指揮パターンのための最小数学モデル
A Minimal Mathematical Model for Conducting Patterns
指揮動作の幾何学的軌道と時間的パラメータ化を分離した最小数学モデルを提案し、キュービック・エルミート補間とクインティックタイミング則を用いて表現力豊かな指揮ジェスチャを生成する。
著者: Tom Verhoeff
分類: math.HO, cs.GR, cs.RO
原文アブストラクト
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.