用数学模型精准模拟指挥手势的轨迹与节奏，简洁又富有表现力。
A Minimal Mathematical Model for Conducting Patterns
- 用三次埃尔米特曲线连接准备点与击打点，约束水平切线。
- 五次时间规律控制加减速，单一参数调节匀速与强调的平衡。
- 适合音乐可视化、人机交互研究者，可直接用于网页应用。
我们提出一种极简数学模型，用于生成指挥手势的运动模式，将几何轨迹与时间参数分离。模型基于由准备点与击打点构成的循环序列，通过三次埃尔米特曲线连接，且约束水平切线；同时采用五次时间规律控制加速度与减速度。单一参数调节均匀运动与表现性强调之间的平衡。该模型提供了一种紧凑而富有表现力的指挥动作表示方法。已实现为交互式 Wolfram 演示程序「Conducting Patterns」，并集成于 Crusis 网页应用中。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。