4 variable nomogram article

Mathematics about graphical computing
Glen
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4 variable nomogram article

Postby Glen » Thu Mar 13, 2008 11:20 pm

Ron and Liunian (both members here) have an article up on a 4-variable grid-type nomogram at Ron's blog. Check it out.

http://myreckonings.com/wordpress/2008/03/13/a-4-variable-nomogram-%e5%9b%9b%e5%8f%98%e9%87%8f%e8%af%ba%e6%a8%a1%e5%9b%be
Last edited by Glen on Thu Feb 25, 2010 4:38 am, edited 1 time in total.
RonDoerfler
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Re: 4 variable nomogram article

Postby RonDoerfler » Fri Mar 14, 2008 1:38 am

Thanks, Glen. Actually, the design is all Liunian's work, but he was generous enough to ask that my name be included because I helped check it out and format it. It's a really interesting derivation, I think.

This link may work better:

http://myreckonings.com/wordpress/2008/ ... %e5%9b%be/

Ron
liunian
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Joined: Tue Feb 26, 2008 1:42 pm

Re: 4 variable nomogram article

Postby liunian » Fri Mar 14, 2008 5:46 am

Thank you Glen.
I will change a better graph for extended value.That graph will work well for all real number.Can I email for you?
Leif
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Re: 4 variable nomogram article

Postby Leif » Sun Mar 16, 2008 9:06 pm

I looked Allcock's book about grid-nomographs and there seems to be nothing special about grid nomograms compared with line nomograms made by constructional determinant. One has to make projective transformation from four original points to for destination points. Case f+g+h=0 may be an exception. Of course, constructing constructional determinant is not always trivial.

The topic of optimal transformation is interesting. I use one in PyNomo development code where one optimizes sum of squared lengths of lines (axes) with respect to bounding box area. I plan to take outer edges of grid and use them as lines in case of grid nomographs.

I think there is space for some "scientific" contribution, when thinking about optimum algorithms for nomograph construction. In PyNomo I still construct the code base and it takes time before entering this new fun stuff: using computing power to construct better nomographs.

If I understand correctly, this is the issue you talk about; What is the criteria to optimize, is there straight analytical transformation or cheat sheet, how to optimize.

I'm interested if you have, for example from Hall's book, a more sophisticated approach compared to my simple above.

Thanks for link, interesting discussion and best of all, real nomograph made in this millennium!

\leif
liunian
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Joined: Tue Feb 26, 2008 1:42 pm

Re: 4 variable nomogram article

Postby liunian » Thu Mar 20, 2008 4:39 am

Hi Leif,
I don't think optimise is best method.I have tried to for up 4-variable formula.It can not work well.Because optimise just calculate point one by one,and the point mey be everwhere,so I think optimise is not valid for 4,5,6-variable nomography.If you can find out a method optimise all point at one time,and make its result for continue,this problem may be solved.Perhaps,symbol optimise or symbol calculate is a good way.Its likes translate formula to determinant.
RonDoerfler
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Re: 4 variable nomogram article

Postby RonDoerfler » Mon Mar 31, 2008 3:15 am

Hi All,

I haven't seen any kind of universal rule for optimizing a nomogram other than squaring up the nomogram to fill all the available space. Beyond that, I think it depends of the accuracies required of the individual scales as well as spacing between any scales in a grid. It would be an interesting problem to solve. Sometimes the optimum nomogram seems to be a completely different design.

I've spent some time as a learning exercise trying to manually optimize Liunian's 4-variable nomogram by performing transformations of the type from Hall's book as well as central projection transformations. I've just now posted a summary of these efforts in a comment at the end of the blog essay on that nomogram:

http://myreckonings.com/wordpress/2008/ ... %e5%9b%be/

The comment also links to a PDf file of results that lists the modifications to the standard nomographic determinant that are needed to perform Hall's transformation as well as the central projection transformation.

Ron

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