A Minimal Mathematical Model for Conducting Patterns
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914466211299328 |
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| author | Verhoeff, Tom |
| author_facet | Verhoeff, Tom |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10356 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Minimal Mathematical Model for Conducting Patterns Verhoeff, Tom History and Overview Graphics Robotics 00A66 (Primary) 65D07, 65D17 (Secondary) 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. |
| title | A Minimal Mathematical Model for Conducting Patterns |
| topic | History and Overview Graphics Robotics 00A66 (Primary) 65D07, 65D17 (Secondary) |
| url | https://arxiv.org/abs/2604.10356 |