The current context of biodiversity loss is particularly marked by the Colony Collapse Disorder (CCD) of honeybees due to multiple causes, toxicological, parasitic and viral. The beekeeper has to face these difficulties in order to maintain the population of bees to save the species but also to make its exploitation profitable. According studies, one can understand what is happening inside the hive by observing what is going on outside. In this context, we propose to individually capture by video the flight trajectories of bees and then characterize the pace of the global activity in front of the hive to infer observations that will be consolidated and made available to apicultural data scientists. Thus bee are detected and tracked using image and video processing methods, then the trajectory are modeled. Then, from the extracted data outcome of the videos, curves are fitted as the ideal trajectories of each bee path in order to study and classify their behaviors. Thus, for each tracked bee, the points of extracted centered positions are time-ordered approximated on a plan. The chosen method interpolates the abscissae separately from the ordinates as time-dependent functions before plotting the parametric curve for each bee path individually. Thus, the abscissae as the ordinates are interpolated using cubic splines. The consecutive points to be interpolated are connected by polynomials of degree three. The first and second derivatives of these polynomials must be connected too. This allows the curve to look more natural by avoiding tingling and convexity discontinuities. Finally, it represents the continuity of the speed of the bees too. Experiments on synthetic and real videos show precise detections of the bee paths. Looking forward, through the collected data, the bee behavior could be understood by using machine learning and the semi supervised method must be one way to proceed.