Fabricable dihedral Escher tessellations

The growing popularity of 3D digital manufacturing has spurred a high demand for accessible methods for designing and fabricating customized 3D objects. In this paper, we present a novel approach to model and fabricate Escher dual-shape tilings from user-defined shapes. In a nutshell, Escher's dual shape tiling method smoothly transforms one tile pattern into another, generating a dual perception effect of the two shapes. We adapt Escher's dual shape tiling and perception effect to 3D manufacturing. Thus, our method takes two user-defined shapes and computes their dual shape tiling. A key feature of our method is that the dual shape patterns utilize solid and hollow spaces simultaneously. Specifically, our technique maps one shape to solid structure, while the second shape is mapped to hollow background, optimizing both spaces and bringing higher utilization of materials. To conform with 3D printability requirements, our tiling computation accounts for connectivity and strength as well as dense packing for efficiency. Our dual shape tiling algorithm gives rise to novel manufacturing applications such as ornamental texturing with dual perception Escher patterns, decorative window blinds, flexible tiling patterns, and shade effects.