Discontinuities in Splines

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

Combined Curve Segments

• 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