%*********************************************************************
%Csci 2031
%Assignment 6
%Problem 4
%Basic B-Spline properties
%*********************************************************************
function[]= problem4()
 
for i=0:1:4
        a1=bSpline(3,0,i);%orig---Part A
        a2=bSplineDeriv(3,0,i);%deriv---Part B
        fprintf(' B(3,0,i) = %i \t(deriv)B(3,0,i) = %f\n' ,a1, a2);
end
end

%*************************************************************************
%Recursive function to determine the B-spline of degree k
%*************************************************************************
function[bVal] = bSpline(k,i,x)
if(k==0)
       if(i<= x && x <(i+1) )
            bVal = 1;
       else
           bVal = 0;
       end   
else
       bVal = ( (x-i)./k)* bSpline(k-1, i, x) + (( (i+k+1)-x)./ ((i+k+1) - (i+1)))*bSpline(k-1, i+1, x);
end 
end %End bSpline


%*************************************************************************
%Recursive function to determine the derivative of a B-spline of degree k
%*************************************************************************
function [bVal]= bSplineDeriv(k,i,x)
    if(k==0)
        if(i<=x && x <(i+1))
            bVal=1;
        else
            bVal=0;        
        end      
    else
        bVal = (k./k)*bSplineDeriv(k-1, i, x) - (k./k)*bSplineDeriv(k-1, i+1, x);
    end
end %End bSplineDeriv