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pcap
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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!
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!
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