We introduce mesh quilting, a geometric texture synthesis algorithm in which a 3D texture sample given in the form of a triangle mesh is seamlessly applied inside a thin shell around an arbitrary surface through local stitching and deformation. We show that such geometric textures allow interactive and versatile editing and animation, producing compelling visual effects that are difficult to achieve with traditional texturing methods. Unlike pixel-based image quilting, mesh quilting is based on stitching together 3D geometry elements. Our quilting algorithm finds corresponding geometry elements in adjacent texture patches, aligns elements through local deformation, and merges elements to seamlessly connect texture patches. For mesh quilting on curved surfaces, a critical issue is to reduce distortion of geometry elements inside the 3D space of the thin shell. To address this problem we introduce a low-distortion parameterization of the shell space so that geometry elements can be synthesized even on very curved objects without the visual distortion present in previous approaches. We demonstrate how mesh quilting can be used to generate convincing decorations for a wide range of geometric textures.