Rethinking Prototyping

Fig. 9 This architectural design is a modern extension of a historical building. All glass elements are conical panels, aligned with the surface’s border.

In this work we presented a new way for approximating curves on a surface with developable strips, consisting of conical and cylindrical panels. This can also be seen as a new design tool with panels that are ready to planarize and yet allow for great freedom in the design. The differences from developable strips to planar panels like quadrilaterals and triangles are its advantageous reflection lines and an overall smooth look. In contrast to double curved panels, they can be built at reduced cost.

An easy-to-use algorithm is presented, that can be directly implemented into any CAD system without the help of external libraries or optimization frameworks.

Alliez, P.; Cohen-Steiner, Dl; Devillers, O.; L’Evy, B.; Desbrun, M., 2003: Anisotropic Polygonal Remeshing. ACM Trans. Graphics 22 (3) , pp. 485–493.

Aumann, G., 2004: Degree Elevation and Developable Bézier Surfaces. Comp. Aided Geom. Design 21 , pp. 661–670.

Bommes, D.; Zimmer, H.; Kobbelt, L., 2009: Mixed-Integer Quadrangulation. ACM Trans. Graphics 28, 3 (2009) , # 77, pp. 1–10.

Chu, C.H.; Séquin, C., 2002: Developable Bèzier Patches: Properties and Design. Computer-Aided Design 34 , pp. 511–528.

Do Carmo, M.P., 1976. Differential Geometry of Curves and Surfaces. New Jersey: Prentice-Hall .

Frey, W., Modeling Buckled Developable Surfaces by Triangulation. CAD 36(4) , pp. 299–313.

Glaeser, G.; Gruber, F., 2007. Developable Surfaces in Contemporary Architecture. J. of Math. And the Arts 1 , pp. 1–15.

Julius, D.; Kraevoy, V.; Sheffer, A., 2005: Dcharts: Quasi-Developable Mesh Segmentation. Computer Graphics Forum (Proc. Eurographics) 24 , 3, pp. 581–590.

Kahlert, J.; Olson, M.; Zhang, H., 2011: Width-Bounded Geodesic Strips for Surface Tiling, The Visual Computer , Vol. 27/1 , pp. 45-56.

Kruppa, E., 1957: Analytische und konstruktive Differentialgeometrie . Wien: Springer.

Liu, Y.; Pottmann, H.; Wallner, J.; Yang, Y.-L.; Wang, W., 2006. Geometric Modeling with Conical Meshes and Developable Surfaces. ACM Transactions on Graphics 25 , 3, pp. 681–689.

Pottmann, H.; Asperl, A.; Hofer, M.; Kilian, A., 2007: Architectural Geometry. Bentley Institute Press .

Pottmann, H.; Schiftner, A.; Bo, P.; Schmiedhofer, H.; Wang, W.; Baldassini, N.; Wallner, J., 2008: Freeform Surfaces from Single Curved Panels. ACM Trans. Graphics, 27/3 , Proc. SIGGRAPH.

Raun, C.; Kristensen, M.K.; Kirkegaard, P.H., 2012: Dynamic Double Curvature Mould System . Computational Design Modelling , Springer, pp. 291-300.

Rose, K.; Shefter, A.; Wither, J.; Cani, M; Thibert, B., 2007: Developable Surfaces from Arbitrary Sketched Boundaries. In Symp. Geom. Processing, A. Belyaev and M. Garland, Eds. Eurographics, pp. 163–172 .

Schober, H., 2002: Geometrie-Prinzipien für wirtschaftliche und effiziente Schalentragwerke. Bautechnik 79, Heft 1 .

Shelden, D.R., 2002: Digital Surface Representation and the Constructibility of Gehry’s Architecture. PhD thesis, Cambridge: MIT Press .

Subag, J.; Elber, G.; 2006: Piecewise Developable Surface Approximation of General NURBS Surfaces with Global Error Bounds. In GMP 2006, vol. 4077 of LNCS. Springer, pp. 143–156 .

Wallner, J.; Schiftner, A.; Kilian, M.; Floery, S.; Hoebinger, M.; Deng, B.; Huang, Q.; Pottmann, H., 2010: Tiling Freeform Shapes With Straight Panels: Algorithmic Methods. Proc. Advances in Architectural Geometry.

Wang, C.; Tang, K., 2004. Achieving Developability of a Polygonal Surface by Minimum Deformation: A Study of Global and Local Optimization Approaches. Vis. Computer 20, pp. 521–539.

Текст предоставлен ООО «ЛитРес».

Прочитайте эту книгу целиком, купив полную легальную версию на ЛитРес.

Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.