Second Order Differential Properties of Tensor Product Fractal Surfaces

Clement Poull, Christian Gentil, Celine Roudet, Lucie Druoton, Michaël Roy

2025

Abstract

Many domains require non-smooth surface geometries: industry with quality control or CAD, computer graphics with geometric texture generation or terrain synthesis... Fractal models like the Iterated Function Systems (IFS) model are capable of generating self-similar multiscale objects, allowing the generation of a large variety of surfaces with non-standard geometries. Preceding works on IFS have demonstrated how to compute and control pseudo-tangents (defined by two different directions for the right and left tangents at each point) everywhere on these nowhere differentiable geometries. The second-order differential form, that provides even more control possibilities, was only proposed for fractal curves via the introduction of the Differential Characteristic Function (DCF). In this paper, we introduce the Surface Differential Characteristic Function (SDCF), an analytical form that helps characterising and analysing the differential properties (tangents and curvatures) of tensor product non-differentiable surfaces. We use the SDCF to compute the pseudo-curvatures for surfaces generated by tensor products of IFS.

Paper Citation

in Harvard Style

Poull C., Gentil C., Roudet C., Druoton L. and Roy M. (2025). Second Order Differential Properties of Tensor Product Fractal Surfaces. In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP; ISBN 978-989-758-728-3, SciTePress, pages 284-291. DOI: 10.5220/0013191700003912

in Bibtex Style

@conference{grapp25,
author={Clement Poull and Christian Gentil and Celine Roudet and Lucie Druoton and Michaël Roy},
title={Second Order Differential Properties of Tensor Product Fractal Surfaces},
booktitle={Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP},
year={2025},
pages={284-291},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013191700003912},
isbn={978-989-758-728-3},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP
TI - Second Order Differential Properties of Tensor Product Fractal Surfaces
SN - 978-989-758-728-3
AU - Poull C.
AU - Gentil C.
AU - Roudet C.
AU - Druoton L.
AU - Roy M.
PY - 2025
SP - 284
EP - 291
DO - 10.5220/0013191700003912
PB - SciTePress