Abstract: Modeling lane changes realistically play an important role in traffic animations. Existing models for traffic simulations mostly focus on lane-changing decision-making. They cannot describe how lane-changing processes go on. Though some methods in motion planning can be further used to describe the processes, they are time-consuming. In this paper, we present an all-in-one model for lane-changing animations. We transform all conditions for lane-changing decision-making into constraints on lane-changing trajectories. We use two polynomials designed in moving reference frames to describe the trajectories. The whole lane-changing process, whether it can occur and how it goes on, is determined by whether there is a valid trajectory. It only takes O(1) time for the determination. Experiment results show that our model can describe lane-changing processes realistically and efficiently.