Why Map Z?

• 3D 2D projections map all z to same value.
• Need z to determine occlusion, so a 3D to 2D projective transformation doesn't work.
• Further, we want 3D lines to map to 3D lines (this is useful in hidden surface removal)
• The mapping maps lines to lines, but loses all depth information.
• We could use

  

  Thus, if we map the endpoints of a line segment, these end points will have the same relative depths after this mapping.

  BUT: It fails to map lines to lines

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• In this figure, P,Q,R map to P',Q',R' under a pure projective projection.
• With the mapping P,Q,R actually map to , which fail to lie on a straight line.
• The map

  

  does map lines to lines, and it preserves depth information.

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