function [gc,gcquality] = sepcircle(A,xyz,ntries)% SEPCIRCLE : Good great circle for geometric partitioning.%% [gc,gcquality] = sepcircle(A,xyz,ntries)% Generate a great circle on the unit sphere in d dimensions,% trying to find one that gives a good edge separator of the graph A.% "xyz" is the input points, conformally mapped on the unit sphere%       in d-space so that the approximate centerpoint is at the origin.%% We return the best of ntries (default 40) attempts.%% The circle is returned only as a direction, a d-vector normal to its plane.% The second output is the partition quality as measured by sepquality.%% See GEOPART.%% John Gilbert and Shanghua Teng, 1992-1993.% Copyright (c) 1990-1996 by Xerox Corporation.  All rights reserved.% HELP COPYRIGHT for complete copyright and licensing notice.if nargin < 3    ntries = 40;end;[npoints,d] = size(xyz);% For inertial weighting, we weight the randomly chosen great circles% according to a power (say 2) of the inertial matrix of the points.M = (xyz' * xyz) ^ 2;% Now choose all ntries random great circles.  % Each circle is represented by a vector normal to its plane.% Normally distributed points give vectors with uniformly distributed % directions, which we then weight by the matrix M from above.vv = randn(ntries,d) * M;quality = Inf * ones(ntries,1);for i = 1 : size(vv,1)    v = vv(i,:);    if norm(v) ~= 0        quality(i) = sepquality(v,A,xyz);    end;end;[gcquality,i] = min(quality);gc = vv(i,:)';