Hermite interpolation and basis functions.

259 Views Asked by At

I am using piecewise quintic Hermite interpolation at the joint level for a robot (1000 Hz) from a more time-sparse, but smooth trajectory (100 Hz). I have tested this according to the elegant mathematics in some lecture notes by Professor D.L. Finn[1].

It works nicely, and I wish to document it, but I can not find any bibliographic reference to the "basis functions"; $H_i^n$ for spline order $n$ in the lecture notes. What are they called, and where do I find something published on Hermite interpolation using these basis functions?

Example for the cubic case, from the lecture notes:

$$\begin{align} H_0^3(t) &= 1 - 3t^2 + 2t^3 \\ H_1^3(t) &= t - 2t^2 + t^3 \\ H_2^3(t) &= -t^2 + t^3 \\ H_3^3(t) &= 3t^2 - 2t^3 \end{align}$$

I have sent professor Finn the same question, and will post here if I get some information from him.

[1] D.L. Finn, "MA 323 Geometric Modelling, Course Notes: Day 09, Quintic Hermite Interpolation", 2004, \url{https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf}