拓扑判断在双层曲面系统修正中的应用

Application of topological judement to the correction of the dual-layer surface system

建筑复杂形体设计已广泛采用参数化方法。参数化方法易于描述几何体尺寸、位置、角度等方面的数量变化,而难于处理几何体特征、相互关系等涉及拓扑关系的问题。本文基于计算几何的拓扑判断技术,以双层曲面系统为研究对象,对其中出现的凹凸形态识别和表皮重叠问题,提出了数值判断和几何判断两种判断方法,进行凹凸修正和重叠修正。将判断方法编写为计算机程序,通过程序自动执行修正操作。程序运行结果对两种判断方法进行了验证,证实了拓扑判断可以作为参数化方法的补充,更为有效地处理建筑复杂形体设计问题。

The parametric method has been extensively applied to the design of complex architectural forms. With the parametric method, it is easy to describe such quantitative changes as the size, position and angle of geometric forms, but difficult to deal with such issues of topological relationship as features of geometric forms and mutual relations. Based on the technology of topological judgement for computational geometry, with the dual-layer surface system as the target of research regarding the identification of convex and concave forms and overlapped surfaces. This thesis has put forward two methods of judgment （i.e. numerical judgement and geometric judgement） to conduct correction. Methods of judgment have been programmed to automatically enforce correction. As tested and proved by the results of programmed operation, these two methods of topological judgement can serve as supplements to the parametric method and deal with complex architectural forms more effectively.