Spline Continuity

Smoother Blending Functions:

• Can be replace by smoother functions?
  • Piecewise polynomials on
  • Continuous derivatives
• Yes, but we lose one degree of freedom
  • Curve has no corner if segments share a common tangent
  • Tangent is given by the chords ,
  • An equation constrains , ,

    

• This equation leads to combinations:

Spline Basis

• Combined functions form a smoother spline basis

Smoother Curves

• Control points used with this basis produce smoother curves