**Bézier Discontinuities:**-
- Two Bézier segments can be completely disjoint
- Two segments join if they share last/first control point

**Common Parameterization and Blending Functions**-
- Joined curves can be given common parameterization
- Parameterize first segment with
- Parameterize next segment with , etc.

- Look at blending/basis polynomials under this parameterization
- Combine those for common into a single piecewise polynomial

- Joined curves can be given common parameterization
**Combined Curve Segments**-
- Curve is , where:

- Curve is , where:
**Curve Discontinuities from Basis Discontinuities**-
- is scaled by , which has a discontinuous derivative
- The corner in the curve results from this discontinuity

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab