%CreateBkN.m
%Math 128B Spring 2005
%Returns B1(i,j)=Bjk(Xi)
% =j'th B-spline (k > 1) evaluated at Xi

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Functions called:
%BSpline, CreateOmega

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function	[X, B1]	= CreateBkN(knots, k, N)

%X	= knots(1):h:knots(end);
knotN	= length(knots);
X	= [];
for j=2:knotN
	h	= (knots(j)-knots(j-1))/(N-1);
	X	= [X(1:end-1) knots(j-1):h:knots(j)];
end

%create B1 whose (i,j) entry is Bj,1(Xi)
B1	= BSpline(X, knots);

for K=2:k
	B	= B1;
	%create Omega and then B2 whose (i,j) entry is Bj,k(Xi)
	w	= CreateOmega(X, knots, K);
	B1	= B(:,1:end-1) .* w(:,1:end-1) + B(:,2:end) .* (1 - w(:,2:end));
end

return