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Authors: Mohamad Janbein ; Christian Gentil ; Céline Roudet and Clement Poull

Affiliation: Laboratoire d’Informatique de Bourgogne (LIB), Université de Bourgogne, 9 Av. Alain Savary, 21000 Dijon, France

Keyword(s): Curve, Fractal Geometry, Iterated Function System (IFS), Nowhere Differentiability, Tangent, Curvature.

Abstract: Fractal geometry is a valuable formalism for synthesizing and analyzing irregular curves to simulate non-smooth geometry or roughness. Understanding and controlling these geometries remains challenging because of the complexity of their shapes. This study focuses on the curvature of fractal curves defined from an Iterated Function System (a set of contractive operators). We introduce the Differential Characteristic Function (DCF), a new tool for characterizing and analyzing their differential behavior. We associate a family of DCF to the fixed point of each operator. For each dyadic point of the curve, there exist left and right families of DCF inducing left and right ranges of curvatures: the pseudo-curvatures. A set of illustrations shows the influence of these pseudo-curvatures on the geometry of fractal curves. We propose a first approach for applying our results to roughness generation and control.

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Paper citation in several formats:
Janbein, M.; Gentil, C.; Roudet, C. and Poull, C. (2024). Pseudo-Curvature of Fractal Curves for Geometric Control of Roughness. In Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - GRAPP; ISBN 978-989-758-679-8; ISSN 2184-4321, SciTePress, pages 177-188. DOI: 10.5220/0012574800003660

@conference{grapp24,
author={Mohamad Janbein. and Christian Gentil. and Céline Roudet. and Clement Poull.},
title={Pseudo-Curvature of Fractal Curves for Geometric Control of Roughness},
booktitle={Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - GRAPP},
year={2024},
pages={177-188},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012574800003660},
isbn={978-989-758-679-8},
issn={2184-4321},
}

TY - CONF

JO - Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - GRAPP
TI - Pseudo-Curvature of Fractal Curves for Geometric Control of Roughness
SN - 978-989-758-679-8
IS - 2184-4321
AU - Janbein, M.
AU - Gentil, C.
AU - Roudet, C.
AU - Poull, C.
PY - 2024
SP - 177
EP - 188
DO - 10.5220/0012574800003660
PB - SciTePress

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