Abstract

Full paper prices: €32 / €24 / €60

Open Access price: €400

Symmetry: Culture and Science
Volume 32, Number 2, pages 177-180 (2021)
https://doi.org/10.26830/symmetry_2021_2_177

GIELIS TRANSFORMATIONS FOR THE AUDIOVISUAL GEOMETRY DATABASE

Dominik Chapman¹, Johan Gielis²

¹ Zurich CH-8037, Switzerland
E-mail: audiovisualgeometry@gmail.com

² Geniaal BV, B-2018 Antwerpen, Belgium

Abstract: This publication introduces the audiovisual geometry database with Gielis transformations as initial records for a prototype of the database. A concise overview is given of the rationale behind the database and studying wave phenomena with Gielis transformations. First results on a form of timbral polyphony observed in Gielis curves and future work are briefly discussed.

Keywords: audiovisual synthesis, geometry, database, Gielis transformations

References:
Chapman, D., Grierson, G. (2014) N-gon waves – audio applications of the geometry of regular polygons in the time domain. Proc. Int. Computer Music Conference/Sound and Music Computing Conf., 1707-1714.

Creese, D. (2010) The Monochord in Ancient Greek Harmonic Science. Cambridge University Press, 409 pp.

Fox, R. (accessed April 19, 2021) Laser Show, Backscatter DVD (2004). https://robinfox.com.au

Gielis, J. (2003) A generic geometric transformation that unifies a wide range of natural and abstract shapes. American Journal of Botany, 90, 3, 333-338. https://doi.org/10.3732/ajb.90.3.333

Gielis, J., Caratelli, D., Fougerolle, Y., Ricci, P.E., Tavkelidze, I., Gerats, T. (2012). Universal natural shapes: From unifying shape description to simple methods for shape analysis and boundary value problems. PloSONE, 7, 9, e29324. https://doi.org/10.1371/journal.pone.0029324

Hohnerlein, C., Rest, M., Smith, J.O. (2016) Continuous order polygonal waveform synthesis. Proc. Int. Computer Music Conference, 533-536.

Ikeshiro, R. (2010) Generative, emergent, self-similar structures: construction in self. Proc. Int. Computer Music Conference, 365-368.

Putnam, L.J. (2012) The Harmonic Pattern Function: A Mathematical Model Integrating Synthesis of Sound and Graphical Patterns. Ph.D. Thesis, Santa Barbara: University of California.

Robert, A. (1994) Fourier series of polygons. The American Mathematical Monthly, 101, 5, 420-428. https://doi.org/10.1080/00029890.1994.11996967

Sampath, J. (accessed April 19, 2021) Din Is Noise. https://dinisnoise.org

Singh, J. (accessed April 19, 2021) Super Sound Shaper. http://flexibeatz.weebly.com/supersoundshaper.html

Vieira-Barbosa, L. (accessed May 7, 2021) Polar Polygon, post February 12, 2013; https://1ucasvb.tumbler.com