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Re: Color grid with x and y args to visualize effects of 2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116584] Re: Color grid with x and y args to visualize effects of 2D
  • From: "Christopher O. Young" <cy56 at comcast.net>
  • Date: Mon, 21 Feb 2011 04:19:14 -0500 (EST)
  • References: <ijo58j$lkg$1@smc.vnet.net>

Finally got a fast grid plot going, thanks to Heike's suggestion to use
ParameterPlot with two parameters and the right Hue ranges.

The following puts up a window with two sliders for visualizing the effects
of a twist added to a rotation, a kind of "pinwheel" effect.

Manipulate[ParametricPlot[
  ( {
     {Cos[(1 + \[ScriptK] Sqrt[u^2 + v^2]) \[Theta]],
     -Sin[(1 + \[ScriptK] Sqrt[u^2 + v^2]) \[Theta]]},
     {Sin[(1 + \[ScriptK] Sqrt[u^2 + v^2]) \[Theta]],
      Cos[(1 + \[ScriptK] Sqrt[u^2 + v^2]) \[Theta]]}
    } ).( {
     {u},{v}
    } ), {v, 0, 1}, {u, 0, 1},
  Mesh -> {20, 20},
  MeshShading -> Table[
    Hue[h, s, 1],
    {h, Range[0, 0.85, 0.85/20]},
    {s, Range[0.1, 1, 0.9/20]}
    ],
  MeshStyle -> None,
  Axes -> False,
  Frame -> False,
  BoundaryStyle -> None,
  PlotStyle -> {Opacity[0.1]}
  ],
 {\[Theta], 0, 2 \[Pi]}, {\[ScriptK], 0, 4}
 ]

A notebook and a picture and are at:

http://home.comcast.net/~cy56/TwistingRotation.nb and
http://home.comcast.net/~cy56/TwistingRotation.png

Wish I could put the rotation into a single function, but then it won't
perform the matrix multiplication correctly.

On 2/19/11 5:15 AM, in article ijo58j$lkg$1 at smc.vnet.net, "Christopher O.
Young" <cy56 at comcast.net> wrote:

> You can see my website at
> http://intumath.org/Math/Geometry/Projective%20geometry/projectivegeomet.htm
> l for an example of the kind of color grid I'm trying to plot. Again, I have
> to be able to transform this via standard matrices, in order to illustrate
> the basics of various transformations. So I need either the x and y
> arguments available, or else I need the t parameter available. Unless
> there's some way in Mathematica to apply transformations in matrix form
> directly to an image.
> 
> Thank you again for any help.
> 
> Chris Young
> cy56 at comcast.net
> 
> 



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