Graphics rarely stores every quantity in one coordinate system. Instead, the same point is represented in several coordinate spaces, each chosen for a particular task.

A typical chain is:

• object/model space: coordinates attached to one object;
• world space: objects placed together in a common scene;
• view/camera space: the scene expressed relative to the camera;
• clip/projective space: coordinates prepared for projection and clipping;
• screen space: positions on the output image.

Each step is a change of representation produced by a transformation. If column vectors are used, a model point may reach view space through a product such as

$$\mathbf{x}{view}=V M\mathbf{x}{model}.$$

The multiplication order matters because matrix composition is generally not commutative.

Separating spaces lets an object keep simple local geometry while its placement, the camera and the final projection change independently.