Re: Questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg27288] Re: Questions*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Sat, 17 Feb 2001 03:31:08 -0500 (EST)*References*: <96iq59$d7v@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Tony, Mathematica can do all of these things, with a little programming. Here are some suggestions. Trans, below transforms a function that maps from R2 into R2 into one that goes inside objects and acts appropriately on Points, Lines and Polygons. One issue whether, as here you regard polyagons as rigid or as bendable -- in the latter case we have to replace lines by fine segmets, replace polygons by polygons with disected sides and circles by lines and disks by polygons. The following works also in 3D. Please note that the function from R2 to R2 defined list to list : f[{x,y}] = , not f[x,y] =. Trans[f_][ a:(Polygon|Line)[_]] :=Map[f,a ,{2}]; Trans[f_][ a_Point] :=Map[f,a,{1}] Trans[f_][x_]:= x/.a:(Polygon|Line|Point)[_]:>Trans[f][a] Check the composition rules: Trans[g][Trans[f][Polygon[{{0,0},{1,0},{1,1}}]]] Polygon[{g[f[{0,0}]],g[f[{1,0}]],g[f[{1,1}]]}] Trans[Composition[g,f]][Polygon[{{0,0},{1,0},{1,1}}]] Polygon[{g[f[{0,0}]],g[f[{1,0}]],g[f[{1,1}]]}] Example Make a picture gr=Show[Graphics[{{Hue[.2],Polygon[{{0,0},{1,0},{1,1}}]}, {AbsolutePointSize[22],Hue[0],Point[{.25,.6}]}, AbsoluteThickness[10],Hue[.7], Line[{{0,.5},{1,0}}]}], Frame->True] Define a function f[pnt_]:= {{1,2},{-2,1}}.pnt Apply the function Show[Trans[f][gr]] Try, g[{x_, y_}] := {Sin[x + y], x - y}; in place of f. -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Tony" <tony at magic101.freeserve.co.uk> wrote in message news:96iq59$d7v at smc.vnet.net... > Does mathematica do reflections rotations of a given shape. > I mean if I plot a triangle if I had a fuction such as > > f: R2 --> R2 > (x,y) I--->(y,x) > > Would mathematica do this and would it carry out composite function such as > GoF and FoG etc > > Oh so many questions to ask and so little time to ......... > > Tony > > >