Nurbs continuity

Applications in architecture, product and digital fabrication

Authors

  • Federico Del Blanco García Universidad Politécnica de Madrid, DCTA
  • Ismael García Ríos Universidad Politécnica de Madrid, DIGA
  • Ana González Uriel Universidad Politécnica de Madrid, DIGA
  • Miguel Fernández Cabo Universidad Politécnica de Madrid, DCTA

DOI:

https://doi.org/10.37467/revtechno.v13.4811

Keywords:

NURBS, Computer Aided Design, Construction technology, Algorithm thinking, Architectural geometry, Digital fabrication, Parameterization

Abstract

The increasing complexity in contemporary architectural design has given rise to free-form surfaces that cannot be solved by traditional design and construction methods. The study of the continuity of NURBS surfaces and curves becomes especially relevant, either to segment a complex surface in fragments that allow its rationalization, or for the design through the aggregation of several surfaces looking for the uniformity of the whole. Different methods of establishing continuity between NURBS are analyzed, taking into account the different parameters that define the NURBS and their influence on the level of smoothness and deviation obtained.

References

Aparicio Pérez, D., & del Blanco García, F. L. (2022). Diseño de experiencias inmersivas para una ciudad utópica. Reconstrucción gráfica y virtual de “The Walking City”. EGA Revista de Expresión Gráfica Arquitectónica, 27(44), 98–109. https://doi.org/10.4995/ega.2022.14305 DOI: https://doi.org/10.4995/ega.2022.14305

Álvarez Ayuso, L., & del Blanco García, F. (2021). Aplicación de redes neuronales al diseño de vivienda colectiva. Procesos generativos de combinatoria y automatización mediante inteligencia artificial. Rita_revista Indexada de Textos Académicos, 16, 214–231. DOI: https://doi.org/10.24192/2386-7027(2021)(v16)(20) DOI: https://doi.org/10.24192/2386-7027(2021)(v16)(20)

Barsky, B. A. and DeRose, T. D. (1989). Geometric continuity of parametric curves: three equivalent characterizations, IEEE Computer Graphics and Applications, 9(6), pp. 60–69. doi: 10.1109/38.41470. DOI: https://doi.org/10.1109/38.41470

Bartolomei, C. et al. (2020). From anamorphosis to vision: “3D Sidewalk Chalk Art”. Disegnarecon, 13(24), 1–14. DOI: https://doi.org/10.20365/disegnarecon.24.2020.1

Bedi S, Ali I, Quan N (1993). Advanced interpolation techniques for NC machines. Trans ASME J Eng Ind 115:329–336 DOI: https://doi.org/10.1115/1.2901668

Block, P., Kilian, A. and Pottmann, H. (2015). ‘Steering of form - New integrative approaches to architectural design and modeling’, CAD Computer Aided Design. doi: 10.1016/j.cad.2014.04.007. DOI: https://doi.org/10.1016/j.cad.2014.04.007

de Boor, C. R. (1980). A Practical Guide to Splines. Mathematics of Computation, 34(149), p. 325. doi: 10.2307/2006241. DOI: https://doi.org/10.2307/2006241

de Molina, L. & Valero, E. (2021). Habitar en la era digital. Modelos colaborativos y su respuesta en tiempos de crisis. Rita Revista Indexada de Textos Académicos, 5, pp 94-101. DOI: 10.24192/2386-7027(2020)(v14)(04) DOI: https://doi.org/10.24192/2386-7027(2020)(v14)(04)

del Blanco García, F. L. and García Ríos, I. (2017). Las cúpulas de Félix Candela. Análisis y reconstitución de las instalaciones deportivas de la Universidad Brown, 1965-1972, EGA Expresión Gráfica Arquitectónica, 22(29), pp. 228–239. https://doi.org/10.4995/ega.2017.7358 DOI: https://doi.org/10.4995/ega.2017.7358

del Blanco García, F. L. and García Ríos, I. (2018). Fernando Higueras y Félix Candela en un retorno a la geometría de paraguas invertidos. Análisis y reconstitución gráfica del aeropuerto de Murcia, 1983, EGA Expresión Gráfica Arquitectónica, 23(32), pp. 232–243. https://doi.org/10.4995/ega.2018.9813 DOI: https://doi.org/10.4995/ega.2018.9813

del Blanco García, F. L. (2021). Virtual reconstruction and geometric analysis of Félix Candela’s inverted umbrellas for The Villahermosa Cathedral. Disegnarecon, 14(27), 1–14. https://doi.org/10.20365/disegnarecon.27.2021.10

del Blanco García, F. L. & García Ríos, I. (2022). Félix Candela and Fernando Higueras. Eight years and seven projects in common.” VLC arquitectura 9, no. 1: 161-188. https://doi.org/10.4995/vlc.2022.15288 DOI: https://doi.org/10.4995/vlc.2022.15288

del Blanco García, F. L. (2022). Reconstructing Pérez Piñero’ s Anoeta Velodrome. Nexus Network Journal. https://doi.org/10.1007/s00004-022-00590-3 DOI: https://doi.org/10.1007/s00004-022-00590-3

Canestrino, G (2021). Considerations on Optimization as an Architectural Design Tool. Nexus Network Journal 23, 919–931. https://doi.org/10.1007/s00004-021-00563-y DOI: https://doi.org/10.1007/s00004-021-00563-y

DeRose, T. D. and Barsky, B. A. (1988) ‘Geometric Continuity, Shape Parameters, and Geometric Constructions for Catmull-Rom Splines’, ACM Transactions on Graphics (TOG), 7(1), pp. 1–41. doi: 10.1145/42188.42265. DOI: https://doi.org/10.1145/42188.42265

De Vicente Domínguez, A. M., & Sierra Sánchez, J. (2021). Technicalities in scientific communication: Analysis of the dissemination strategies used by the SINC Agency in the information published on its Twitter profile. TECHNO REVIEW. International Technology, Science and Society Review, 10(2), 147–158. https://doi.org/10.37467/gka-revtechno.v10.3011 DOI: https://doi.org/10.37467/gka-revtechno.v10.3011

Ding GL (2008). Research on modeling and interpolation of the tool-path based on cylindrical helix spline. Dissertation, Huazhong University of Science and Technology.

Du DS, Liu YD, Yan CL, Li CX (2006) An accurate adaptive parameter curve interpolator for NURBS curve interpolation. Int J Adv Manuf Technol DOI: 10.1007/S00170-006-0412-y DOI: https://doi.org/10.1007/s00170-006-0412-y

Fallica, S., Garozzo, R., & Santagati, C. (2021). Retraced memories - virtual reconstruction of an architectural landmark. Virtual Archaeology Review, 12(25), 124–139. https://doi.org/10.4995/var.2021.15302 DOI: https://doi.org/10.4995/var.2021.15302

Felicetti, A., Paolanti, M., Zingaretti, P., Pierdicca, R., & Malinverni, E. S. (2021). Mo.Se.: Mosaic image segmentation based on deep cascading learning. Virtual Archaeology Review, 12(24), 25–38. https://doi.org/10.4995/var.2021.14179 DOI: https://doi.org/10.4995/var.2021.14179

Flöry, S., & Pottmann, H. (2010). Ruled surfaces for rationalization and design in architecture. Life In:Formation: On Responsive Information and Variations in Architecture - Proceedings of the 30th Annual Conference of the Association for Computer Aided Design in Architecture, ACADIA 2010, 103–109. DOI: https://doi.org/10.52842/conf.acadia.2010.103

García Pino, F. (2020). Ron Resch. Patrones de doblado. El diseño topológico desde la geometría computarizada. Ron Resch. Bending Patterns. The Topological design from computerizes geometry. Rita Revista Indexada de Textos Academicos, 13, 148–156. DOI 10.24192/2386-7027(2020)(v13)(10) DOI: https://doi.org/10.24192/2386-7027(2020)(v13)(10)

García, F. L., & Ríos, I. (2016). De las estructuras laminares a las estructuras metálicas en la arquitectura de Félix Candela. Análisis y reconstitución de la sala de exposiciones para el concurso del Palacio Olímpico de los Deportes, México 1968. Rita Revista Indexada de Textos Academicos, 5, 98–105. DOI: https://doi.org/10.24192/2386-7027(2016)(v5)(05) DOI: https://doi.org/10.24192/2386-7027(2016)(v5)(05)

Hartmann, E. (2003) ‘Geometry and Algortihms for Computer Aided Design’, Journal of computational physics, 212(October), pp. 393–399.

Ingleby, T., Orlando, S (2021). Translating Movement into Architectural Form. Nexus Network Journal 23, 1017–1037. https://doi.org/10.1007/s00004-021-00567-8 DOI: https://doi.org/10.1007/s00004-021-00567-8

Kilian, M., Pellis, D., Wallner, J., & Pottmann, H. (2017). Material-minimizing forms and structures. ACM Transactions on Graphics, 36(6). https://doi.org/10.1145/3130800.3130827 DOI: https://doi.org/10.1145/3130800.3130827

Lee, E. T. Y. (1986) ‘Comments on some B-spline algorithms’, Computing, 36(3), pp. 229–238. doi: 10.1007/BF02240069. DOI: https://doi.org/10.1007/BF02240069

Liua X, Ahmada F, Yamazakia K, Morib M (2005). Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics. Int J Mach Tools Manuf 45:433–444 DOI: https://doi.org/10.1016/j.ijmachtools.2004.09.009

Li W, Liu YD, Yamazaki K, Fujisima M, Mori M (2008). The design of a NURBS pre-interpolator for five-axis machining. Int J Adv Manuf Technol. doi:10.1007/s00170-006-0905-8 DOI: https://doi.org/10.1007/s00170-006-0905-8

Lluis i Ginovart, J., Lluis-Teruel, C., & Ugalde-Blázquez, I. (2021). Bóvedas tabicadas en la ingeniería militar española (s. XVIII). Informes De La Construcción, 73(562), e393. https://doi.org/10.3989/ic.80000 DOI: https://doi.org/10.3989/ic.80000

Morales Guzman, C. (2021). Desarrollo de un sistema de aspas transformable en las cubiertas plegables. Informes De La Construcción, 73(562), e397. https://doi.org/10.3989/ic.73030 DOI: https://doi.org/10.3989/ic.73030

Moreno Latorre, Arturo; del Blanco García, F. L. (2021). Graphic communication in Architecture Competitions. Data visualization as an analysis tool in EGA. EGA Expresión Gráfica Arquitectónica, 26(41), 190–205. https://doi.org/10.4995/ega.2021.14054 DOI: https://doi.org/10.4995/ega.2021.14054

Parrinello, S. (2020). The virtual reconstruction of the historic districts of Shanghai European identity in traditional Chinese architecture. Disegnarecon, 13(25), 1–13. https://doi.org/10.20365/disegnarecon.25.2020.18

Piegl L, Tiller W (2003) The NURBS book, 2nd edn. Springer, Berlin

Pottmann, H. (2010). Architectural geometry as design knowledge. Architectural Design, 80(4). https://doi.org/10.1002/ad.1109 DOI: https://doi.org/10.1002/ad.1109

Quaresma, A. (2021). Weak artificial intelligence and computational brute strength. TECHNO REVIEW. International Technology, Science and Society Review, 10(1), pp. 67–78. https://doi.org/10.37467/gka-revtechno.v10.2815 DOI: https://doi.org/10.37467/gka-revtechno.v10.2815

Salazar Lozano, María del Pilar, and Antonio José Cidoncha Pérez (2021). Living in a metal shed. Quonset Huts on Naval Station Rota. VLC arquitectura 8, no. 2: 91-116. https://doi.org/10.4995/vlc.2021.13423 DOI: https://doi.org/10.4995/vlc.2021.13423

Sun YW, Jia ZY, Ren F, Guo DM (2008) Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties. Int J Adv Manuf Technol. doi:10.1007/s00170-006-0817-7 DOI: https://doi.org/10.1007/s00170-006-0817-7

Tang, C. et al. (2016) ‘Interactive design of developable surfaces’, ACM Transactions on Graphics, 35(2). doi: 10.1145/2832906. DOI: https://doi.org/10.1145/2832906

Yazar, T. (2021). Compass Construction of Bézier Curves and B-Splines. Nexus Network Joural 23, 789–811. https://doi.org/10.1007/s00004-020-00542-9 DOI: https://doi.org/10.1007/s00004-020-00542-9

Wolff, Cecilia, and Mauricio Cárcamo (2021). Enactive or symbolic representation? When the order alters the product. VLC arquitectura 8, no. 1: 173-188. https://doi.org/10.4995/vlc.2021.12534 DOI: https://doi.org/10.4995/vlc.2021.12534

Downloads

Published

2023-02-28

How to Cite

Del Blanco García, F., García Ríos, I. ., González Uriel, A. ., & Fernández Cabo, M. . (2023). Nurbs continuity: Applications in architecture, product and digital fabrication. TECHNO REVIEW. International Technology, Science and Society Review /Revista Internacional De Tecnología, Ciencia Y Sociedad, 13(4), 1–18. https://doi.org/10.37467/revtechno.v13.4811

Issue

Vol. 13 No. 4 (2023): Monograph: "Technology that advances the future"

Section

Research Articles (Special Issue)

License

Those authors who publish in this journal accept the following terms:

  1. Authors will keep the moral right of the work and they will transfer the commercial rights.
  2. After 1 year from publication, the work shall thereafter be open access online on our website, but will retain copyright.
  3. In the event that the authors wish to assign an Creative Commons (CC) license, they may request it by writing to publishing@eagora.org