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RE: Re: A 3D Plot Query

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94419] RE: [mg94374] Re: A 3D Plot Query
  • From: "David Park" <djmpark at comcast.net>
  • Date: Fri, 12 Dec 2008 06:56:35 -0500 (EST)
  • References: <31362096.1228736527369.JavaMail.root@m02> <200812091159.GAA20944@smc.vnet.net> <31958869.1228906532926.JavaMail.root@m02> <000001c95ae9$3810e180$a832a480$@net> <8990753.1228988099177.JavaMail.root@m02>

Which all inspires me to write a few thoughts on plotting and making custom
plots with Mathematica.

Essentially, making a nice custom graphic is WORK. You have to specify each
thing that is in there. In the plot below there is one statement for the
surface, one for the 3 arrows that make the axes, one for each of the
labels, and two directives. And then options that control the overall
appearance of the graphic.

If you were doing this in a class, on the fly, it would be MUCH faster to
draw it by hand on whatever kind of board they use these days.

The advantage of making the graphic in Mathematica is that you have a nicer
rendition AND a permanent specification. One that you can also copy, modify
or embellish.

The objection I have to something like DrawingTools is that it does not
leave one with a SINGLE permanent specification. You may start by specifying
some Plot statement and then add things to it with DrawingTools. (And with
Presentations the Draw2D statement might contain a number of computed
primitives.) Then if you want to change something in the Plot statement (or
Draw2D statement) you have to redo everything done with DrawingTools.
I think it is better to have a complete textual specification in one
statement.

The fact that Mathematica provides a number of set-piece plot types that
produce some fantastic graphics is misleading. In many cases you cannot just
fall back on these plot types and one has to make one's own detailed
specifications. And that is when things get difficult because it is not
always easy to twist the set-piece plot to the form you want - especially
for beginners or casual users.

So general custom graphics takes a lot more work, and often each situation
requires its own design. Better than trying to find a single command that
will automatically produce the graphic you want, just settle to trying to be
an artist and specify all the things you need. It's fun. And also, making a
nice graphic or dynamic diagram often teaches one a lot about the underlying
mathematics.

(And Murray does know how to make excellent graphics.)


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  




From: Murray Eisenberg [mailto:murray at math.umass.edu] 

As always with "Presentations" results, lovely.

It's still galling to me that Mathematica doesn't make it MUCH easier to 
reproduce the kind of 3D axes mathematicians routinely draw.

David Park wrote:
> Needs["Presentations`Master`"]
> 
> With[
>  {a = 1},
>  Draw3DItems[
>   {Opacity[.5, Brown], 
>    ParametricDraw3D[{r Cos[\[Theta]], r Sin[\[Theta]], 
>      2 - r^2}, {\[Theta], 0, \[Pi]/2}, {r, 0, a}, 
>     PlotPoints -> {30, 10},
>     Mesh -> None,
>     MaxRecursion -> 3],
>    Opacity[1, Black],
>    DrawArrow3DAxes[{0, 0, 1}, 1, .1],
>    VerticalText3D["x", {1.2 a, 0, 2 - a^2}, 0, {.1, .1}],
>    VerticalText3D["y", {0, 1.2 a, 2 - a^2}, 90 \[Degree], {.1, .1}],
>    VerticalText3D["z", {0, 0, 2.1}, 90 \[Degree], {.1, .1}],
>    VerticalText3D["a", {0, a/2, 2 - .9 a^2}, 90 \[Degree], {.1, .1}]},
>   NeutralLighting[.0, .5, .1],
>   NiceRotation,
>   PlotRange -> {{-.2 a, 1.4 a}, {-.2 a, 1.4 a}, All},
>   ViewPoint -> {5, 5, 3},
>   BoxRatios -> Automatic,
>   Boxed -> False,
>   PlotLabel -> Style[z == 2 - Sqrt[x^2 + y^2], 16]]
>  ]
> 
> 
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/  
> 
> 
> 
> 
> From: Murray Eisenberg [mailto:murray at math.umass.edu] 
> 
> 
> Another "for engineers and scientists" version of a graph -- and not 
> what the poster requested.  As I understand the query, what is desired 
> is the positive semi-axes shown emanating from the origin, with z up, x 
> forward, and y to the right (roughly).  No frame.
> 




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