Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

On the cubic hermite spline Wikipedia page, the formula for interpolating between $x_k$ and $x_{k+1}$ is given by

$$h_{00}(t)p_k+h_{10}(t)(x_{k+1}-x_k)m_k+h_{01}(t)p_{k+1}+h_{11}(t)(x_{k+1}-x_k)m_{k+1}$$

Where $t = (x-x_k)/(x_{k+1}-x_k)$ and $h$ refers to the basis functions.

I have a slight problem in understanding this: When given $h(t)$, is it $h \times t$, or $h$ of $t$?

This of course makes a big difference in the equation. Judging from the 0 to 1 interval, I'd say it's $h$ of $t$, but I'd rather make sure.

share|cite|improve this question
up vote 1 down vote accepted

Yes, it's the function $h$ applied to $t$. It's a linear combination of basis functions, stretched to fit the interval $[x_k, x_{k+1}]$.

If they had meant $h$ times $t$, they would probably just have written $ht$.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.