Re: Geometry- transformations
- To: mathgroup at smc.vnet.net
- Subject: [mg34368] Re: Geometry- transformations
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 17 May 2002 06:30:49 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <abvubg$m53$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
a 2d point {x,y} has the homogen coordinates ph={x,y,1}
a translation is
T.ph
with T={{1,0,tx},
{0,1,ty},
{0,0,1}}
a rotation is
R.ph
with R={{Cos[phi],Sin[phi],0},
{-Sin[phi,Cos[phi],0},
{0,0,1}}
a scaling ist
S.ph
with S={{sx,0,0},
{0,sy,0},
{0,0,1}}
To combine all transformations multiply T.R.S=M
and compute M.ph
finaly return to normal coordinates and strip the
last component.
Regards
Jens
Hrvoje Posilovic wrote:
>
> Dear Mathematica experts,
>
> I am very new Mathematica user and have one problem
> which is for me impossible to solve.
> I must define geometric shape by set of points in XY plane and than rotate
> that shape (points) in steps of 1 deg around Z axis for 3 or 4 revolutions,
> at the same time that
> shape must be resized (magnified) by sale fator R for 1 deg reolution
> step, and translated downward Z axis by translation factor T for 1 deg
> revolution step.
> All three transforations must be done at the same time.
> That will generate shape similat to snail shell.
> At the end must read all coordinate points generated.
> I do not want to render or draw generated shape but only
> to have coordinates of all the points generaded from the
> initial points.
>
> I do not know is it possible to do something like that with Mathematica.
> I will appreciate any help.
>
> Best Regards
> Hrvoje Posilovic
> 10000 Zagreb
> Croatia
> hposilovic at inet.hr
>
> coordinates
> --
> Hrvoje
>
> hposilovic at inet.hr