A Minimal Mathematical Model for Conducting Patterns

April 11, 2026 Β· Grace Period Β· + Add venue

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Authors Tom Verhoeff arXiv ID 2604.10356 Category math.HO Cross-listed cs.GR, cs.RO Citations 0
Abstract
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.
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