Short note: 2D viewing pipeline

The 2D viewing pipeline is the series of steps that maps a picture from the world coordinate system to the device coordinate system.

World coords -> Viewing coords -> Normalised -> Viewport
 (modelling)   (window rotate     coords      (device
                & translate)    + clipping     coords)

1. Objects are made in modelling coordinates and placed into world coordinates.
2. A window is chosen in the world. It is converted to viewing coordinates (translate to the origin, rotate to align with the axes if the window is tilted).
3. The scene is mapped to normalised coordinates (0 to 1, device independent) and clipped against the window, so that parts outside are discarded.
4. The window is mapped to the viewport on the screen using

xv = xvmin + (xw − xwmin)·sx,   yv = yvmin + (yw − ywmin)·sy
sx = (xvmax − xvmin)/(xwmax − xwmin),  sy = (yvmax − yvmin)/(ywmax − ywmin)

As a matrix: M = T(xvmin, yvmin) · S(sx, sy) · T(−xwmin, −ywmin). The pipeline lets the same scene be shown at different sizes, positions and parts (zoom, pan) on different devices.