function [x_out,y_out]=pseudoKnot(x_cp,y_cp,P,k)
% function [x_out,y_out]=pseudoKnot(x_cp,y_cp,P,k) adds a new knot at
% position k, using the refinement matrix P. 

[s1,s2]=size(P);
if s1 ~= 5 & s2 ~=4
   error('The size of P should be 5x4.');
end

if min(size(x_cp)) > 1
   error('The first parameter should be a vector.');
end
if min(size(y_cp)) > 1
   error('The second parameter should be a vector.');
end

if max(size(x_cp)) ~= max(size(y_cp))
   error('The first two vectors must have the same length');
end

s=max(size(x_cp));
x_out=zeros(1,s+1);
y_out=zeros(1,s+1);
x_out(1:k-3)=x_cp(1:k-3);
y_out(1:k-3)=y_cp(1:k-3);
x_out(k+3:s+1)=x_cp(k+2:s);
y_out(k+3:s+1)=y_cp(k+2:s);
x_out(k-2:k+2)=x_cp(k-2:k+1)*P';
y_out(k-2:k+2)=y_cp(k-2:k+1)*P';