function [U, V] = nobasis(A, ia)
%NOBASIS Column space basis with SNNN and NO properties.
% [U, V] = NOBASIS(A, inter_active)
[U, V] = nobasis(A, ia);
[sor, dim] = size(U);
if dim==2
P = [1 0; -1 1];
XM = U/P;
mine = min(XM(:,2));
maxe = max(XM(:,2));
TG = [1 mine; 1 maxe];
elseif dim==3
P = [1 0 0; -1 1 0; 0 -1 1];
XM = U/P;
x = XM(:,2); %x=XM(1:10,2);
y = XM(:,3); %y=XM(1:10,3);
figure(2);
plot(x,y,'x');
hold on;
G = XM;
n1 = size(U, 1);
Igo = input('input: 1->input 3 row #, 2->Geometric Geometry , 3->input 3 points, ');
if Igo==1
Imin = input('Input convex Hull #1: ');
Imed = input('Input convex Hull #2: ');
Imax = input('Input convex Hull #3: ');
TG = G([Imin Imed Imax],:);
elseif Igo==2
m1 = (G(2,3)-G(1,3))/(G(2,2)-G(1,2));
m2 = (G(n,3)-G(n-1,3))/(G(n,2)-G(n-1,2));
x = (m1*G(1,2)-m2*G(n-1,2)-(G(1,3)-G(n-1,3)))/(m1-m2);
y = m1*(x-G(1,2))+G(1,3);
TG = [G(1,:);G(n,:);1 x y];
elseif Igo==3
Imin = input('Input point #1: ');
Imed = input('Input point #2: ');
Imax = input('Input point #3: ');
TG = [1 Imin;1 Imed;1 Imax];
end
figure(2)
TTT = [TG;TG(1,:)];
% subplot(3,2,1)
plot(TTT(:,2),TTT(:,3),'g')
hold off;
else
error('dimension error: dim = %d', dim);
end
U = XM/TG;
V = TG*P*V;
%h=max(max(abs(Y-U*V)))
