Plotting a 3D matrix on a normal 2D plot

I have a 3D matrix that contains the positions of different objects over time.

There are

• four rows, one for each object
• two colums, giving the xy position of each object
• 5000+ pages, that tracks how these values change over time.

Now I would like to draw these objects on a plot as they change over time. So four points for every page, preferably connected by lines. So I only need a 2D surface.

This is the code that generates the 3D matrix:

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%         PLANETARY MOTION
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %%%%%%%%%%%%%%%%%%%%%%%%%%%

A CLEAN SLATE

    clear
    close all

    %%%%%%%%%%%%%%%%%%%%%%%%%%%

TITLE

      disp('PLANETARY MOTION')
      disp(' ')

    %%%%%%%%%%%%%%%%%%%%%%%%%%%

SETUP

    %%Based on F = G*M*m/r^2
    % Program constants
      delta_t = 0.1;
      t = 1;
      G = 1;

    % In lieu of user input
    nbodies = 4;

    %%INITIAL CONDITIONS %%
      mass = zeros(1,nbodies);    % preallocation of vectors
      position = zeros(nbodies,2);
      distance = zeros(nbodies,nbodies);
      alpha = zeros(nbodies,nbodies);    % xy angle, as seen from body n
      velocity = zeros(nbodies,nbodies);
      acceleration = zeros(nbodies,nbodies);

    % In lieu of user input
      position = [0 0;100 30;500 150;840 325];
      mass = [3 0.01 0.02 0.03];

    %%START LOOP %%
      for t = [1:5000]
         for n = [1:nbodies]
           for m = [1:nbodies]
             if n == m || distance(m,n) > 0      % this hopefully speeds up computation
               distance(n,m) = distance(m,n);
               alpha(n,m) = pi-alpha(m,n);
             else
               distance(n,m) = sqrt( (position(n,1,t)-position(m,1,t))^2 + (position(n,2,t)-position(m,2,t))^2);
               alpha(n,m) = atan( (position(n,1,t)-position(m,1,t)) / (position(n,2,t)-position(m,2,t)) );
             end

             if n ~= m           % only compute necessary elements
               acceleration(n,m) = G*mass(m)/distance(n,m)^2;
               velocity(n,m) = velocity(n,m) + acceleration(n,m)*delta_t;
               position(n,1,t+1) = position(n,1,t) + cos(alpha(n,m))*velocity(n,m)*delta_t;
               position(n,2,t+1) = position(n,2,t) + sin(alpha(n,m))*velocity(n,m)*delta_t;
             else
             end
           end
         end
         distance = zeros(nbodies,nbodies);        % clear the distance matrix for next iteration
       end

    disp('initial positions = ')
    disp(position(:,:,1))
    disp('final positions = ')
    disp(position(:,:,t))

    %%%%TODO    
    %%Fix acceleration (1/r per element)
    %%Make delta_t depend on acceleration. High acc => small delta_t
    %%Only capture certain timesteps for the position vector, not every t

I appreciate any input. Thank you.

Answer 1

[Mike Garrity]

The animatedline function is usually a good tool for this type of problem. Here's an animation of one of your objects:

h = animatedline;
xlim([min(position(1,1,:)), max(position(1,1,:))])
ylim([min(position(1,2,:)), max(position(1,2,:))])
for i=1:size(position,3)
  addpoints(h,position(1,1,i),position(1,2,i))
  drawnow
end

As you can see, it is basically moving in a straight line, so it's not terribly interesting as an animation.

The problem is that your four objects are quite a ways away from each other relative to the amount of motion each one has. This means that if we animate all of them together, we basically don't see anything:

h = [animatedline, animatedline, animatedline, animatedline];
for i=1:size(position,3)
  for j=1:4
      addpoints(h(j),position(j,1,i),position(j,2,i))
  end
  drawnow
end

Another option would be to use markers instead of animatedline.

h = [line('Marker','o'), line('Marker','x'), line('Marker','s'), line('Marker','p')];
for i=1:size(position,3)
  for j=1:4
      h(j).XData = position(j,1,i);
      h(j).YData = position(j,2,i);
  end
  drawnow
end

If we do that, we can at least see where the objects are. But you really can't see any relative motion. That's because the motion is quite small relative to the overall size of the scene.

Hopefully there are some ideas there that can get you started.

[mirshafie]

Thank you so much Mike, this helps a lot.

I'm going to use a lot more data once the program is finished, but this way of plotting will do the job and look beautiful. (I will use the tic/toc trick described here to get a suitable animation speed.)

[Mike Garrity]

Another thing to look at when you're animating while simulating is the new "limitrate" option to drawnow. I talked about that a bit in this post about simulating reaction diffusion systems .

BTW, I'd be interested in seeing what you've built when you're done. It looks like it'll be pretty interesting.