Lecture 6¶

Q 6.1¶

Question¶

Task: Plot mobious strip in 3D, using method described as the following:

1. Draw a circle in the x-y plane
2. Draw a vertical line at the beginning of the circle, rotate it around the circle, and draw the path of the line

Requirements:

A GIF animation of the process.

Solution¶

The code is pretty much self-explanatory with the comments.

In [ ]:

% goal: plot mobious strip.

% details:
%
% 1. in 3d, draw x^2 + y^2 = 1 as the base.
% 2. for every t in [0,2pi) corresponding to the point (cos(t), sin(t)),
% 3. draw a line that have slope (=t, in radian) and pass through the point, with a length of 2.
% 4. now, split t into 2pi/1000, and repeat 2-3.
% 5. create image for every t, and save it as a gif.

line_length=0.2;
image_count=100;

for i=1:image_count
    step = 2*pi/image_count;
    t_end = i * step;

    % circle
    t=0:0.01:2*pi;
    x=cos(t);
    y=sin(t);
    z=zeros(size(t));
    plot3(x,y,z,'k','LineWidth',2);
    hold on;

    % lines
    for t=0:0.05:t_end
        x=[cos(t)*(1-line_length*sin(t/2)), cos(t)*(1+line_length*sin(t/2))];
        y=[sin(t)*(1-line_length*sin(t/2)), sin(t)*(1+line_length*sin(t/2))];
        z=[-line_length*cos(t/2), line_length*cos(t/2)];
        plot3(x,y,z,'k','LineWidth',2);
    end

    % plotting:
    grid on;
    daspect([1 1 1])
    drawnow;
    frame = getframe(1);
    im = frame2im(frame);
    [imind,cm] = rgb2ind(im,256);
    if i == 1
      imwrite(imind,cm,'math-expt/week_3/imgs/Q6_1.gif','gif', 'Loopcount',inf);
    else
      imwrite(imind,cm,'math-expt/week_3/imgs/Q6_1.gif','gif','WriteMode','append');
    end
end

% goal: plot mobious strip. % details: % % 1. in 3d, draw x^2 + y^2 = 1 as the base. % 2. for every t in [0,2pi) corresponding to the point (cos(t), sin(t)), % 3. draw a line that have slope (=t, in radian) and pass through the point, with a length of 2. % 4. now, split t into 2pi/1000, and repeat 2-3. % 5. create image for every t, and save it as a gif. line_length=0.2; image_count=100; for i=1:image_count step = 2*pi/image_count; t_end = i * step; % circle t=0:0.01:2*pi; x=cos(t); y=sin(t); z=zeros(size(t)); plot3(x,y,z,'k','LineWidth',2); hold on; % lines for t=0:0.05:t_end x=[cos(t)*(1-line_length*sin(t/2)), cos(t)*(1+line_length*sin(t/2))]; y=[sin(t)*(1-line_length*sin(t/2)), sin(t)*(1+line_length*sin(t/2))]; z=[-line_length*cos(t/2), line_length*cos(t/2)]; plot3(x,y,z,'k','LineWidth',2); end % plotting: grid on; daspect([1 1 1]) drawnow; frame = getframe(1); im = frame2im(frame); [imind,cm] = rgb2ind(im,256); if i == 1 imwrite(imind,cm,'math-expt/week_3/imgs/Q6_1.gif','gif', 'Loopcount',inf); else imwrite(imind,cm,'math-expt/week_3/imgs/Q6_1.gif','gif','WriteMode','append'); end end