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Downgrade the sigma-tau-phi version |
replies to PAR |
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::That sounds good, for the sigma-tau coordinates. I think the 3D images are EXCELLENT, but they show up a bit dark on my machine. I don't know whether that is me or the images. How did you generate them? [[User:PAR|PAR]] ([[User talk:PAR|talk]]) 16:27, 4 February 2008 (UTC)
:::I'm really glad that you like them. I made them with [[Blender (software)|Blender]], which I started learning late at night at Christmas time. It's amazingly powerful. I find the images a little dark, too, but I'm just beginning to learn how to use the program, so I hope to learn eventually how to fix it. I wanted the isosurfaces to look like blown glass, but without being too shiny. [[User:WillowW|Willow]] ([[User talk:WillowW|talk]]) 19:25, 4 February 2008 (UTC)
==Different conventions==
Hey [[User:PAR|PAR]],
I went to the library and dug up a few books that had stuff about these coordinates. Morse and Feshbach have really pretty stereo images, have you seen them? Basically, they use your definitions
:<math>
x = a \cos \phi \sqrt{\left( \xi^{2} + 1 \right)\left( 1 - \eta^{2}\right)}
</math>
:<math>
y = a \sin \phi \sqrt{\left( \xi^{2} + 1 \right)\left( 1 - \eta^{2}\right)}
</math>
:<math>
z = a \xi \eta
</math>
where ξ = sinh μ and η = sin ν. They express it slightly differently, though, using (ξ<sub>1</sub>, ξ<sub>2</sub>, ξ<sub>3</sub>) defined as
:<math>
\xi_{1} \equiv = a \xi, \xi_{2} \equiv \eta, \xi_{3} = \cos \phi
</math>
I found the same definitions in the ''Handbook of Integration'' by Daniel Zwillinger, except using (''u''<sub>1</sub>, ''u''<sub>2</sub>, ''u''<sub>3</sub>). It seems that most people use the [[colatitude]] θ instead of the latitude ν; I don't know how I got the impression that the latitude was more commonly used? Do you think we should switch from ν to θ? I rather like your 2D plot and would be sorry to see it go. [[User:WillowW|Willow]] ([[User talk:WillowW|talk]]) 19:25, 4 February 2008 (UTC)
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