The digital representation of real-world 3D shapes involves the development of powerful algorithms to provide high-quality modeling based on laser scans or a set of multi-view images. This problem is traditionally studied in computer vision, algorithmic geometry, and digital geometry processing, and has even seen renewed interest with the advent of deep neural networks. Most approaches rely on the use of specific a priori assumptions or correspond to a corpus of examples of similar shapes.

In this thesis, we are interested in the reconstruction of specific surfaces that constitute fabrics with local but nevertheless highly structuring a priori assumptions. Fabrics can be seen as surfaces with controlled elasticity and a quasi-developability property. There are approaches for reconstructing the clothing of people in motion, but here we are interested in the static case and in preserving the fine detail of the surface, integrating the smallest folds, potentially down to the relief of the weave. Our goal is to integrate the geometric control of developability and elasticity, but also the physical behavior of fabrics that allows folds to emerge.

In a second section, we will address the case where the scanned surface is no longer a fabric, but an artistic representation of a fabric, such as the toga of a statue, for example. We will study the possible relationships between the exaggeration of folds and the lines of interest that characterize a drape in order to adapt our reconstruction algorithms.

Finally, the third part of the thesis will focus on the generation of drapery for statues by transferring drapery from one statue to another.