A Minimal Mathematical Model for Conducting Patterns

2026/04/11 by Tom Verhoeff · 1 voice
Computer Science · Mathematics · #cs.GR #cs.RO #math.HO

paper · pdf · doi:10.48550/arxiv.2604.10356

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.

Citations

• Bézier and B-Spline Techniques

Discussions

• Tom Verhoeff: A Minimal Mathematical Model for Conducting Patterns https://arxiv.org/abs/2604.10356 https://arxiv.org/pdf/2604.10356 https://arxiv.org/html/2604.10356 [bsky, 1 points, 0 comments]

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