Abstract: High-level control of fire is very attractive to artists, as it facilitates a detail-free user interface to make desirable flame effects. In this paper, a unified framework is proposed for modeling and animating fire under general geometric constraints and evolving rules. To capture the fire projection on user's model animation, we develop a modified closest-point method (MCPM) to handle dynamic situations while maintaining the robustness of the closest-point method. A control blue core (CBC) is designed and generated automatically from the fire projection at each time step. It translates the geometric constraints and the user-specified evolving rules into implicit control conditions. Our L-Speed function leverages CBC's shape information and conducts the large-scale motion of fire, leaving the basic physically-based model to refine simulation details. The experimental results show the effectiveness of our method for modeling fire propagation along complex curves or surfaces, or forming a flaming shape and following its motion.