Re: Questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg27282] Re: [mg27267] Questions*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sun, 18 Feb 2001 02:52:15 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I am not sure what you mean by "reflections rotations". Do you mean reflections and rotations or just reflections? For rotations you can use the Geometry`Rotations` package or for thre dimensional objects the RotateShape function from the Graphics`Shapes` package. Reflections you have to program yourself, but it is pretty easy. For example, here is a function that will reflect the vector p in the line through the origin determined by the vector v: reflect[p_, v_] := 2(v.p)v/v.v - p Now, suppose yo want to reflect polygons. You can then define: reflectPolygon[p_Polygon, v_] := Map[reflect[#, v] &, p, {2}] Let's see how this works. for example, consider the triangle t1 = Polygon[{{1, 2}, {3, 4}, {4, 1}}]; Now reflect it about the vector {1,1}: t2 = reflectPolygon[p1, {1, 1}] Now you can display them together: Show[Graphics[{t1, t2}], AspectRatio -> Automatic] You can use a similar method to define relections with respect to planes through the orign in three dimensions (given by specifying a normal vector). (Another and equivalent approach is based on defining a reflection matrix, with respect to the standard basis in the 2 or 3 dimensional euclidean space. ) -- Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ on 01.2.16 5:58 PM, Tony at tony at magic101.freeserve.co.uk wrote: > 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 > > > >