function [Ps,As]=singleKnot(ts)
%function [Ps,As]=singleKnot(ts) Construct matrices to handle single knot removal, 
%given the positions of the seven surrounding knots.  

if min(size(ts)) > 1
   error('The input should be a vector.');
end
if max(size(ts)) ~= 7
   error('7 knots are expected for the input.');
end

a2=(ts(4)-ts(1))/(ts(5)-ts(1));
b2=1-a2;
a3=(ts(4)-ts(2))/(ts(6)-ts(2));
b3=1-a3;
a4=(ts(4)-ts(3))/(ts(7)-ts(3));
b4=1-a4;

Ps=[1, 0, 0, 0;b2, a2, 0, 0;0, b3, a3, 0;0, 0, b4, a4;0, 0, 0, 1];
As=pinv(Ps);