A frustum is the part of a solid that remains after the top has been cut off by a plane parallel to the base.
For example:
- a cone with its tip cut off gives a conical frustum
- a pyramid with its top cut off gives a pyramidal frustum
So a frustum is basically a “truncated” cone or pyramid.
Main idea
The word frustum is used in geometry, but in computer graphics and vision it usually refers to a view frustum.
A view frustum is the region of 3D space that a camera can see.
It looks like a pyramid with the tip cut off.
That cutoff happens because we usually do not render:
- objects that are too close to the camera
- objects that are too far from the camera
So instead of an infinite viewing pyramid, we keep only the portion between two planes.
View frustum in graphics
A camera frustum is bounded by 6 planes:
- left
- right
- top
- bottom
- near
- far
Together, these planes form the visible 3D volume.
If an object lies outside this volume, it is not visible in the final image.
Why the near and far planes matter
The near plane is the closest distance from the camera that will be rendered.
The far plane is the furthest distance that will be rendered.
So the view frustum is the set of points that are:
- inside the camera’s field of view
- farther than the near plane
- closer than the far plane
This is one of the most important ideas in rendering pipelines.
Why it has this shape
In perspective rendering, rays spread outward from the camera.
That means the visible region gets wider as distance increases.
So the visible volume is not a box. It expands outward, which is why it looks like a truncated pyramid.
Connection to perspective projection
The frustum is closely tied to perspective projection.
Points inside the frustum are projected onto the image plane to form the final 2D image.
So the frustum describes what part of 3D space is eligible to be projected.
This also connects to Homogeneous Coordinates, because perspective projection is usually implemented with matrices in homogeneous coordinates.
Frustum culling
A common optimization in graphics is frustum culling.
This means:
- test whether an object is inside the camera frustum
- skip rendering it if it is completely outside
This speeds up rendering because the engine avoids drawing objects the camera cannot see.
Intuition
The best mental model is:
A frustum is the camera’s visible chunk of 3D space.
If you imagine looking through a camera, the frustum is the 3D region that can actually appear in the image.
So in pure geometry, a frustum is a truncated cone or pyramid.
In graphics, it is the truncated viewing volume of a camera.