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

*To*: mathgroup at smc.vnet.net*Subject*: [mg116577] Re: Color grid with x and y args to visualize effects of 2D transformations?*From*: Heike Gramberg <heike.gramberg at gmail.com>*Date*: Sun, 20 Feb 2011 05:26:54 -0500 (EST)

I'm not entirely sure how you want to use your function, but if you're interested in drawing the image of a rectangular grid after a 2D transformation you could do something like this: mesh[fx_, fy_, opts___] := ParametricPlot[{fx[x, y], fy[x, y]}, {x, 0, 1}, {y, 0, 1}, Mesh -> 9, MeshShading -> Table[Hue[xi, (1 - yi), 1], {yi, Range[0, 1, 1/10]}, {xi, Range[0, 1, 1/10]}], opts] This would draw the image of the square 0<x,y<1 with a 10x10 coloured grid under the mapping {x,y}->{fx[x,y],fy[x,y]}. Heike. On 19 Feb 2011, at 10:15, Christopher O. Young wrote: > I'm trying to get a simple kind of color chart function that I can pass x > and as arguments to. I want to have it running across by hue and up by > saturation and value. This is to illustrate 2D transformations, so I need to > have arguments that I can _inversely_ transform in order to illustrate the > effects of 2D transformations, whether linear or not. > > One direct approach would seem to have nested loops, but I can't see how to > do this if the body of the For loop in Mathematica is part of the function. > > Any help getting a "jump start" in this kind of thing would be a huge help > to me. > > For[i = 0, i < 10, i++, > > For[j = 0, j < 10, j++, > > RegionPlot[(i < x < i + 1) && (j < y < j + 1), {x,0,10}, {y,0,10}] > > ] > > ] > > Chris Young > cy56 at comcast.net > >