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Reducing the Number of Different Faces in Free-Form Surface Approximations Through Clustering and Optimization

Published: 01 January 2024 Publication History

Abstract

Free-form structures are highly valued for their aesthetic appeal in architecture, but they typically comprise panels of many different shapes, which can pose great challenges for building construction. In this study, we aim to address this issue by proposing a novel clustering–optimization method to reduce the number of different n-gonal faces in free-form surface approximations. The method partitions the faces into several groups of similar shapes through clustering and transforms the ones within each group toward congruent forms through optimization. By utilizing this approach, the number of geometrically different panels can be reduced while also satisfying a user-specified error threshold. The potential practical application of this method is demonstrated by redesigning the façade of a real architectural project to achieve cost-effective solutions.

Highlights

This study reduces the number of different faces in free-form surface approximations.
The proposed method is based on an iterative clustering-and-optimization strategy.
The proposed method can be applied to geometries composed of general n-gons.
The practical relevance of the method is demonstrated by redesigning a real project.

References

[1]
Adriaenssens S., Block P., Veenendaal D., Williams C., Shell structures for architecture: form finding and optimization, Routledge, 2014, ISBN 978-0415840606.
[2]
Li Q., Su Y., Wu Y., Borgart A., Rots J.G., Form-finding of shell structures generated from physical models, Int J Space Struct 32 (1) (2017) 11–33,.
[3]
Wang H., Pellis D., Rist F., Pottmann H., Müller C., Discrete geodesic parallel coordinates, ACM Trans Graph (ISSN ) 38 (6) (2019) 1–13,.
[4]
Austern G., Capeluto I.G., Grobman Y.J., Rationalization methods in computer aided fabrication: A critical review, Autom Constr (ISSN ) 90 (2018) 281–293,.
[5]
Pottmann H., Asperl A., Hofer M., Kilian A., Architectural geometry, Bentley Institute Press, Exton, Pennsylvania, 2007, ISBN 978-1934493045.
[6]
Pottmann H., Eigensatz M., Vaxman A., Wallner J., Architectural geometry, Comput Graph (ISSN ) 47 (2015) 145–164,.
[7]
Liu Y., Pottmann H., Wallner J., Yang Y.-L., Wang W., Geometric modeling with conical meshes and developable surfaces, ACM Trans Graph (ISSN ) 25 (3) (2006) 681–689,.
[8]
Huang W., Wu C., Hu J., Gao W., Weaving structure: A bending-active gridshell for freeform fabrication, Autom Constr (ISSN ) 136 (2022) pp. 104184,.
[9]
Schling E., Repetitive structures, [Ph.D. thesis] Technische Universität München, 2018.
[10]
Castañeda E., Lauret B., Lirola J., Ovando G., Free-form architectural envelopes: Digital processes opportunities of industrial production at a reasonable price, J Facade Design Eng 3 (1) (2015) 1–13,.
[11]
Fu C.-W., Lai C.-F., He Y., Cohen-Or D., K-set tilable surfaces, ACM Trans Graph (ISSN ) 29 (4) (2010) 1–6,.
[12]
Brownell P., Merchant K.A., The budgetary and performance influences of product standardization and manufacturing process automation, J Account Res 28 (2) (1990) 388–397,.
[13]
Baud-Lavigne B., Agard B., Penz B., Mutual impacts of product standardization and supply chain design, Int J Prod Econ 135 (1) (2012) 50–60,.
[14]
Koronaki A., Shepherd P., Evernden M., Rationalization of freeform space-frame structures: Reducing variability in the joints, Int J Architect Comput 18 (1) (2020) 84–99,.
[15]
Brütting J., Senatore G., Fivet C., Design and fabrication of a reusable kit of parts for diverse structures, Autom Constr (ISSN ) 125 (2021) pp. 103614,.
[16]
Lu H., Xie Y.M., Reducing the number of different members in truss layout optimization, Struct Multidiscip Optim 66 (3) (2023) 52,.
[17]
Lee T.-U., Liu Y., Xie Y.M., Dividing a sphere hierarchically into a large number of spherical pentagons using equal area or equal length optimization, Comput Aided Des (ISSN ) 148 (2022),.
[18]
Liu Y., Lee T.-U., Rezaee Javan A., Xie Y.M., Extending goldberg’s method to parametrize and control the geometry of goldberg polyhedra, Royal Soc Open Sci 9 (8) (2022) pp. 220675,.
[19]
Zimmer H., Lafarge F., Alliez P., Kobbelt L., Zometool shape approximation, Graph Models (ISSN ) 76 (5) (2014) 390–401,.
[20]
Liu Y., Lee T.-U., Koronaki A., Pietroni N., Xie Y.M., Reducing the number of different nodes in space frame structures through clustering and optimization, Eng Struct (ISSN ) 284 (2023),.
[21]
Lobel A., Lobel frame, 2005, URL https://www.equilatere.net. [Accessed on 17 February 2023].
[22]
Huard M., Eigensatz M., Bompas P., Planar panelization with extreme repetition, in: Advances in architectural geometry 2014, London, England. Springer, Cham, Switzerland, ISBN 978-3-319-11418-7, 2015, pp. 259–279,. September 2014.
[23]
Jiang C., Tang C., Tomičí M., Wallner J., Pottmann H., Interactive modeling of architectural freeform structures: Combining geometry with fabrication and statics, in: Advances in architectural geometry 2014, London, England. Springer, Cham, Switzerland, 2015, pp. 95–108,. September 2014.
[24]
Eigensatz M., Kilian M., Schiftner A., Mitra N.J., Pottmann H., Pauly M., Paneling architectural freeform surfaces, ACM Trans Graph (ISSN ) 29 (4) (2010) 1–10,.
[25]
Singh M., Schaefer S., Triangle surfaces with discrete equivalence classes, ACM Trans Graph (ISSN ) 29 (4) (2010) 1–7,.
[26]
Liu Z., Zhang Z., Zhang D., Ye C., Liu L., Fu X.-M., Modeling and fabrication with specified discrete equivalence classes, ACM Trans Graph (ISSN ) 40 (4) (2021) 1–12,.
[27]
Li Y., Liu Y., Wang W., Planar hexagonal meshing for architecture, IEEE Trans Vis Comput Graphics 21 (1) (2015) 95–106,.
[28]
Jiang C., Tang C., Vaxman A., Wonka P., Pottmann H., Polyhedral patterns, ACM Trans Graph (ISSN ) 34 (6) (2015) 1–12,.
[29]
Sidelko J., Museo Soumaya: facade design to fabrication, Lulu. com, 2013, ISBN 978-1622098507.
[30]
Meekes M., Vaxman A., Unconventional patterns on surfaces, ACM Trans Graph (ISSN ) 40 (4) (2021),.
[31]
Vaxman A., Müller C., Weber O., Regular meshes from polygonal patterns, ACM Trans Graph (ISSN ) 36 (4) (2017),.
[32]
Peña de Leon A., Rationalisation of freeform façades: A technique for uniform hexagonal panelling, in: Proceedings of the 17th international conference on computer aided architectural design research in Asia, 2012, pp. 243–252,.
[33]
Sorkine-Hornung O., Rabinovich M., Least-squares rigid motion using SVD, 2017, URL https://igl.ethz.ch/projects/ARAP/svd_rot.pdf. [Accessed on 17 February2023].
[34]
Eldar Y., Lindenbaum M., Porat M., Zeevi Y.Y., The farthest point strategy for progressive image sampling, IEEE Trans Image Process 6 (9) (1997) 1305–1315,.
[35]
Lloyd S., Least squares quantization in PCM, IEEE Trans Inform Theory 28 (2) (1982) 129–137,.
[36]
Hennig C., Meila M., Murtagh F., Rocci R., Handbook of cluster analysis, CRC Press, 2015, ISBN 978-0429185472.
[37]
Maxwell J.C., L. on the calculation of the equilibrium and stiffness of frames, Lond Edinb Dublin Philos Mag J Sci 27 (182) (1864) 294–299,.
[38]
Pellegrino S., Calladine C.R., Matrix analysis of statically and kinematically indeterminate frameworks, Int J Solids Struct 22 (4) (1986) 409–428,.
[39]
Rhino FitPlaneToPoints method, 2023, https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.plane/fitplanetopoints. [Accessed 12 August 2023].
[40]
Zong C., Xu J., Song J., Chen S., Xin S., Wang W., Tu C., P2M: a fast solver for querying distance from point to mesh surface, ACM Trans Graph (ISSN ) 42 (4) (2023),.
[41]
Rhino mesh.ClosestPoint method, 2023, https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.mesh/closestpoint. [Accessed 12 August 2023].
[42]
Rhino polyline.ClosestPoint method, 2023, https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.polyline/closestpoint. [Accessed 12 August 2023].
[43]
Dai Y.-H., Yuan Y., A nonlinear conjugate gradient method with a strong global convergence property, SIAM J Optim 10 (1) (1999) 177–182,.
[44]
Botsch M., Kobbelt L., A remeshing approach to multiresolution modeling, in: Proceedings of the 2004 eurographics/acm SIGGRAPH symposium on geometry processing, Association for Computing Machinery, New York, NY, USA, ISBN 3905673134, 2004, pp. 185–192,.
[45]
Burden R.L., Faires J.D., Burden A.M., Numerical analysis, Cengage learning, 2015, ISBN 978-1305253667.
[46]
Herzog T., Krippner R., Lang W., Facade construction manual, DETAIL, 2017, ISBN 978-3955533694.
[47]
Pariafsai F., A review of design considerations in glass buildings, Front Architect Res (ISSN ) 5 (2) (2016) 171–193,.
[48]
Botsch M., Kobbelt L., Pauly M., Alliez P., Lévy B., Polygon mesh processing, CRC Press, New York, 2010, ISBN 978-1568814261.
[49]
Bhimani J., Leeser M., Mi N., Accelerating K-means clustering with parallel implementations and GPU computing, in: 2015 IEEE high performance extreme computing conference, 2015, pp. 1–6,.

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          Published In

          cover image Computer-Aided Design
          Computer-Aided Design  Volume 166, Issue C
          Jan 2024
          117 pages

          Publisher

          Butterworth-Heinemann

          United States

          Publication History

          Published: 01 January 2024

          Author Tags

          1. Architectural geometry
          2. Rationalization
          3. Clustering
          4. Optimization
          5. Façade design
          6. Free-form surface

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