**Projection: linear transformations then normalize**-
- Linear transformation
- Normalization

- Linear transformation
**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

- Ambiguity after normalization
**Clip in homogeneous coordinates:**-
- Compare unnormalized coordinate against

- 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 thatlies on the plane

*w*+*x*=0 - Solving for
*a*gives us

- Projected coordinates: Clip to
- 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