Trouble understanding a derivative used in Hermite curve reparameterization

1. Oct 31, 2009

pcap

Hello,

I am trying to understand how to reparameterize a Hermite curve described by the parametric vector function $\vec{P}(t)$ to a curve described by $$\vec{Q}(T)$$ where $$T = at + b$$. In particular, I am having trouble finding the derivative of the reparameterized curve.

We know $$T_i = at_{i} + b$$ and $$T_j = at_j + b$$. We also know, $$\frac{dT}{dt} = a$$.

The http://books.google.com/books?id=m0...#v=onepage&q=hermite curve parameter&f=false" I am looking at arrives at the following equation:

$$\frac{d\textbf{Q}(T)}{dT} = \frac{d\textbf{P}(t)}{dt} \frac{dt}{dT}$$

I do not understand how they arrived at this derivative, so I would appreciate any insight into this.

My thinking is a bit foggy now, so hopefully some rest will help. At any rate, I can provide more clarification as needed. Thanks!

Last edited by a moderator: Apr 24, 2017
2. Oct 31, 2009

HallsofIvy

Staff Emeritus
That looks to me like it is just the chain rule!