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Communication processes are characterized by three components: the encoding of a message by the sender, the content of the message, and the process of decoding by the receiver. In honeybee waggle dance communication, the dancing bee encodes the vector as defined by the distance and direction of its outbound flight; the content of the message is a vector that defines a location by its endpoint in a rectangular (Cartesian) or circular diagram; and the dance follower (the recruited bee) translates (decodes) this message into search behavior. Analyses of this communication process have so far depended on the experimenter's knowledge of the geographic location of the hive and the feeder. We applied an approach fully independent of the experimenter's knowledge by quantifying the encoding process by video recording the dance behavior (the waggle runs) and tracking the recruits' flights with harmonic radar. The vector code of the dancer and the search pattern of the recruits led to 2D density distributions that are embedded in the landscape. These density maps (heatmaps) of the encoding and decoding processes were compared quantitively. We found (1) a non-linear relation between the distance code (number of waggles per waggle run) and the centroid of the search, (2) the dependence of the search pattern on the landscape structure, and (3) effects of the training procedure of the dancers. Importantly, recruits search more precisely than expected from the distribution of vector endpoints as encoded in the dancers' waggle runs. The high search precision can be modeled by assuming an averaging over eight waggle runs, but other phenomena may also be involved (systematic deviations in the vector code, structure of the landscape memory). The high precision of the recruits' search pattern explains why previous analyses of the dance communication of bees are largely adequate.