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 > >