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A Minimal Mathematical Model for Conducting Patterns

History and Overview 2026-04-14 v1 Graphics Robotics

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.

Cite

@article{arxiv.2604.10356,
  title  = {A Minimal Mathematical Model for Conducting Patterns},
  author = {Tom Verhoeff},
  journal= {arXiv preprint arXiv:2604.10356},
  year   = {2026}
}

Comments

11 pages, 5 figures

R2 v1 2026-07-01T12:04:35.781Z