This paper presents a new dense method to compute the odometry of a free-flying range sensor in real time. The method applies the range flow constraint equation to sensed points in the temporal flow to derive the linear and angular velocity of the sensor in a rigid environment. Although this approach is applicable to any range sensor, we particularize its formulation to estimate the 3-D motion of a range camera. The proposed algorithm is tested with different image resolutions and compared with two state-of-the-art methods: generalized iterative closest point (GICP)  and robust dense visual odometry (RDVO) . Experiments show that our approach clearly overperforms GICP which uses the same geometric input data, whereas it achieves results similar to RDVO, which requires both geometric and photometric data to work. Furthermore, experiments are carried out to demonstrate that our approach is able to estimate fast motions at 60 Hz running on a single CPU core, a performance that has never been reported in the literature. The algorithm is available online under an open source license so that the robotic community can benefit from it.