数字建筑形态创建中的几何方法——经典二维不可定向流形在E^3中的浸入

Eometric Method in the Creation of Digital Architectural Form——Immersion of Classical 2D Non-orientable Manifold in E^3

形态学是近年来创建的一门新型的基础理论学科,建筑设计作为由设计构思发展起来的一种塑造物质形体和空间的造型艺术,自然拥有"形态的优先权"。数学本身也是一种文化,而几何学是描述自然现象及其变化规律的最佳语言。当代建筑造型的思想与方法正在突破传统的欧氏空间观念的束缚,开始运用流形来进行创作。本文从几何学的角度讨论了经典二维不可定向流形在E3中的浸入的几何造型。对国内外的几个经典数字建筑的形态创建进行了分析,并且在Rhino平台上利用NURBS技术进行了三维演示。集中展示了各种经典的克莱茵瓶、实射影平面在E3中的浸入。

Morphology is a new basic theoretical subject created in recent years.The architectural design naturally has the 'priority of morphology'as a modeling art developed from design concept for moulding substance shape and space.Mathematics is also a kind of culture,and geometry is the best language describing the natural phenomenon and rule.The thought and method of contemporary architectural modeling are breaking through the constraint of traditional concept of Euclidean space,and it starts creating with manifold.This paper discusses the geometric modeling of immersion of classical 2D non-orientable manifold in E3 from the perspective of geometry.The creations of several classical digital building forms at home and abroad are analyzed,and it also provides the 3D demonstration on Rhino platform by NURBS technology.It focuses on presenting the immersions of various classical Klein bottle and real projection plane in E3.