How to rotate the camera view around a point in OpenGL with gluLookAt

Question

I'm trying to use the gluLookAt function to set up the correct view transformation for the camera's position and orientation. In my program there is a sphere centered in the origin and when the arrows key are pressed the camera moves according (left, right, up and down) around the sphere.

I tried to use this transformation: gluLookAt(xc, yc, zc, 0.0, 0.0, 0.0, 0.0, 1,0, 0,0);

To verify its correctness I printed out the three axes. It doesn't seem to properly work. When I move up and down the y axis doesn't seem to move.

Can you help understand what is wrong with that transformation?

Answer 1

Constant up vector is wrong !

When your xc=0,yc=?,zc=0 (which is when you move up/down in y axis) then your up vector is (anti)parallel to your view direction which means gluLookAt can not create 3 perpendicular basis vectors using cross product which it needs for constructing the transform matrix .

In such case the up vector should be different... I usually use dot product

if (dot(a,b)/(|a|.|b|)>0.9)

to detect near to (anti)parallel vectors and set different one in your case its simplied like this:

if (fabs(yc*yc)/(xc*xc+yc*yc+zc*zc)>(0.9*0.9)) use different up vector

You can use (+/-1,0,0) or (0,0,+/-1) which one and which sign depends on your coordinate system conventions (so your view does not twist/mirror/rotate on going through this singularity).

The 0.9 threshold means:

cos(da) = 0.9
da = acos(0.9)
da = 25.84 deg

which is the max allowed angular difference between the two vectors...