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
>
>
>
>