adaptivePL.m

function adaptivePL
    t = linspace(0, 7, 1000);          % the default number of points, 100, may be not enough here
    points = refine(t(1), t(end));     % determine the nodes of interpolation 
    plot(points, f(points), 'r-*')     % piecewise linear plot with asterisks for data points
    hold on
    plot(t, f(t))                      % the original function for comparison 
end

function points = refine(x1,x2)
    xm = (x1+x2)/2;
    if abs((f(x1)+f(x2))/2-f(xm)) < .005     % decide whether to subdivide   
        points = [x1, x2];                   % decided not to  
    else
        left = refine(x1,xm);                % decided to divide
        right = refine(xm,x2);
        points = [left, right(2:end)];       % merge without duplication
    end
end

function y = f(x)                            % used f as named function, so it can be accessed from any other function
  y = exp(-x/4).*sin(x.^2+6);
end