Abstract
The theory of the previous chapters is applied on surfaces and parametrizations. Elements involved in the study of regular surfaces are shown and illustrated with examples. Some classical surfaces in architecture are analyzed from the point of view of the theory described previously in the chapter.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Costa, A. F., J. M. Gamboa, and A. M. Porto. (1997). Notas de Geometría diferencial de curvas y superficies, ed. Sanz y Torres.
do Carmo, M.-P. (1976). Differential geometry of curves and surfaces. Englewood Cliffs, NJ: Prentice-Hall, Inc.
Dörrie, H. (2013). 100 great problems of elementary mathematics: their history and solution. New York, NY: Dover.
Eastwood, M., and R. Penrose. (2000). Drawing with complex numbers. The Mathematical Intelligencer No.4, 8–13.
Effekt (2020a). Camp adventure. effekt, accessed 1 april 2020. https://www.effekt.dk/camp.
Erdös, P. (2000). Spiraling the earth with c. g. j. jacobi. American Journal of Physics 68:888–895.
Frazier, L., and D. Schattschneider. (2008). Möbius bands of wood and alabaster. Journal of Mathematics and the Arts 2(3):107–122.
Gauss, C. F. (1876). Werke, Zweiter, Band, Königlichen Gesellschaft der Wissenschaften. Göttingen.
Gray, A. (1997). A different klein bottle. In modern differential geometry of curves and surfaces with mathematica, 327–330. Boca Raton, FL: CRC Press.
Hoffmann, C. M. (1989). Geometric and solid modeling: An introduction. San Mateo, CA: Morgan Kaufmann.
Klein, F. (2004). Elementary mathematics from an advanced standpoint. Geometry. Reprint of the 1949 translation. Dover Publications.
Lastra, A., J. R. Sendra, and J. Sendra. (2018). Hybrid trigonometric varieties. Preprint. https://arxiv.org/pdf/1711.07728.pdf.
Marsden, J. E., and A. Tromba. (2012). Vector calculus. New York: W.H. Freeman.
Mathcurve (2019a). Courbe sphérique, accessed 20 may 2019. https://www.mathcurve.com/courbes3d/spheric/spheric.shtml.
Munkres, J. R. (1974). Topology; a first course. Englewood Cliffs, NJ: Prentice-Hall.
Nadenik, Z. (2005). Lame surfaces as a generalisation of the triaxial ellipsoid. Studia Geophysica et Geodaetica 49:277.
Narváez-Rodríguez, R., A. Martín-Pastor, and M. Aguilar-Alejandre. (2014). The Caterpillar Gallery: Quadratic Surface Theorems, Parametric Design and Digital Fabrication. In Advances in Architectural Geometry, ed. P. Block, J. Knippers, N. Mitra, and W. Wang. Cham: Springer.
Pottmann, H., A. Asperl, M. Hofer, and A. Kilian. (2007). Architectural geometry. Bentley Institute Press.
Samyn, P. (2017). Between light and shade, transparency and reflection. https://samynandpartners.com/17_e-books/ombreetlumiere-EN/mobile/index.html.
Samynandpartners (2020b). Samyn and partners. architects & engineers, accessed 1 april 2020. https://samynandpartners.com/fr/portfolio/walloon-branch-of-reproduction-forestry-material/.
Sendra, J., F. Winkler, and S. Perez-Diaz. (2007). Rational algebraic curves: A computer algebra approach. Series: algorithms and computation in mathematics, Vol. 22. Springer Verlag.
Séquin, C. H. (2008). Algorithmically acquired architectural and artistic artifacts. In Proc. AAG, 9–12.
Séquin, C. H. (2018). Möbius bridges. Journal of Mathematics and the Arts. Académie Royale de Belgique. Series Pocket Book Academy.
Tapp, K. (2016). Differential geometry of curves and surfaces. Undergraduate Texts in Mathematics. Springer.
Thulaseedas, J., and R. J. Krawczyk. (2003). Möbius concepts in architecture. Proceedings of Bridges (2003): Mathematics, Music, Art, Architecture, Education, Culture, 353–360.
Umehara, M., Y. Kotaro, and W. Rossman. (2017). Differential geometry of curves and surfaces. World Scientific.
Wikiarquitectura (2021a). Klein bottle house, accessed 10 february 2021. https://en.wikiarquitectura.com/building/klein-bottle-house/.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Lastra, A. (2021). Parametrizations and Regular Surfaces. In: Parametric Geometry of Curves and Surfaces. Mathematics and the Built Environment, vol 5. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-81317-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-81317-8_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-81316-1
Online ISBN: 978-3-030-81317-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)