your head to the top of your head it pointing to the right. You are still looking from the same point (more or less) to the same point, but your 'up' has changed. A look vector of(0,-1,0) would make the camera be up side down, like if you where doing a hand stand.

One way you could think about this, your arm is a vector from the camera position (your shoulder) to the camera look at point (your index finger) if you stick you thumb out, this is your up vector.

This picture may help you http://images.gamedev.net/features/programming/oglch3excerpt/03fig11.jpg

EIDT

Perpendicular or not.

I see what you are asking now. example, you at (10,10,10) looking at (0,0,0) the resulting vector for your looking direction is (-10,-10,-10) the vector perpendicular to this does not matter for the purpose of you up vector glLookAt, if you wanted the view to orientated so that you are like a normal person just looking down a bit, just set you up vector to (0,1,0) In fact, unless you want to be able to roll the camera, you don't need this to be nay thing else.