Creating 3D texture tessellation on planar surface using a single tile or a few tiles

Tessellations have been widely used in architectural designs to create visually striking surfaces by repeating a small number of elements. While there has been extensive research on 2D tiling over the past 2000 years, this study focuses on the systematic development of a technique for the modular construction of 2D tiling with 3D texture surfaces using identical tiles, which is of great importance in architectural designs for cost-effective constructions through the mass production of repeating components. This study applies parametric geometrical modelling using Grasshopper scripting to generate a wide range of 3D reliefs on planar surfaces by repeating a single tile or a few different tiles. Based on the findings of this study, it is possible to arrange tiles with an identical 3D texture surface in multiple configurations, resulting in a range of 3D reliefs on tessellated surfaces that exhibit smooth transitions across adjacent tiles. A significant application of this technique is in producing stunning facades and other 3D surfaces using identical modules, offering affordable modular construction through repetition. The study also demonstrates the versatility of the technique by creating various attractive non-periodic 3D surfaces using triangular, square, hexagonal, or even non-regular tiles.