effectively emulating a laser pointer for my cat using Matlab

Question

I'm trying to write a code using matlab that emulates a laser pointer in a way that my cat will enjoy chasing it on the screen. This is what I've done so far:

figure('menubar','none','color','k')
h = plot(0,'r.','MarkerSize',20);
xlim([-1 1]);  ylim([-1 1])
axis off
phi1=(1+sqrt(5))/2;
phi2=sqrt(3);
step= 0.0001; % change according to machine speed
for t=0:step:100
    set(h,'xdata',sin(t+phi1*t),'ydata',cos(phi2*t))
    drawnow
end

The "issues" with this code are the following:

1. the pointer moves more or less at a constant speed and doesn't slow to a near stop and then unexpectedly proceed.

2. The trajectory is somewhat repeating itself, though I tried to make it using irrational numbers, the overall motions is continuous from right to left. I think a sharper trajectory change will help.

I know this is not a traditional programming question but still I want to solve a programming issue. I'd appreciate your help and of course open to new ways to answer my question that doesn't use the code I added.

Finney

Fantastic project. But at the cost of potentially sacrificing a monitor?! – Chrominance

you could implement the notion of position, velocity, and acceleration, with parameters to control each. Look for inspirations in gamedev.stackexchange.com – Benco

Fun. You might even learn some new stuff in doing it. Simulate a strange attractor or other chaotic attractor. :-) The famous Lorenz attractor is pretty easy to do. Or look into 2-D random walks and Wiener processes for ways to add noise to some other system/process. – Ammons

By the way, to maximize the potential for claw damage, you can make your figure window full screen via: set(gcf,'Position',get(0,'Screensize')); or set(gcf,'Units','Normalized','OuterPosition',[0 0 1 1]);. – Ammons

A chaotic oscillator should suit your needs. Perhaps The Rossler oscillator with appropriate parameters. If that's not weird enough, you can use a more complicated system. – Quincentenary

Don't get too complicated. I'm positive all it would talk is a random walk (still using sine and cosine functions) to address issue 2, and to address issue 1 you can use a series of simple pauses (at random intervals of course) to slow the dot down. – Chrominance

you can add a slow random sign variable to create a discontinuous trajectory via sign flips, and also add a slow random step size modification that will change the effective speed of the pointer... – Halfhour

What sort of cat is it? Siamese cats are typically satisfied by the Lorenz attractor paths, whereas the discerning Russian Blue is more partial to Rossler oscillators proposed by @Nigel. Random Walks would only be suitable for a common moggy. – Herl

Maybe try something like 2D Brown noise? (with bounds that will "kick" the dot if it gets too close to screen borders) – Donndonna

@Herl Wow, how did you know that? – Donndonna

Also, consider using projector instead of monitor. It is safer. One issue though - cat's shadow, but it is not worse than with real laser pointer. – Donndonna

Answer 1

Brilliant question, so good I thought I'd take 15 minutes of my life to have a go myself. After extensive YouTube research on laser technique i thought using the equations of motion to move between random points would work well:

n = 20; %number of steps
pos = [0,0]; % initial position
vel = 4; % laser velocity
acc = 400; % laser acelertation
dt = 0.01; % timestep interval
figure
set(gcf,'Position',get(0,'Screensize'));
for i=1:n
    point = rand(1,2);
    dist = 1;
    while dist > 0.05 % loop until we reach the point
        plot(pos(1),pos(2),'o','color','r','MarkerFaceColor','r')
        axis equal
        xlim([0,1])
        ylim([0,1])
        drawnow
        % create random point to move towards
        dist = pdist([point;pos],'euclidean');
        % calculate the direction & mag vector to the point
        dir = (point-pos)/norm((point-pos));
        mag = norm(point-pos);
        % update position
        displ = vel*dt - 0.5*acc*mag*dt^2;
        pos = pos + dir*displ;
    end
end

Play around with the parameters till you find something your cat likes :0)

Getaway

For more natural movements, I suggest not using a normal distribution, but a power law, or Levy distribution. A log-normal distribution would work in a pinch, too. – Quincentenary

I tried the normal distribution, but I still prefer the uniform distribution! I suppose the real arbiter has to be the cat, although I'm not sure how you would setup a quantitative experiment to asses this...! – Getaway