The algorithm presented by M. de Berg (ie Trapezoidal Map -> central nodes) is refered to as the "cell-decomposition" method of computing a collision-free path.

Another method, known as one-shot uses visibility graph to compute a path in the free space.







Please enable Java for an interactive construction (with Cinderella).

Yellow path is a shorter path, not THE shortest path.

Now that we have computed a road map and shortest path for a robot R, the next question are:

We now look at Minkowski Sums for the purpose of answering these questions. We will see that the goal is to "expand" the obstacles in P.