Moire is an appealing visual effect observable when two or more repetitive patterns are superposed. Fabrication of moire effects has already proven to be useful in a range of applications, from art to engineering. Here, we introduce a method for designing and fabricating level-line moires on curved surfaces. These moire shapes are obtained by superposing a partly absorbing layer and a layer formed by an array of cylindrical lenses or by two layers of cylindrical lenses. We formulate the problem of placing an array of cylindrical lenses on a curved surface as a design problem with a small number of dimensions. The range of possible solutions can therefore be explored by a human observer. We demonstrate the quality of our method by rendered simulations and by fabrication. The resulting static displays can be manufactured using different fabrication techniques, from multi-material 3D printing to molding. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement