Generate the motion (Trajectory) of a sphere (or point) with given velocity value

Hi. I have this file 'DATA'. The first 3 columns are the nodes in space (X,Y,Z in [m]). The 4th column is not of interest. The fifth column is the velocity in [m/s].

Is it possible to visualize the motion (green direction) of a sphere (e.g., the red one in the figure) moving following the velocity values in the fifth column of DATA?

load("DATA.mat");

figure
plot3(DATA(:,1),DATA(:,2),DATA(:,3),'-k','LineWidth',0.1);
hold on
plot3(DATA(1,1),DATA(1,2),DATA(1,3),'r.','MarkerSize',30);
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
grid off

Answer 1

[Aquatris]

If you dont care about the actual timing and things, here is one way where the colors of the path indicate the speed and a simple animation show the full motion:

load('data.mat')

x = [DATA(:,1);nan];
y = [DATA(:,2);nan];
z = [DATA(:,3);nan];
v = [DATA(:,5);nan];

l = length(x);
 
figure(1)
for i = 1:1 % change it to 1:l to animate 
   clf
colormap(winter)
patch(x,y,z,v,'Facecolor','none','EdgeColor','interp')
colorbar
view(150,15)
grid on 
grid minor
hold on
plot3(x(i),y(i),z(i),'ro','MarkerSize',15)
hold off
pause(0.1)
end

[Alberto Acri]

Thank you. It might be helpful. If I would like to display multiple 'DATA' matrices present in a cell 'newData_SEL_cell' how can I display the trends simultaneously in the same figure?

I've tried a for loop but it doesn't seem to work the way it's supposed to. Suggestion?

load('newData_SEL_cell.mat')

figure

for S = 1:height(newData_SEL_cell)

    DATA = newData_SEL_cell(S,1);   % 1 e 50
    DATA = cell2mat(DATA);
    
    x = [DATA(:,1);nan];
    y = [DATA(:,2);nan];
    z = [DATA(:,3);nan];
    v = [DATA(:,5);nan];
    l = length(x);
     
    %figure
    for i = 1:l % change it to 1:l to animate 
        clf
        colormap(winter)
        patch(x,y,z,v,'Facecolor','none','EdgeColor','interp')
        colorbar    
        view(150,15)
        grid off 
        %grid minor
        hold on
        plot3(x(i),y(i),z(i),'ko','MarkerSize',2)
        plot3(x(i),y(i),z(i),'ko','MarkerSize',1)
        plot3(x(i),y(i),z(i),'ko','MarkerSize',3)
        hold off
        axis equal
        pause(0.1)
    end


end

[Aquatris]

Assuming each row happens at the same time:

load('newData_SEL_cell.mat')

% get x,y,z,v as cell arrays
x = cellfun(@(x) {[x(:,1);nan]},newData_SEL_cell);
y = cellfun(@(x) {[x(:,2);nan]},newData_SEL_cell);
z = cellfun(@(x) {[x(:,3);nan]},newData_SEL_cell);
v = cellfun(@(x) {[x(:,5);nan]},newData_SEL_cell);

% maximum number of data points in the whole data set
L = max(cellfun(@(A) length(A),x));
 
figure(1)
% loop through data points
for i = 1:1 % change it to 1:(L-1) to animate
   clf
   for j = 1:length(x) % loop through data sets
      colormap(winter)
      patch(x{j},y{j},z{j},v{j},'Facecolor','none','EdgeColor','interp')
      colorbar
      view(150,15)
      grid on
      grid minor
      hold on
      % because the 3 datasets are not the same length we need to check
      if (length(x{j}) >= i) % check if we are not at the end point
         plot3(x{j}(i),y{j}(i),z{j}(i),'ro','MarkerSize',15)
      else
         % (end-1) cause last element we put a 'nan' to prevent unnecessary
         % connection between last point and first point during 'patch'
         plot3(x{j}(end-1),y{j}(end-1),z{j}(end-1),'ro','MarkerSize',15)
      end
   end
   hold off
   pause(0.1)
end

Answer 2

[Madheswaran]

Hello,

The data appears somewhat unclear, as it specifies the object's velocity only at certain spatial positions, necessitating some assumptions. Here is the assumption made regarding the object's velocity in the intermediate position between the position mentioned in any two rows:

For the space between DATA(i, 1:3) and DATA(i+1, 1:3), the object is assumed to moving at a constant velocity as described in DATA(i, 5).

Below is a simple script to visualize the object's movement using a loop:

load DATA.mat

figure
plot3(DATA(:, 1), DATA(:, 2), DATA(:, 3));

% changing the aspect ratio and view to get the similar view as the posted image
pbaspect([1 1 4])
view([154.8 19.8])

ln = size(DATA, 1);
time_unit_divisor = 10;

hold on
pt = plot3(DATA(1, 1), DATA(1, 2), DATA(1, 3), 'r.', 'MarkerSize',30);

for i = 2:ln
    distance = norm(DATA(i, 1:3) - DATA(i-1, 1:3));
    velocity = DATA(i-1, 5);
    time_taken = distance/velocity;
    adjusted_time = time_taken/time_unit_divisor;
    
    pause(adjusted_time);
    
    %update the new position
    pt.XData = DATA(i, 1);
    pt.YData = DATA(i, 2);
    pt.ZData = DATA(i, 3);
end

hold off

The above code would produce the plot like this:

You can adjust the speed of the animation by modifying the ‘time_unit_divisor’ variable. To enhance the smoothness of the animation, consider plotting additional points within each iteration by interpolating the intermediate positions of the object.

Hope this answers your question!