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. Copyright © 2014 John Wiley & Sons, Ltd.