% equipartitoin the graph 5.6 into 
% n=4 and n=20 equal length parts

% to do this:
% use part 2 for s = i/n
clear
clc
close all
for n=4:16:20
    for i = 1:n
        s(i+1) = i/n;
    end

    % call part 2 for these s's
    % make a vector of all t_star outputs
    for i = 1:n
        t_stars(i) = part2(s(i));
    end

    % draw  plot for given t's
    x = @(t) .5+.3*t+3.9*t^2-4.7*t^3;
    y = @(t) 1.5+.3*t+.9*t^2-2.7*t^3;
    figure
    hold on
    for i = 1:length(t_stars)
        x_vec(i) = x(t_stars(i));
        y_vec(i) = y(t_stars(i));
    end
    plot(x_vec,y_vec,'bx')
    xlabel('x')
    ylabel('y')
    title(['Number of points= ', num2str(n)])
    axis([0 1.4 0 1.7])
end