We present a minimal mathematical model for conducting patterns that separates geometric trajectory from temporal parametrization. The model is based on a cyclic sequence of preparation and ictus points connected by cubic Hermite segments with constrained horizontal tangents, combined with a quintic timing law controlling acceleration and deceleration. A single parameter governs the balance between uniform motion and expressive emphasis. The model provides a compact yet expressive representation of conducting gestures. It is implemented as the interactive Wolfram Demonstration "Conducting Patterns" and is used in the Crusis web app.

翻译：我们提出了一个用于指挥模式的最小数学模型，该模型将几何轨迹与时间参数化分离。该模型基于由三次埃尔米特线段（带有水平切线约束）连接的准备点和击拍点循环序列，并结合了控制加速与减速的五次时序法则。单一参数用于调节匀速运动与表现性强调之间的平衡。该模型提供了一种紧凑且具有表现力的指挥手势表征。其实现在交互式Wolfram演示《指挥模式》中，并应用于Crusis网络应用程序。