There is a polygon with N(N>=4)vertexs,how to use a
minimum circle to cover the polygon,(the vertexs is allowed
to be on the circle)?I don't know how to find the centre
and the minimum radius of the circle.Help me please.Anyone
who knows how to solve it can post your algorithm or your
code here or mail to lee_0560@sina.com.cn. Thanks a
lot!

try every triangle from that N pts.
With a triangle ABC, If the all the angels <= 90, you find
the R = radius of the circle cover it. If one is greater
than 90, for instant it's A > 90, so you chose R = BC/2.
The maximum R is the number you must find. i think so :-/

QH@

> try every triangle from that N pts.
> With a triangle ABC, If the all the angels <= 90, you
find
> the R = radius of the circle cover it. If one is greater
> than 90, for instant it's A > 90, so you chose R = BC/2.
> The maximum R is the number you must find. i think so :-/
>
> QH@
Thanks,but how to find the centre of the circle?

with my algorithm, with each triangle, when you find out
the radius R, u have the centre of circle for it, if you
update the value of R, u also update the coordinate of the
centre point,

good luck !

QH@

> with my algorithm, with each triangle, when you find out
> the radius R, u have the centre of circle for it, if you
> update the value of R, u also update the coordinate of
the
> centre point,
>
> good luck !
>
> QH@
Oh,I see,but can you prove your algorithm for me please?i.e
How can you know that the circle with the centre and the
radius can cover all the vertices?Thanks again.

> > with my algorithm, with each triangle, when you find
out
> > the radius R, u have the centre of circle for it, if
you
> > update the value of R, u also update the coordinate of
> the
> > centre point,
> >
> > good luck !
> >
> > QH@
> Oh,I see,but can you prove your algorithm for me please?
i.e
> How can you know that the circle with the centre and the
> radius can cover all the vertices?Thanks again.

First check every two vertext, if the segment formed by them
can be a diameter of a circle that covers all others then
this is tha answer. Therwise check all triangles by finding
the center of their thricirles (orthocenters).
To find the center of the orthocenter of a triangle, choose
to sides, create thair simetrals, the cross point is your
aim.