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Camera

We will use a very simple camera that only requires three vectors to define: what we are looking at, which way is up, and the camera location. Given these vectors, we can compute the basis of the camera. We will define $\mathbf{g}$ as the look vector, $\mathbf{t}$ as the up vector, and $\mathbf{e}$ as the position vector. The basis vectors will continue to be $\mathbf{u}$ $\mathbf{v}$, $\mathbf{w}$.

If we begin by saying that the camera is oriented so that the positive x-axis goes right and the positive y-axis goes up, then we are looking down the negative z-axis. So, the look vector will point down negative z. From this we can construct the camera basis:

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

If you make sure the look and up vector are normalized before building the basis, then the resulting camera basis is orthonormal.