| solving equation consisting of points - sort of... [message #63328] |
Thu, 06 November 2008 06:49  |
shokland
Messages: 4
Registered: January 2008
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Junior Member |
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I have a parametric curve, where I wish to calculate the parameter
value, t, at fixed positions along the trace, g. I calculate the
arclength a_i for a set of parameter values t_i, and now wish to
somehow solve the equations: t_j = a_j with t_j as the unknown. Does
anyone have a suggestion for performing this in an elegant (and
mathematically sound) manner? Obviously, given, a_k, one could find l,
such that a(t_l)<a_k and a(t_(l+1)) > a_k and perform a linear
interpolation to find t_k, but as said, I'm wondering if there's a
better way...
Thanks in advance for any help you can offer.
Kind regards,
Steffen
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| Re: solving equation consisting of points - sort of... [message #63513 is a reply to message #63373] |
Fri, 07 November 2008 06:56  |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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shokland wrote:
>> So you are trying to solve int_0^t f(x)dx=A for t given A and f?
> Exactly! wasn't sure if LaTeX-style notation would be acceptable, but
> certainly makes communication of problems easier...
>
>> I would probably just use the simpler method with interpolate
> OK - was that the (rather unsatisfying) solution that I originally
> proposed?
Yes, that would be computing the integral for different values
[t1,t2,...] and interpolate [A1,A2,...] at your desired t.
If your function is smooth, that should work pretty well...
If the function is not smooth, you may want to be
careful....
Ciao,
Paolo
>
> Thanks,
> Steffen
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