Hermite Interpolation

“Hermite interpolation” is the problem of fitting a polynomial given function values and derivatives.

Why hermtie?

So you can get better smoothness of the curve as opposed to Polynomial Interpolation.

Some terminology:

  • Knots: Points where the interpolant transitions from one polynomial / interval to another.
  • Nodes: Points where some control points/data is specified.

For Hermite interpolation, these are the same.

For other curve types (e.g. Bezier Curves), they can differ.