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RE: Re: Graphics package in v6

• To: mathgroup at smc.vnet.net
• Subject: [mg78463] RE: [mg78428] Re: Graphics package in v6
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Mon, 2 Jul 2007 06:54:09 -0400 (EDT)
• References: <f65aq2$9jg$1@smc.vnet.net> <200707011145.HAA15125@smc.vnet.net>

Thanks to all who have given responses.

I must admit that ImplicitPlot is now obsolete because ContourPlot can 
do the same if you add Frame->False and Axes->True...

But after reading your posts and the discussion Carl Woll talked about 
(http://tinyurl.com/3duktb*) , I'm really disappointed of 
RevolutionPlot3D.

I'm in the same situation as Helen Read : Sure I can obtain a revolution 
around x-axis by using
RevolutionPlot3D[{f[x],x},{x,0,2},ViewVertical->{-1,0,0},AxesLabel->{"y","z","x"}] ,
but I'm afraid my calculus students will be all mixed up... so I will 
continue to use SurfaceOfRevolution and I really hope Wolfram will add 
the option RevolutionAxis for the future release !


Have a nice week!
  
Florian Jaccard



-----Message d'origine-----
De=A0: Helen Read [mailto:hpr at together.net]
Envoy=E9=A0: dimanche, 1. juillet 2007 13:46
=C0=A0: mathgroup at smc.vnet.net
Objet=A0: [mg78428] Re: Graphics package in v6

Jaccard Florian wrote:
> Dear group,
>
> I'm a convinced Mathematica user, I love the new features I discover
> in v6, but I think the Graphics package was very useful in v5 and I'm
> missing it.
>
> For example, it was very easy to obtain the 3D plot of a surface of
> revolution around the x-axis with SurfaceOfRevolution.
>
> Let us take the revolution of y=x^2 around the x-axis :
>
> << "Graphics`"
> SurfaceOfRevolution[x^2, {x, 0, 2}, RevolutionAxis -> {1, 0, 0}]
>
> Not possible without cheating if using RevolutionPlot3D, isn't 
it=A0?

I posted several weeks ago about the lack of an option for setting the
revolution axis in RevolutionPlot3D, and someone from Wolfram (I forget
who) replied that they will look into it and most likely add it in a
future release.

In the meantime, you can use the following workaround, which I showed my 

Calculus II students yesterday when we started the unit on volumes of
solids of revolution. Some of them are complete Mathematica newbies (the 
class just started this past week), and they didn't have any problem
with it.

Here's what I had them do. To revolve say, y=x^2 around the y-axis, just
use RevolutionPlot3D on the ordered pair {x,x^2}. (We are essentially
using a parametric representation for the curve, which I found sets the
BoxRatios more to my liking than just using the function by itself.)

RevolutionPlot3D[{x,x^2},{x,0,2}]

To revolve the same curve around the x-axis, reverse the ordered pair
and flip the axes around by setting ViewVertical.

RevolutionPlot3D[{x^2,x},{x,0,2},ViewVertical->{-1,0,0}]

We would actually define a function for x^2 (or whatever) first, and use 
{x,f[x]} when revolving around y-axis and {f[x],x} for revolving around
the x-axis. The ordered pair idea also makes it simple to revolve
functions in the form x=f(y) around either axis, using {f[y],y} or
{y,f[y]} depending on the direction.

I hope that WRI will add a RevolutionAxis option to RevolutionPlot3D
soon, but the above works OK in the meantime, and the graphs are so much 
better looking than they were in 5.2, and we can spin them around with
the mouse without having to load any packages.

> Or you could have a nice plot of implicit functions, with the ticks
> on  the x- and y-axis, using ImplicitPlot...
>
> Example :
>
> << "Graphics`"
> ImplicitPlot[x^3*y + x*y^3 == 2, {x, -3, 3}, {y, -3, 3}]
>
> Not possible using CountourPlot without cheating, isn't it?
>
> (I consider the following as cheating :
> Show[Plot[0, {x, -3, 3}, PlotRange -> {-3, 3},
>   AspectRatio -> Automatic],
>    ContourPlot[x^3*y + x*y^3 == 2, {x, -3, 3}, {y, -3, 3},
>   Axes -> True,
>      AxesOrigin -> {0, 0}, PerformanceGoal -> "Quality",
>   PlotPoints -> 150]]
> )

I'm not sure what your objection is to

ContourPlot[x^3 y + x y^3==2,{x,-3,3},{y,-3,3}]

or

ContourPlot[x^3 y + x =
y^3==2,{x,-3,3},{y,-3,3},Frame->False,Axes->True]

if you'd rather have Axes instead of a Frame.

To me the graph looks much smoother (with the new anti-aliasing
graphics) than

ImplicitPlot[x^3 y + x y^3==2,{x,-3,3},{y,-3,3}] in 5.2.

--
Helen Read
University of Vermont

• Follow-Ups:
  • new behavior of Plot
    • From: Selwyn Hollis <sh2.7183@earthlink.net>

• References:
  • Re: Graphics package in v6
    • From: Helen Read <hpr@together.net>