How to get camera Right vector when Front vector and WorldUp vector are collinear

Question

Get the title problem when implementing a walkthrough camera.

I use normlize(cross(WorldUp, Front)) to get Right vector. And when they are collinear, I get a zero vector.

Is there any more robust fake version? Or do I need to store the "previous" Right vector as a backup?

Answer 1

You can't have a camera with collinear look/front and up vectors. It doesn't make geometric sense. The whole point of the up vector is to disambiguate roll.

As russ says, for a "first-person" camera it's reasonable to always use world-up for the up vector and simply lock the pitch angle to within (say) 85 degrees of horizontal, to avoid degenerate cases.

For a CAD viewer where the user would expect to pitch the camera arbitrarily, you should rotate both the up and front vectors about the right vector when the user pitches the camera, to ensure they are always perpendicular. Beware that when you do this kind of arbitrary rotation, it's easy for the user to get stuck in unfortunate roll angles. You need to do at least one of the following to let them get themselves out:

1. Have a "reset up" button that applies the pitch angle limits and resets the up vector to world up.
2. Give the user arbitrary control over camera roll. (This can be confusing, so it's best to offer the first option as well if you do this.)
3. Constrain the up vector so that its dot product with the world up is non-negative. That is, if the user pitches so far up or down that they are upside-down, roll the camera 180 degrees.

Answer 2

First of all instead of taking Cross(WorldUp, Front/LookAt) you can use Gram-Schmidt orthogonalization to produce an orthogonal vector that's close to the WorldUp vector. Then you take the cross of this orthogonal vector and the look at to get the side vector. However as you mentioned this'd fail if the vectors are parallel.

Hence the usual solution is to pick another vector that's not parallel to the look at one and again use Gram-Schmidt orthogonalization to produce the orthogonal vector ( camera up) and then take the cross.

The maths is like this.

CameraUp = c
WorldUp = w
LookAt = l

c = w - ( (w.l) / ||l||^2 ) * l 

What it does is this. We know that world up isn't pure orthogonal to the look at vector. So we take the projection of world up onto the direction of the look at vector. Subtract the parallel part of this projection from the world up vector to obtain the remaining i.e. the orthogonal part. This vector is closer to the world up but is purely orthogonal to the look at vector.