Question about matrix representations of certain points

Akin Babayigit akin.babayigit at
Wed Nov 26 19:28:18 PST 2003

Hi All, 

I have a question that I have been dealing with and I thought I could 
get some help here.  It is as follows: 

I have n points in the plane and I know all of their x-y coordinates.   
Each point is the center of a circle with radius 'r'.  For simplicity 
let me continue by considering only three points n1,n2,n3 (Although 
eventually I would like to work with an arbitrary number of points). 
n1's coordinates are (x1,y1), n2's are (x2,y2) and n3's are (x3,y3). 

These points are the centers of three circles C1,C2,C3.  Let us assume 
also that the intersection of these circles are non-empty.   

What I would like to be able to do is figure out the coordinates of a 
point (x,y) such that I can write x = [h1 h2 h3]*[x1 x2 x3]'   and 
y = [k1 k2 k3]*[y1 y2 y3]' 

such that: 
1)  (x,y) is either in the intersection C1,C2,C3 or in the smallest 
circle containing the convex hull if points n1,n2,n3 

2)  AND h1+h2+h3 = 1 and k1+k2+k3=1.  i.e.:  eventually i will have n 
of these points (points with locations x,y) and the I want the matrices 
K and H to be stochastic. 

Any thoughts would be greatly appreciated.   

Thank you for your time in advance, 

Akin Babayigit 

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