How do I ensure that the animation remain within the axis limit?

I defined an axis limit for my simulation. However, after my simulation is running, the animation still goes out of the limit that was set. How can I ensure that my animations stay within the defined axis? I do not want to increase the axis limit, instead I would like to display an error message to show that animation is required to stay within the axis limit that was defined. Thank you

clear;
close all;
%Number of agents
prompt = 'Enter number of Agents: ';
Agents = input(prompt);

if Agents > 200
    error('Error! Too many agents, decrease the number of agents');
end
if Agents < 2
    error('Error! Too little agents, increase the number of agents');
end

%Number of iterations
Step_Num = 600;

%Initial condition
D = 2;
p = 10*randn(D,Agents); %Vector Position p
v = 5*randn(D,Agents); %Vector Velocity v

%Separation/Collision Avoidance
S = 1;        %Controls the distance between agents
              %Bigger number, further the agents are from each other
%Cohesion/Flock Centering
K = 1;        %Controls the collision between the agents
              %Bigger number the smaller the flock
%Alignment/Velocity Matching
M = 1;        %Controls the flock motion

%Separation/Collision avoidance gain
ca = 5;           %Larger gain -- agents more spread out
%Cohesion/Flock centering gain
fc = 0.1;         %Larger gain -- flock centering is smaller

%Time
t = 0.01;

%Accleration of agents
acc = 10;         %Controls the acceleration speed of the agents
%Axis Limit
Li = 50;

%Flocking Model
result = zeros(Step_Num,Agents);
for n=1:Step_Num          %For every iteration from 1 to desired step
s = zeros(D,Agents);      %Collision avoidance vector / Seperation Vector
k = zeros(D,Agents);      %Flock centering vector / Cohesion Vector
vx = sum(v(1,:))/Agents;   %Velocity of X direction
vy = sum(v(2,:))/Agents;   %Velocity of Y direction
m = [-vx;vy];               %Average velocity
norm_m = norm(m);          
if (norm_m > acc)          %If statement to control the acceleration of the 
agents
    m = acc*m/norm_m;
end
for i = 1:Agents          
for j = 1:Agents          
    if i~= j                        %Distance = 0 when i = j (ignore)
        r = (p(:,j)-p(:,i));        %Distance between two points i & j
        d = sqrt(r(1)^2+(r(2)^2));  %Euclidean distance
        s(:,i) = s(:,i) - ca*r/d^2; %Collision avoidance/Seperation
        k(:,i) = k(:,i) + fc*r;     %Flock centering/Cohesion
    end
end
v(:,i) = S*s(:,i)+ K*k(:,i)+ M*m;  %Total Velocity
p(:,i) = p(:,i) + v(:,i)*t;           %New Position formula p = p+vt
end

%Plot simulations
result(D*n-1,:) = p(1,:);
result(D*n,:) = p(2,:);
plot(p(1,:),p(2,:),'k.','LineWidth',3,'Markersize',15);
grid on;
axis([-Li Li -Li Li]);   %Axis limit
xlabel('X-axis')         %X-axis
ylabel('Y-axis')         %Y-axis
title(['Step Number :', num2str(n)]);
F(:,n) = getframe;
end

Answer 1

[Bjorn Gustavsson]

Well you could achieve that by doing something like:

plot(p(1,:),p(2,:),'k.','LineWidth',3,'Markersize',15);
axPcurr = axis;
if axPcurr(1) < -Li || axPcurr(2) > Li axPcurr(3) < -Li || axPcurr(4) > Li
    % Insert whatever limit-breaking handling you desire here
end

But I think a better way of going about this is to let your flock wrap around so that points leaving over an edge would appear at the opposite edge, perhaps something like this (untested):

plot(mod(p(1,:)+Li,2*Li),mod(p(2,:)+Li,2*Li))

Then if you need the tickmark to be exactly for the original points you can set them manually and your flock would never escape.

HTH

[Jaren Ho]

Thank you! The code works. I'm able to show the error message to ensure the animation remains within the specified limits. Now i'm trying to make my animation move in specific direction like north, south, east and west. However, when i set M as positive or negative, the animation only moves northeast for positive and southwest when its negative. How can I edit to make it move a specific direction. Thank you

%Alignment/Velocity Matching
M = 1;        %Controls the flock motion

[Bjorn Gustavsson]

You set m in your code, for the x-component to the negative of the average x-velocity, and the y-component to the average x-velocity. If you want your flock to move in a prescribed direction you have to set your m t something more predictable/prescribed. Maybe you can use something like the average speed and then use that to average velocity vector in your desired direction:

m = v_avg*[cos(phi_dir_of_desire);sin(phi_dir_of_desire)];

HTH

[Jaren Ho]

Thanks! I managed to set the flock to move to 8 different directions. However, im unable to control the acceleration of the flock to move to the specified direction.

%Flock Movement Direction
m = [cos(pi/2); sin(1)];              %North Direction

%Accleration of agents
acc = 5;         %Controls the acceleration speed of the agents 

%Flocking model
for n=1:Step_Num           %For every iteration from 1 to desired step
s = zeros(D,Agents);       %Collision avoidance vector / Seperation Vector
k = zeros(D,Agents);       %Flock centering vector / Cohesion Vector
vx = sum(v(1,:))/Agents;   %Velocity of X direction
vy = sum(v(2,:))/Agents;   %Velocity of Y direction
av = [vx;vy];               %Average velocity
norm_m = norm(av);          
if (norm_m > acc)          %If statement to control the acceleration of the agents
    av = acc*av/norm_m;
end
for i = 1:Agents          
for j = 1:Agents          
    if i~= j                        %Distance = 0 when i = j (ignore)
        r = (p(:,j)-p(:,i));        %Distance between two points i & j
        d = sqrt(r(1)^2+(r(2)^2));  %Euclidean distance
        s(:,i) = s(:,i) - ca*r/d^2; %Collision avoidance/Seperation
        k(:,i) = k(:,i) + fc*r;     %Flock centering/Cohesion
    end
end
v(:,i) = S*s(:,i)+ K*k(:,i)+ M*m*av;  %Total Velocity
p(:,i) = p(:,i) + v(:,i)*t;        %New Position formula p = p+vt
end