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Re: Solving difficult integral

• To: mathgroup at smc.vnet.net
• Subject: [mg18895] Re: Solving difficult integral
• From: "Christian Gudrian" <Christian.Gudrian at hermes.kawo1.rwth-aachen.de>
• Date: Mon, 26 Jul 1999 14:27:42 -0400
• Organization: Aachen University of Technology / Rechnerbetrieb Informatik
• References: <7mek2g$9il@smc.vnet.net> <7mjr6q$f3k@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Paul Abbott <paul at physics.uwa.edu.au> schrieb in im Newsbeitrag:
7mjr6q$f3k at smc.vnet.net...

> The real question is why do you need the general solution and, if you
> have it, what do you want to do with it?

(:

Hi, Paul!

Well, what am I trying to do? I want to write a C-program which does the
following: I've got four points in R3 which define one section of a
Catmull-Rom-Spline. With the coordinates of these four points I get a
formula P(t) (0 <= t <= 1) which defines the curve between point two and
thre (the points one and four are needed to calculate the tangents through
the curve at points two and three).

If I now wished (well, I certainly do!) to know the length of the path my
point P(t) left behind at a certain point of time t I need to integrate the
value of the velocity vector Sqrt[(dP/dt)^2] with the limits 0 and t to get
a function s(t).

But my core problem is even more complicated: I need the inverse function
t(s) basically. What makes the whole situation even more complicated is that
I do not know neither of the variables in advance. Right know I'm thinking
about using MathLink to do the respective calculations during runtime when
all things a definite. This should FullSimplify[Everthing] (:

Greetings from Germany,

Christian