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In order to ensure safe lane change and avoid traffic accidents, an effective lane change assist system is required. In a lane change assist system, it is very important to obtain the following elements in time, such as actual distance between vehicles, minimum safety distance, and warning signal. To this end, this paper analyzed four kinds of lane change angle collision scenes. Initial position, initial velocity, acceleration, heading angle, and kinematics of vehicles were used to calculate the position of potential angle collision points between lane change vehicle and obstacle vehicles. Then, actual distance model was constructed based on potential angular collision points. The minimum safety distance model was also established under the two most unfavorable conditions. In order to achieve the lane change warning, three early warning rules were formulated. We verified the validity of models and early warning rules using vehicle driving video data of Interstate 80 in California. Models and early warning rules constructed in our research can be applied to the advanced active safety systems of vehicle, such as vehicle lane change assist system and active collision early warning system, which can improve the active safety and reduce traffic accidents. [ABSTRACT FROM AUTHOR]