Re: How to combine graphics pimitives and Plot function?

• To: mathgroup at smc.vnet.net
• Subject: [mg107024] Re: [mg107011] How to combine graphics pimitives and Plot function?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 1 Feb 2010 06:09:40 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <201001311253.HAA14187@smc.vnet.net>

```Trying to do this kind of thing using Mathematica's built-in paradigm
for graphics causes trouble for many beginners.

Here's one way.  (I changed the x-domain because otherwise the random
polygon collapses to a small blur.)

points = RandomReal[{-1,1},{100,2}];
Show[{
Plot[Sin[x],{x,-Pi,Pi}],
Graphics[{Red,Line[points]}]
}]

The Graphics has to apply only to the {Red,Line[points]}, as the result
of the Plot expression is already a Graphics object.

You don't need the Axes->True option, as that's the default for Plot.
However -- and this really drives folks nuts -- if you reverse the order
of the Graphics objects...

Show[{Graphics[{Red,Line[points]}], Plot[Sin[x], {x,-Pi,Pi}]}]

... then the axes disappear and you have to insert the Axes->True option
within the Graphics[{Red,Line[points]}] expression:

Show[{Graphics[{Red, Line[points]}, Axes -> True],
Plot[Sin[x], {x, - Pi, Pi}]}]

No wonder this sort of thing gives so much trouble!

But a much simpler way to do the whole thing is to use the different
paradigm that's supplied by David Park's Presentations application:

Needs["Presentations`Master`"]

points = RandomReal[{-1,1},{100,2}];

Draw2D[{
Draw[Sin[x],{x,-Pi,Pi}],
{Red,Line[points]}
},
Axes->True]

Notice that the Axes->True option is for the entire Draw2D expression;
this means you'll get axes without any further ado no matter in what
order you list the two objects, Draw[Sin[x]....] and {Red,Line[points]}.

I've deliberately pretty-printed both versions in order to emphasize the
structure of the overall expression.

In the version done with Presentations, notice that all the different
objects to be drawn (by the Draw2D) are "at the same level", one after
the other, so that there's no need for wrapping the {Red,Line[points]
expression with Graphics.

With Presentations, moreover, you don't have to explicitly form pairs of
reals as coordinates of the points, but may instead form complex numbers
directly and plot a "complex line" whose vertices are the corresponding
complex points:

points = RandomComplex[{-1 - I, 1 + I}, 100];
Draw2D[{Draw[Sin[x],{x,-Pi,Pi}],Red,ComplexLine[pts]},Axes->True]

On 1/31/2010 7:53 AM, a boy wrote:
> points = RandomReal[{-1, 1}, {100, 2}]
> Graphics[{Red, Line[points], Plot[Sin[x], {x, -10 Pi, 10 Pi}]},
>   Axes ->  True]

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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