Clipping

Problem

Geometry frequently extends beyond the viewport or clip volume. If you rasterize it as-is, later stages waste work and may even become numerically awkward.

Intuition

Clipping intersects the primitive with the visible region. The result is a new primitive that lies entirely inside the allowed domain, so downstream stages can assume cleaner inputs.

Core idea

• Represent the visible region as a clip rectangle or clip volume.
• Intersect the incoming line, polygon, or curve segment with that region.
• Keep only the portion that remains inside.

Worked example

A line segment that exits the left side of the screen is clipped so the new segment starts exactly on the boundary instead of extending off-screen forever.

Complexity

The cost depends on the primitive type, but classic line and polygon clipping algorithms are modest compared to the work saved downstream.

When to choose it

• Choose clipping before rasterization whenever primitives can cross the visible boundary.
• It is a geometric preprocessing stage, not a fragment-level visibility test like the z-buffer.
• Curves and paths also benefit from being clipped before tessellation or rasterization.

Key takeaways

• Clipping reduces work and simplifies later pipeline stages.
• It happens before rasterization, not instead of it.
• The output remains geometry, just trimmed to the visible domain.
• It is a foundational step in the standard rendering pipeline.

Practice ideas

• Implement Cohen-Sutherland or Liang-Barsky line clipping.
• Clip a polygon to a rectangle before rasterizing it.
• Visualize the difference between unclipped and clipped primitives on a small screen grid.

Relation to other topics

• Rasterization assumes geometry that is already ready for screen-space coverage testing.
• Bezier curves often need clipping or subdivision before later rendering steps.
• The z-buffer only matters after geometry has been clipped and rasterized into fragments.