Re: Graphics package in v6
- To: mathgroup at smc.vnet.net
- Subject: [mg78428] Re: Graphics package in v6
- From: Helen Read <hpr at together.net>
- Date: Sun, 1 Jul 2007 07:45:49 -0400 (EDT)
- References: <f65aq2$9jg$1@smc.vnet.net>
- Reply-to: HPR <read at math.uvm.edu>
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
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- RE: Re: Graphics package in v6
- From: "Jaccard Florian" <Florian.Jaccard@he-arc.ch>
- RE: Re: Graphics package in v6