Carving 2D image onto 3D curved surface using hybrid additive and subtractive 3D printing process

The objective of this paper is to describe that carve 2D image on the 3D curved surface based on surface flattening using hybrid 3D printing approach. Customized logo or trademark is supposed to be displayed on the surface of products, which cannot be completed only by 3D printing techniques. Projection algorithm, which transfers the 2D image to 3D sticker that matches the surface of products, is one of the techniques to satisfy this demand. In this paper, we propose a novel surface flattening algorithm that combines conformal mapping with optimal adjuster based on edge-lengths of the original mesh. By using the proposed algorithm, the surface of 3D model is unfolded. A two dimensional data or figure is mapped onto the unfolded plane. After the plane is mapped onto the 3D surface, a path for carving is obtained to sculpture the indicated figure onto the model. Moreover, compared with the several surface flattening methods, the proposed algorithm can minimize distortion while transferring 2D figure to 3D sticker. Furthermore, the algorithm is physically experimented to proof of the concept on the gantry-type hybrid machine developed in our NTU lab which integrates the additive (3D printing) and the subtractive (carving) process.