2D Collision Detection

Hello Guys,

I am doing a collision analysis in 2D. More precisely, I analyse the movement of a specific robot head on a concave tool. I have already programmed the movement of the robot head on the tool surface. The latter is parameterized over its whole length with an aequidistant parameter t. The robot heads geometry is defined by a set of x-y-coordinates. The collision is analyzed as follows: I analyze for each parameter (first loop) the intersection of two point-pairs of each the tool (ax = x(t), bx = x(t+1), ay = y(t), by = y(t+1) -> second loop) and the robot head (cx = x(j), dx = x(j+1), cy = y(j), dy = y(j+1) -> third loop). Then I calculate the following:

      a = ax - bx;
      b = movement_geometry(i+1,1) - movement_geometry(i,1);
      c = az - bz; 
      d =  movement_geometry(i+1,2) - movement_geometry(i,2);
      e = ax - movement_geometry(i,1);
      f = az - movement_geometry(i,2);
      if i == 560
          j = 1;
      end

      det = a * d - b * c;
      s = 1 / det * ( d * e - b * f);
      t = 1 / det * (-c * e + a * f);

      if (s <= 1 && s >= 0 ) && (t <= 1 && t >= 0)
          collision_boolean = 1;
          break
      else
          collision_boolean = 0;
      end
  end

This concept works, but as you can expect, it is very very slow. Is there a way to avoid the loops. The parameter t is of the size 300, the size of the robot head is 4000. Thus, there are 300*300*4000 steps to compute....

I cant find a way to analyze the stuff with simple matrix operations, do you have some better ideas or alternative ways for this computation?

Thanks in advance, I am looking forward to your help!

Best Wishes, Georg

[Michael]

You are missing the top of the loop and some toy values for the variables. There are a stack of strategies. You could compile the code. You could vectorize it. You could pre-compute and make it a table lookup. You are probably much better off to rely on built-ins than on homebrew, so use an builtin determinant. Do you know "movement geometry" before the loop? If so then you can pull a...f out of the loop. Why are you resetting "j" at 560? Do you predeclare your variables?