DOI QR코드

DOI QR Code

일방향 지오데식을 활용한 곡면 형상의 패널링 - 복합 곡면을 중심으로 -

Paneling of Curved NURBS Surface through Marching Geodesic - Application on Compound Surface -

  • 투고 : 2021.12.28
  • 심사 : 2021.12.29
  • 발행 : 2021.12.31

초록

Paneling building facades is one of the essential procedures in building construction. Traditionally, it has been an easy task of simply projecting paneling patterns drawn in drawing boards onto 3d building facades. However, as many organic or curved building shapes are designed and constructed in modern architectural practices, the traditional one-to-one projection is becoming obsolete for the building types of the kind. That is primarily because of the geometrical discrepancies between 2d drawing boards and 3d curved building surfaces. In addition, curved compound surfaces are often utilized to accommodate the complicated spatial programs, building codes, and zoning regulations or to achieve harmonious geometrical relationships with neighboring buildings in highly developed urban contexts. The use of the compound surface apparently makes the traditional paneling pattern projection more challenging. Various mapping technics have been introduced to deal with the inabilities of the projection methods for curved facades. The mapping methods translate geometries on a 2d surface into a 3d building façade at the same topological locations rather than relying on Euclidean or Affine projection. However, due to the intrinsic differences of the planar 2d and curved 3d surfaces, the mapping often comes with noticeable distortions of the paneling patterns. Thus, this paper proposes a practical method of drawing paneling patterns directly on a curved compound surface utilizing Geodesic, which is faithful to any curved surface, to minimize unnecessary distortions.

키워드

과제정보

이 성과는 2021년도 정부(미래창조과학부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구임(No. 2019R1G1A100914713).

참고문헌

  1. Adriaenssens, S., Gramazio, F., Kohler, M., Menges, A.,Pauly, M. (2016). Advances in Architectural Geometry, vdf, pp. 40-61.
  2. Alacam, S., Guzelci, O. (2016). Computational interpretations of 2D Muqarnas projections in 3D form finding. ASCAAD2016, https://www.researchgate.net/publication/310374670 (Dec. 30, 2021).
  3. Bose, P., Maheshwari, A., Shu, C., Wuhrer, S. (2009). A survey of geodesic paths on 3D surfaces. Computational Geometry. 44, pp. 486-498. https://doi.org/10.1016/j.comgeo.2011.05.006
  4. Chen, H., Pottmann, H. (1999). Approximation by ruled surfaces. Journal of Computational and Applied Mathematics. 102(1), pp. 143-156. https://doi.org/10.1016/S0377-0427(98)00212-X
  5. Eigensatz, M., Kilian, M., Schiftner, A., Mitra, N., Pottmann, H., Pauly, M. (2010). Paneling architectural freeform surfaces.. Association for Computing Machinery. 45, pp. 1-10.
  6. Farin, G. (2014). Curves and surfaces for computer-aided geometric design: a practical guide, Elsevier, pp. 353-362.
  7. Floater, M., Hormann, K. (2005). Surface parameterization: a tutorial and survey, https://www.researchgate.net/publication/226655623 (Dec. 30, 2021).
  8. Gravesen, J. (1996). De Casteljau's algorithm revisited, Mathematical Methods for Curves and Surfaces II. Vanderbilt University Press, pp. 221-228.
  9. Kimmel, R., Kiryati, N. (1995). Finding shortest paths on surfaces by fast global approximation and precise local refinement.. International Society for Optics and Photonics. 2356, pp. 198-209.
  10. Kimmel, R., Sethian, J. (1998). Computing geodesic paths on manifolds. Proceedings of the national academy of Sciences. 95(15), pp. 8431-8435. https://doi.org/10.1073/pnas.95.15.8431
  11. Les, P. (1996). The NURBS book, Springer, pp. 81-116.
  12. Minh, H., Forbes, A. (2012). New Method for free-form surface fitting in precision metrology, https://www.researchgate.net/publication/287552808 (Dec. 30, 2021).
  13. Pottmann, H., Huang, Q., Deng, B., Schiftner, A., Kilian, M., Guibas, L., Wallner, J. (2010). Geodesic patterns. ACM Trans. Graph.. 29(4), pp. 10.
  14. Robert McNeel Associates (2015), Continuity Descriptions, http://docs.mcneel.com/rhino/5/help/en-us/popup_moreinformation/continuity_descriptions.htm (Dec. 30, 2021)
  15. Schot, S. (1978). Aberrancy: Geometry of the third derivative. Mathematics Magazine. 51(5), pp. 259-275. https://doi.org/10.1080/0025570x.1978.11976728
  16. Wallner, J., Pottmann, H. (2011). Geometric computing for freeform architecture.. Journal of Mathematics in Industry. 1(1), pp. 1-19. https://doi.org/10.1186/2190-5983-1-1