I wrote a function caterpillar that takes arrays of x and y values and plots several circles following the line described by the coordinates. Next I need to write a function that will make the caterpillar move inside a rectangle for an input number of iterations. My problem is that I cannot figure out a simple way to calculate the path it would take. When caterpillar reaches the boundaries of the rectangle it should reflect and go in another direction. I am trying to create the whole trajectory beforehand, put it into an array and then feed to caterpillar. I was thinking of somehow using minus signs as to represent reflections but I don’t know how to update my x and y coordinates appropriately.

This is my current code for the function:

function caterpool(pos,spee,bl,tr,n)
  # pos - initial position
  # spee - speed vector
  # bl - bottom left corner of rectangle
  # tr - top right corner of rectangle
  # n - number of iterations

  line = polyfit([pos(1), spee(1)], [pos(2), spee(2)], 1);
  x = linspace(pos(1), tr(1));
  f = @(x)line(1).*x+line(2);
  y = f(x);

  a = line(1);
  b = line(2);
  xbl = bl(1);
  xtr = tr(1);
  ybl = bl(2);
  ytr = tr(2);
  plot(x,y)
  hold on
  rectangle('Position', [bl(1) bl(2) tr(1)-bl(1) tr(2)-bl(2)]);
  axis equal

  f_x = zeros(1, n);
  f_y = zeros(1, n);
  x0 = pos(1); y0 = pos(2);

  for i=1:n
    f_x(i) = x0;
    f_y(i) = y0;
    x0 += spee(1);
    y0 += f(spee(1));
  endfor

  caterpillar(f_x, f_y, 3)

  # points of intersection with the rectangle boundaries
  disp([ybl-line(2), ybl]);
  disp([ytr-line(2), ytr]);
  disp([xbl, f(xbl)]);
  disp([xtr, f(xtr)]);

This is how caterpillar looks like:

function caterpillar(tx,ty,n)
  if n <= length(tx)
    p = polyfit(tx, ty, length(tx) - 1);
    x1 = linspace(min(tx), max(tx), length(tx));
    y1 = polyval(p, x1);
    plot(x1, y1)

    hold on;
    xc=0; yc=0; r=0.5;
    th = 0:pi/50:2*pi;
    x = r * cos(th) + xc;
    y = r * sin(th) + yc;
    h = zeros(n, 1);
    for i=1:n
      h(i) = plot(x,y);
    endfor

    for k=1:length(x1)
      for i=1:n
        if k>i-1
          set(h(i), 'XData', x + x1(k-i+1));
          set(h(i), 'YData', y + y1(k-i+1));
        endif
      endfor
      pause(0.1);
    endfor
  endif

Could anybody please help or give a hint? Thanks in advance.