Architectural geometry

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

doi:10.1016/j.cag.2014.11.002

Cited by 237 publications

(229 citation statements)

References 101 publications

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“…Hyperboloid of one sheet can be generated by using two different surface generation methods (Pottmann et al 2007). In the first method, the surface is created by revolving a hyperbola about a central axis.…”

Section: Geometric Characteristics and Morphology Of Hyperboloidsmentioning

confidence: 99%

Geometric and Kinematic Analysis of Deployable Doubly Ruled Hyperboloids

Maden¹

2017

Megaron

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ÖZThis paper aims to develop deployable doubly ruled hyperboloid surfaces that can be used in architectural applications. First, the study systematically analyzes the geometric principles of hyperboloids generated by the ruled surface generation method and examines the morphology to generate different types of hyperboloids. Then, a method is introduced to construct deployable doubly ruled hyperboloid surfaces. The study demonstrates that deployment behavior of the hyperboloid is directly related to joint types used at the intersection points of the bars. Based on kinematic analysis, the study establishes that deployable hyperboloids with a single degree of freedom can be constructed only by revolute and spherical joints. Finally, various hyperboloids having different number of intersections are constructed according to the proposed joint types and their deployment capabilities are discussed. Keywords: Deployable hyperboloids; doubly-ruled surfaces; kinetic structures; structural mechanisms. ABSTRACT IntroductionThe geometrical simplicity and structural advantages of doubly curved anticlastic surfaces opened a wide range of applications in architecture and engineering. Pioneered by Vladimir Shukhov, Antoni Gaudi and Félix Candela, anticlastic surfaces such as hyperboloid of one sheet and hyperbolic paraboloid (hypar) have been used for cooling towers, oil and water storage tanks, radio and transmission masts, offshore structures and other industrial premises. Over the last century, various different types of structures in the forms of hyperboloid and hypar have been built around the world. Hyperboloid geometry's surface generation method and its form based structural behavior played a fundamental role in constructing hyperboloid structures. Since the straight-line generators can form the anticlastic surface, concrete shell structures have been easily constructed by using straight wooden boards, which not only simplified the formwork but also provided efficient use of construction materials. Hence, various elegant structures with different curvatures could be realized to span over large areas. Likewise, steel and timber grid shells made with lattice of straight beams have been developed to obtain not only

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Section: Geometric Characteristics and Morphology Of Hyperboloidsmentioning

confidence: 99%

Geometric and Kinematic Analysis of Deployable Doubly Ruled Hyperboloids

Maden¹

2017

Megaron

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“…Esto permitió profundizar en el concepto de entrada-salida, tan importante en un sistema computacional. (Pottmann, Asperl, Hofer, & Kilian, 2007) La Manera de entender una curva como un operador que conjunta una lista de puntos nos permite entender los conceptos computacionales y los geométricos al mismo tiempo. Uno de los ejercicios de este módulo fue la producción de curvas sinoidales, espirales y helicoidales a partir de expresiones matemáticas.…”

Section: Planteamiento Del Curso Temariounclassified

El medio es el contenido: Comunicación y evaluación del diseño paramétrico en un ambiente MOOC

Shiordia¹

2017

Blucher Design Proceedings

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El medio es el contenido: Comunicación y evaluación del diseño paramétrico en un ambiente MOOCThe medium is the content: Communication and evaluation of parametric design in a MOOC environment. Rodrigo Shiordia LópezUniversidad Anáhuac México, México rodrigo.shiordia@anahuac.mx AbstractThis paper describes the implementation of a massive online open course of parametric design. Firstly, the justification for understanding design education in an online system is discussed. A conceptualization of computational geometry as a didactic axis for teaching parametric design is posed. To achieve an evaluation of the course, a peer evaluation which had a rubric for each topic, based on a matrix of possibilities, was implemented. The viability of this evaluation system is discussed. Finally, the important and necessary items for success, as well as the disadvantages of this type of courses is concluded.

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“…The goal of Discrete Differential Geometry is to look for mathematical structures on discrete surfaces as rich as their smooth counterparts. It has many applications, for example in computer graphics and architectural design [32].…”

Section: Introductionmentioning

confidence: 99%

Isothermic triangulated surfaces

Lam

Pinkall

2016

Math. Ann.

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Abstract. We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isothermic triangulated surfaces can be characterized either in terms of circle patterns or based on conformal equivalence of triangle meshes. This definition generalizes isothermic quadrilateral meshes.A consequence is a discrete analog of minimal surfaces. Here the Weierstrass data needed to construct a discrete minimal surface consist of a triangulated plane domain and a discrete harmonic function.

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Architectural geometry

Cited by 237 publications

References 101 publications

Geometric and Kinematic Analysis of Deployable Doubly Ruled Hyperboloids

Geometric and Kinematic Analysis of Deployable Doubly Ruled Hyperboloids

El medio es el contenido: Comunicación y evaluación del diseño paramétrico en un ambiente MOOC

Isothermic triangulated surfaces

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