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Nodes in contention-based (beaconless) georouting forward packets towards a known destination position without the knowledge of the neighborhood. The only existing methods that guarantee delivery in unit disk graphs (UDG) require runtime planarization of the communication graph with either unbounded message overhead per hop while preserving the Gabriel graph property of the subgraph, or a constant overhead per hop with up to 13 control messages. In this paper we show that the next hop can be selected directly by a contention mechanism and without prior planarization. Existing greedy routing methods select the next hop with 3 messages using a RTS-CTS-DATA scheme in a timer-based contention where only the next hop neighbor responds. We extend this to provide also recovery from local minima with 3 messages per hop by the Rotational Sweep algorithm. We prove that our algorithm guarantees delivery in UDGs, and also yields routes that are shorter than or equal to the combined greedy and face routing with Gabriel graph planarization. Simulation results show that especially the duration of the contention process can be significantly reduced. Our algorithm can be also used for conventional beacon-based routing with guaranteed delivery without prior planarization, replacing the complicated implementation from by a very simple method which evaluates angular distances to select the proper forwarding neighbor. It also provides a simple network boundary detection algorithm, with or without beacons.