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# Homogeneous Clipping

Projection: linear transformations then normalize
• Linear transformation

• Normalization

Region mapping:

\

\

Clipping not good after normalization:
• Ambiguity after normalization

• Numerator can be positive or negative
• Denominator can be positive or negative
• Normalization expended on points that are subsequently clipped
Clip in homogeneous coordinates:
• Compare unnormalized coordinate against

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

cs488@cgl.uwaterloo.ca