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%%%%%% Homework #10.3 Code Fragment %%%%%%%%%%%%%%%%
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%On entry, variables "k, t, & a" must be provided
%Assumes you provide routines:
%[T, A]		= KnotInsertion(k, t, a, x);
%[Tstar, Astar]	= ControlPolygon(k, t, a);
%You will also need to include in your project the files:
% CreateBk.m, CreateOmega.m, BSpline.m
%  which can be obtained from my webpage
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% To experiment with other F's
%  can uncomment the following line
%a	= rand(1,length(t)-k);

%initialization for knot insertions
Count	= 30;
xrand	= t(1) + (t(end)-t(1)) * rand(1,Count);

%X-discretization for spline creation
h	= 0.01;

figure(99)
for i=1:Count
	%insert next random knot
	x		= xrand(i);
	[t, a]		= KnotInsertion(k, t, a, x);
	[Tstar, Astar]	= ControlPolygon(k, t, a);

	%create the B-spline Bjk (k=4)
	[X, B4]	= CreateBk(t,k,h);

	%create f=sum Aj * Bjk
	F	= repmat(a, length(X), 1);
	F	= F .* B4;
	f	= sum(F');

	%plot resulting spline (these should all = the same f!!)
	% and new control polygon
	plot(X, f, 'k', Tstar, Astar, 'm');
	pause(0.2);
end