function H = hatfun(x, t, k)
% HATFUN   Hat function/piecewise linear basis function.
%
% Input: 
%   x      evaluation points (vector)
%   t      interpolation nodes (vector, length n+1)
%   k      node index (integer, in 0,...,n)
%
% Output:
%   H      values of the kth hat function
%
    n = length(t)-1;
    k = k+1;  % adjust for starting with index=1

    % Fictitious nodes to deal with first, last funcs.
    t = [ 2*t(1)-t(2); t(:); 2*t(n+1)-t(n) ];
    k = k+1;  % adjust index for the fictitious first node
    
    H1 = (x - t(k-1))/(t(k) - t(k-1));   % upward slope
    H2 = (t(k+1) - x)/(t(k+1) - t(k));   % downward slope
    
    H = min(H1, H2);
    H = max(0, H);
end