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Homogeneous Clipping

Projection: linear transformations then normalize

Region mapping:



Clipping not good after normalization:
Clip in homogeneous coordinates:

Clipping Homogeneous Coordinates

  • Assume NDC window of
  • To clip to X=-1 (left):
    • Projected coordinates: Clip to X=-1
    • Homogeneous coordinate: Clip to
    • Homogeneous plane:


    • Point is visible if
    • For line segment want a such that

      lies on the plane w+x=0

    • Solving for a

      gives us

  • Repeat for remaining boundaries:
    • Near and far clipping planes

Readings: Jim Blinn's Corner, Chapters 13, 18

CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab