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

Abstract

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.

Keywords

3D tile / Isohedral tiling / 3D relief on planar surface / Non-periodic tessellation

References

[1] Abdelaal, A. , Gomaa, M. , Xie, Y.M. , 2023. A novel modular technique for manufacturing free-form rammed earth walls. In: Proc IASS Annu Symp., vol. 18, pp. 1-12.

[2] ArchDaily , 2011. Harpa Concert Hall and Conference Centre/Henning Larsen Architects.

[3] Chang, W. , 2018. Application of tessellation in architectural geometry design. In: E3S Web of Conferences. EDP Sciences, vol. 38, 03015.

[4] Chen, R. , Qiu, P. , Song, P. , Deng, B. , Wang, Z. , He, Y. , 2023. Masonry shell structures with discrete equivalence classes. ACM Trans. Graph. 42 (4), 115.

[5] Durn, J. , Behnejad, S.A. , 2021. A New Family of Lattice Domes: Spherical Caps with Aperiodic Tiling. Master dissertation. University of Surrey.

[6] Etherington, R. , 2008. Oxford Street Facade by Future Systems.

[7] Fu, C.W. , Lai, C.F. , He, Y. , Cohen-Or, D. , 2010. K-set tilable surfaces. ACM Trans. Graph. 29 (4), 1- 6.

[8] Gawell, E. , Rokicki, W. , Nowak, A. , 2014. Aperiodic tessellations in shaping the structural surfaces in the contemporary architecture. Journal Biuletyn of Polish Society for Geometry and Engineering Graphics 26, 47- 53.

[9] Grünbaum, B. , Shephard, G.C. , 1987. Tilings and Patterns. Courier Dover Publications.

[10] Howison, M. , Séquin, C.H. , 2009. CAD tools for creating space-filing 3D Escher tiles. Computer-Aided Design and Applications 6 (6), 737- 748.

[11] Huard, M. , Eigensatz, M. , Bompas, P. , 2014. Planar panelization with extreme repetition. In: Advances in Architectural Geometry. Springer, pp. 259-279.

[12] Isenburg, M. , Gumhold, S. , Gotsman, C. , 2001. Connectivity shapes. In: Proceedings Visualization IEEE, pp. 135-552.

[13] Iwamoto, L. , 2013. Digital Fabrications: Architectural and Material Techniques. Princeton Architectural Press.

[14] Lee, T.U. , Liu, Y. , Xie, Y.M. , 2022. Dividing a sphere hierarchically into a large number of spherical pentagons using equal area or equal length optimization. Comput. Aided Des. 148, 103259.

[15] Liu, Y. , Lee, T.U. , Koronaki, A. , Pietroni, N. , Xie, Y.M. , 2023. Reducing the number of different nodes in space frame structures through clustering and optimization. Eng. Struct. 284, 116016.

[16] Lobel, A. , 1997. Formes et structures engendrées par des éléments identiques: famille PNT-POT. group PNT-POT. A. Lobel.

[17] Pellis, D. , Kilian, M. , Wang, H. , Jiang, C. , Müller, C. , Pottmann, H. , 2021. Architectural freeform surfaces designed for cost-effective paneling through mold re-use. In: Proceedings of the Advances in Architectural Geometry, Paris, France, pp. 1-4.

[18] Pottmann, H. , Schiftner, A. , Wallner, J. , 2008. Geometry of architectural freeform structures. In: Symp on Solid and Physical Modeling. Citeseer.

[19] Pugnale, A. , Echenagucia, T.M. , Sassone, M. , 2014. Computational Morphogenesis. Shell Structures for Architecture-form Finding and Optimization, pp. 224-236.

[20] Rezaee Javan, A. , Seifi, H. , Xu, S. , Xie, Y.M. , 2016. Design of a new type of interlocking brick and evaluation of its dynamic performance. In: Proc IASS Annu Symp., vol. 7, pp. 1-8.

[21] Rezaee Javan, A. , Lee, T.U. , Xie, Y.M. , 2021. Creating novel nonperiodic patterns for flat and curved surfaces from a single pentagonal element. In: Proc IASS Annu Symp. Surrey, UK.

[22] Rezaee Javan, A. , Lee, T.U. , Xie, Y.M. , 2022. Dividing a sphere into equal-area and/or equilateral spherical polygons. Journal of Computational Design and Engineering 9 (2), 826- 836.

[23] Schling, E. , 2018. Repetitive Structures - Design and Construction of Curved Support Structure with Repetitive Parameter. Dissertation. Technische Universität München.

[24] Séquin, C.H. , 2008. Intricate isohedral tilings of 3D Euclidean space. In: Bridges Conference, Leeuwarden, Netherlands, pp. 139-148.

[25] Singh, M. , Schaefer, S. , 2010. Triangle surfaces with discrete equivalence classes. In: ACM SIGGRAPH 2010, pp. 1-7.

[26] Takva, Ç. , İlerisoy, Z.Y. , 2023. Structural analysis of steel load-bearing systems using tessellation method in geometric architectural design. Sādhanā 48 (3), 118.

[27] Wang, H. , 2016. The Hall-Room Pattern of Southwestern Minorities’ Traditional Residence. Published by Tongji University Press.

[28] Wang, Z. , Song, P. , Pauly, M. , 2021. MOCCA: modeling and optimizing cone-joints for complex assemblies. ACM Trans. Graph. 40 (4), 1- 4.

[29] Yasseen, A. , 2018. Architecture of the great pyramid of Giza concept and construction. Resource 1 (2), 97- 108.

RIGHTS & PERMISSIONS

The Author(s). Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.