View Frustum

Definition

The view frustum is the region of space visible through the camera:

• A truncated pyramid (for perspective) or box (for orthographic)
• Contains everything that will be rendered

Six Clipping Planes

Plane	Purpose
Near	Objects closer than this are clipped
Far	Objects beyond this are clipped
Left, Right	Horizontal bounds
Top, Bottom	Vertical bounds

Frustum Culling

Objects entirely outside the frustum are not rendered:

• Test each object’s bounding volume against frustum planes
• If completely outside, skip rendering
• Important optimisation for large scenes

Field of View

The field of view (FOV) determines how much of the scene is visible:

• Vertical FOV: Angle from top to bottom of frustum
• Horizontal FOV: Derived from aspect ratio

Higher FOV: More visible (wide-angle). Lower FOV: Zoomed in (telephoto).

Aspect Ratio

The ratio of viewport width to height: $\text{aspect} = \frac{\text{width}}{\text{height}}$

Determines horizontal FOV from vertical FOV.

Summary

• The frustum defines the visible region of 3D space
• Bounded by six clipping planes
• Frustum culling removes non-visible objects
• FOV and aspect ratio define the frustum shape