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MathGroup Archive 2005

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Re: MultipleListPlot MakeSymbol Issue

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53423] Re: [mg53404] MultipleListPlot MakeSymbol Issue
  • From: "David Park" <djmp at earthlink.net>
  • Date: Tue, 11 Jan 2005 01:31:07 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Dimitri,

It is a bit difficult to follow exactly what you want. I'll do the simple
case of a  starburst effect using the DrawGraphics package from my web site
below.

Needs["DrawGraphics`DrawingMaster`"]

The following routine creates a fitted triangle to a circle with angular
width 2 alpha. One side of the triangle fits the circle and a single line is
produced by using the StichLineSegments routine from the package.

fittedpoint[\[Alpha]_, height_] :=
  StitchLineSegments[{Line[{{Cos[\[Alpha]], Sin[\[Alpha]]}, {height,
            0}, {Cos[\[Alpha]], -Sin[\[Alpha]]}}],
      ParametricDraw[{Cos[a], Sin[a]}, {a, -\[Alpha], \[Alpha]}]}]

The following routine then produces a starburst plot.

Module[{figure},
    figure = fittedpoint[\[Pi]/32.0, 1.3];
    figure = {Gold, figure /. Line -> Polygon, Black, figure};
    Draw2D[
      {RoyalBlue, Disk[{0, 0}, 1],
        Table[
          figure /.
            DrawingTransform[#1Cos[n \[Pi]/16] - #2Sin[n \[Pi]/16] &, #1Sin[
                      n \[Pi]/16] + #2Cos[n \[Pi]/16] &], {n, 0, 31}],
        Black, Circle[{0, 0}, 1]},
      AspectRatio -> Automatic,
      Background -> Linen,
      PlotRange -> {{-1, 1}, {-1, 1}}1.4,
      ImageSize -> 450]];

First, a basic pointed figure was produced centered at 0 degrees, with a
width pi/16 and a height of 1.3 and fitted to a unit circle.

Then the figure was extended to a Gold polygon with a Black outline.

Then, using the Draw2D routine, which is just a shortcut for
Show[Graphics...], I drew a RoyalBlue disk, then a table of 32 figures
rotated in increments of pi/16. The DrawingTransform routine from the
package was used to produce the rotations. Finally I drew a Black outline
for the unit circle.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: Pennyrue at aol.com [mailto:Pennyrue at aol.com]
To: mathgroup at smc.vnet.net

I am trying to rotate an elipse about a fixed point, so that
every pi/16, or so, increment is shown.  A sort or spirograph type effect.

So far I've got the elipse rotating around a circle, but the
axes stay fixed as it rotates, it looks like a fat football.

MultipleListPlot[mycircle,SymbolShape->MakeSymbol[{Line[{myelipse}]}]]

Is there a way to transform the myelipse list as it rotates
according to mycircle or the origin?

Another related question.  Increasing the size of myelipse is easily done by
n*myelipse, but what about increasing the line thickness?

I assume there must be another package beyond standard add-ons
that can allow both of these tasks?

By the way I'm actually rotating complicated looking parametric equations
following other parametric equations, I just thought a circle and elipse
would be easy to visualize.  Thus a solution that would work for any object
to follow the path around any other object with orientation towards the
origin would be ideal.  For example, a W looking line rotating around a
circle so the result is a starburst/ray effect.

Thanks,

Dimitri Vorkapich
pennyrue at aol.com
-----------------




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