In this thesis, we address the problem of completing surfaces representing fabric. Digital objects are either created directly virtually or scanned from real objects. Even today, digital capture is still imperfect, and the resulting surfaces regularly contain holes. In the case of garment scanning, this is particularly true because of the many folds that complicate the capture process.
To solve this problem, we propose two surface completion methods specific to fabric surfaces, which we model as developable surfaces, i.e. surfaces that can be unfolded in the plane without distortion. The first method uses variational geometry approaches, while the second is based on learning. In both cases, we propose to estimate the area and shape of the hole by flattening the region surrounding it in the plane. This allows us to deduce the intrinsic properties of the missing surface. From this information, the first approach uses a tissue model to replace the geometry on the surface in 3D while the second approach involves a network completing partial parametric maps to fill in the surface.