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Trouble understanding a derivative used in Hermite curve reparameterization

  1. Oct 31, 2009 #1
    Hello,

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

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

    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:

    [tex]\frac{d\textbf{Q}(T)}{dT} = \frac{d\textbf{P}(t)}{dt} \frac{dt}{dT}[/tex]

    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. jcsd
  3. Oct 31, 2009 #2

    HallsofIvy

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