  Two mobile agents (robots) have to meet in an a priori unknown bounded
terrain modeled as a polygon, possibly with polygonal obstacles. Agents are
modeled as points, and each of them is equipped with a compass. Compasses of
agents may be incoherent. Agents construct their routes, but the actual walk of
each agent is decided by the adversary: the movement of the agent can be at
arbitrary speed, the agent may sometimes stop or go back and forth, as long as
the walk of the agent in each segment of its route is continuous, does not
leave it and covers all of it. We consider several scenarios, depending on
three factors: (1) obstacles in the terrain are present, or not, (2) compasses
of both agents agree, or not, (3) agents have or do not have a map of the
terrain with their positions marked. The cost of a rendezvous algorithm is the
worst-case sum of lengths of the agents' trajectories until their meeting. For
each scenario we design a deterministic rendezvous algorithm and analyze its
cost. We also prove lower bounds on the cost of any deterministic rendezvous
algorithm in each case. For all scenarios these bounds are tight.
