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Re: Trouble Getting Graphic Primitives in a Module to Display with Show Command

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125429] Re: Trouble Getting Graphic Primitives in a Module to Display with Show Command
  • From: "djmpark" <djmpark at comcast.net>
  • Date: Tue, 13 Mar 2012 03:08:37 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <17979570.11446.1331544406716.JavaMail.root@m06>

The problem is that the behavior of Mathematica with respect to the display
of Graphics has changed since Nancy wrote her book. The display of graphics
used to be a side effect and the notebook output was uninteresting and so
was suppressed with a ";".  Now the display is the directly generated output
and you no longer want to suppress it. So just use (without the terminating
semicolon):

sketchEarthOrbit[] 

With the Show statement you have to use a lot of what I call "Graphics level
jumping". And what if you want to include a curve produced by some plot
statement? The Presentations Application makes this much easier, natural and
more intuitive. Here is the way to produce the elements of the graphic
separately and then combine them. I added color for the earth and sun.
Notice that we have to draw the orbit first so the earth disk will fall on
top of it. 

<<Presentations` 

orbit = Circle[{0, 0}, {1., .5}]; 

earth = {Green, Disk[{-.7, .35}, 0.05], Black, 
   Text["Earth", {-.7, .45}]}; 

sun = {Yellow, Disk[{.3, 0}, 0.1], Black, Text["Sun", {.3, .17}]}; 

Draw2D[{orbit, earth, sun}] 

Draw2D replaces Show and by default uses Automatic AspectRatio.

Of course, this plot is wildly incorrect. The sun is nowhere near the focus
of the ellipse. Nancy probably took some pains to place the earth on top of
the ellipse. And earth's orbit is nowhere near that elliptical.  So let's
change earth to a comet and use a simple parameterization of the ellipse (s
is not the time along the orbit - that's a more complicated calculation),
and introduce a function that calculates the position of one focus.

ellipse[a_, b_][s_] := {a Cos[s], b Sin[s]} 

ellipseFocus[a_, b_] := 
 If[a >= b, {Sqrt[a^2 - b^2], 0}, {0, Sqrt[a^2 - b^2]}] 

Then we draw the elements using the ellipse definitions. ParametricDraw is
equivalent to ParametricPlot but just produces the graphics primitives and
not an entire plot. Now we can calculate the positions of the comet and sun.

orbit = ParametricDraw[ellipse[1, 0.5][s], {s, 0, 2 \[Pi]}];

earth =
  With[{position = ellipse[1, 0.5][3 \[Pi]/4]},
   {Green, Disk[position, 0.04], Black, 
    Text["Comet", position, {0, -3}]}];

sun =
  With[{position = ellipseFocus[1, 0.5]},
   {Yellow, Disk[position, 0.08], Black, 
    Text["Sun", position, {0, -4}]}];

The diagram is produced with the very same statement we used before.  Notice
that we have combined standard primitives and a plotted curve without having
to worry about graphics levels.

Draw2D[{orbit, earth, sun}]


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


From: Kenneth Bures [mailto:kenbures at gmail.com] 


I have been trying to display graphics primitives (lines, circles) from
inside a module, but I can't get it to work. If you have Nancy Blachman's
book, MATHEMATICA: A Practical Approach, 2nd Edition, she gives an example
on page 399 of a 4-line module that generates 3 graphics objects and then
has a Show command (inside the module) to display them. I've listed the code
below. The book illustrates that when you call this module from the main
program with the instruction sketchEarthOrbit[] it displays the 3 graphics
objects. When I copy this program exactly, it does not work. I get no
output. If I cut & paste the exact four lines of code to outside of the
module, they do display the desired result, so there seems to be is
something wrong with her basic approach.

Why doesn't this example work? Actually, what I would really like to do is
pass the graphics objects out of the module, and display them from the main
program, rather than having the Show inside the module.
But I decided that I should understand what is wrong with Blachman's
approach before I spend too much time on the other. Any help would be
appreciated, either with explaining Blachman's approach and/or how to
transfer graphics objects out of a module.

Here is Blachman's code (I put the Clear command there):

Clear[sketchEarthOrbit];
sketchEarthOrbit[] :=
  Module[{earth, sun, orbit},
   earth =
    Graphics[{ Disk[{-.7, .35}, 0.05], Text["Earth", {-.7, .45}] }];
   sun = Graphics[{ Disk[{.3, 0}, 0.1], Text["Sun", {.3, .17}] }];
   orbit = Graphics[{ Circle[{0, 0}, {1., .5}] }];
   Show[orbit, sun, earth, AspectRatio -> Automatic]
   ];
sketchEarthOrbit[];




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