Re: Fit rectangle to set of points
- To: mathgroup at smc.vnet.net
- Subject: [mg69341] Re: Fit rectangle to set of points
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 7 Sep 2006 23:58:11 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <edom0n$hu2$1@smc.vnet.net>
buttgereit at biomediclab.de wrote:
> Dear Group,
>
> I have a set of 2D points given for which I would like to find the
> smallest rectangle circumscribing all the points.
>
> Doing this with a circle instead of a rectangle was easy --- for the
> rectangle I don't see the trick.
>
> Any hints?
>
> TIA + Best Regards,
>
> Peter
>
HI Peter,
Do you mean something like that:
In[1]:=
pts = Table[Random[], {10}, {2}]
Out[1]=
{{0.830387, 0.0810041}, {0.123819, 0.121942},
{0.0578849, 0.938962}, {0.773195, 0.00453692},
{0.858906, 0.0116332}, {0.678336, 0.100916},
{0.862732, 0.780806}, {0.283974, 0.056643},
{0.600934, 0.766803}, {0.242359, 0.669791}}
In[2]:=
xleft = Min[pts[[All,1]]]
Out[2]=
0.0578849
In[3]:=
xright = Max[pts[[All,1]]]
Out[3]=
0.862732
In[4]:=
ybottom = Min[pts[[All,2]]]
Out[4]=
0.00453692
In[5]:=
ytop = Max[pts[[All,2]]]
Out[5]=
0.938962
In[6]:=
ListPlot[pts, Epilog ->
{Line[{{xleft, ybottom}, {xleft, ytop},
{xright, ytop}, {xright, ybottom},
{xleft, ybottom}}]}];
Regards,
Jean-Marc