% 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
n=4;
    figure
    for i = 1:n
        s(i) = 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) = part4(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;
    for i=1:100
        cont_x(i) = x(i/100);
        cont_y(i) = y(i/100);
    end
    MakeQTMovie('start','part_4_n_4.mov')
    plot(cont_x,cont_y,'LineWidth',1)
    hold on
    grid on
    x_vec(1) = .5;
    y_vec(1) = 1.5;
    for i = 1:length(t_stars)
        x_vec(i+1) = x(t_stars(i));
        y_vec(i+1) = y(t_stars(i));
    end
    plot(x_vec,y_vec,'rx')
    xlabel('x')
    ylabel('y')
    title(['Number of points= ', num2str(n)])
    axis([0 1.4 0 1.7])
    set(gca, 'Xlim',[0,2],'Ylim',[0,2], 'Drawmode', 'fast','Visible','on')
    axis square
    ball = line('color', 'r', 'Marker','o','Markersize', 10,...
        'LineWidth',2,'erase','xor','xdata',[],'ydata',[]);
    for i = 1:length(t_stars)+1
            set(ball,'xdata',x_vec(i),'ydata',y_vec(i)); drawnow;pause(1)
            MakeQTMovie('addfigure')
    end
    MakeQTMovie('finish')

    n = 20;
        figure
    for i = 1:n
        s(i) = 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) = part4(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;
    for i=1:100
        cont_x(i) = x(i/100);
        cont_y(i) = y(i/100);
    end
    MakeQTMovie('start','part_4_n_20.mov')
    plot(cont_x,cont_y,'LineWidth',1)
    hold on
    grid on
    x_vec(1) = .5;
    y_vec(1) = 1.5;
    for i = 1:length(t_stars)
        x_vec(i+1) = x(t_stars(i));
        y_vec(i+1) = y(t_stars(i));
    end
    plot(x_vec,y_vec,'rx')
    xlabel('x')
    ylabel('y')
    title(['Number of points= ', num2str(n)])
    axis([0 1.4 0 1.7])
    set(gca, 'Xlim',[0,2],'Ylim',[0,2], 'Drawmode', 'fast','Visible','on')
    axis square
    ball = line('color', 'r', 'Marker','o','Markersize', 10,...
        'LineWidth',2,'erase','xor','xdata',[],'ydata',[]);
    for i = 1:length(t_stars)+1
            set(ball,'xdata',x_vec(i),'ydata',y_vec(i)); drawnow;pause(.3)
            MakeQTMovie('addfigure')
    end
    MakeQTMovie('finish')