Video – vid2

1. First place the camera at origin, and rotates it so that the direction vector coincides with the negative z axis, and the up vector coincides with the y axis. This bit of the transformation is done via the Camera matrix
2. Convert things in the viewing volume of the camera (which is a Truncated pyramid) to Image space (which is a Cube) in homogeneous coordinates. This is the Viewing transformation
3. Divide by the fourth component in homogeneous coordinates to get back to Cartesian coordinates in Image space

The camera transform corresponds to these steps (vid)

See Vertex shader, for more, about how it fits into the graphics pipeline

Viewing transformation

After the camera is in the origin is rightly oriented (pointed along the negative z direction, and up direction along y direction), we then vonvert things in the viewing volume of the camera (which is a Truncated pyramid) to Image space (which is a Cube).

This can be done with a 4x4 matrix – this is the beginning of the matrix – this is the rest of the matrix

After the camera transform, one projects points in image space perpendicularly to the $x-y$ plane, called the Screen space