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Deriving Equations Given Graphs

 
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jabronyo
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Joined: 16 Apr 2012
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PostPosted: Mon Apr 16, 2012 4:57 pm    Post subject: Deriving Equations Given Graphs Reply with quote

Hi Guys,

I'm trying to make a database of values for a given graph that seems to be semi-linear in nature. (See below)




I'm also trying to do the same for something that seems logarithmic, but not entirely. (See below)




Any ideas on how to pull this off?

Thanks,
JR
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UmTheMuse
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Joined: 05 Apr 2012
Posts: 33
Location: United States

PostPosted: Mon Apr 23, 2012 12:23 pm    Post subject: Reply with quote

You don't have any of the original numbers, right? If you did, you could maybe do a line of best fit for each curve. You could also use a statistical analysis software, such as gretl (freeware for econometrics) with multiple offsets.

Without the original data, you'd probably have to eyeball, guestimate it. Draw a line to more or less fit the existing line. Check the change in height over the change in length to give you the slope of a line and give the lines different (negative) y-intercepts for the offset between each line.

The non-linear equations would be more complicated, but basically the same thing. The hard part would be calculating the slope. You'll need to know calculus to figure out the slope of whatever equation you think will fit best. For example, the derivative of the natural log, ln(x) = 1/x. Draw a curve that would fit your equation and superimpose it over the graph so you can figure out the intercepts.
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jrkrideau
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Joined: 08 Aug 2005
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Location: Kingston ON Canada

PostPosted: Thu Apr 26, 2012 4:09 am    Post subject: Reply with quote

I have never used them but I believe that there are several "graph digitizers' available. Have a look at http://digitizer.sourceforge.net/ for one Open Source example.
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jrkrideau
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Currently using Windows 7 & OOo 3.4.0 and Ubuntu 12.04 & LibreOffice 3.5.2.2
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