# Understanding of Camera Up Vector

Assume eye position e, gaze direction g, view-up vector t, right-handed base. As the graphs shows:

$$w=-\frac{g}{||g||}$$
$$u=\frac{t\times w}{||t\times w||}$$
$$v=w\times u$$

I am really confused about the 2nd equation $$u=\frac{t\times w}{||t\times w||}$$.
What if the camera rotate around its gaze direction? The v rotates while the t stays the same.
Then the vector t will not in the plane that w and v lies in which means the second equation is wrong.

I know I have something misunderstood.
Could someone please give me some clues?

• @NicolBolas Sorry. I have made a mistake. I have edited my question. "Then the vector t will not in the plane that w and u" should be "Then the vector t will not in the plane that w and v" Commented Oct 5, 2018 at 2:01
• It isn't supposed to be in that plane. W is the direction of the view. V is supposed to be to the right of the view. If T is up, you can't have the right of the view in the same plane as up. Commented Oct 5, 2018 at 2:04
• @NicolBolas I have added two pictures. The v here is top of the view. Commented Oct 5, 2018 at 2:16