特殊建筑双微方法几何造型

Geometric Modeling of Special Buildings by Two-differential Method

莫斯科水晶岛和伦敦再保险大厦以奇特、优美的建筑造型给人以强烈的视觉冲击。莫斯科水晶岛的基本造型曲面是压缩后的伪球面,再保险大厦的基本造型曲面是接近于劣圆弧回转面的自由曲面。采用微分几何、微分方程方法(简称双微方法)讨论了这二个造型曲面上的斜驶线网格。平直的欧氏空间中的斜直线,具有定向和短程二个重要性质。将斜直线的定向性引伸到二维弯曲空间(回转曲面)上,就是斜驶线的内蕴定向性。从斜驶线的定义入手,推导出回转曲面上斜驶线的微分方程,求介得到劣圆弧回转面和伪球面上斜驶线方程,并通过相应的解析解或数值解,得到斜驶线上各离散点的坐标。用样条曲线依次连接相邻坐标点,得到样条逼近的斜驶线。再经过旋转阵列和镜像,就得到建筑表面的斜驶线网格。可供其他类似建筑的几何造型提供参考。

It's very impressive that Crystal Island in Moscow and Re-Insurance Building in London because of their excellent architectural style. The geometrical modeling of these two buildings are investigated by the method of differential geometry and differential equation,which is known as two-differential in brief. The inclined straight line in Euclidean space is oriental and short-range. Similar to this orientation,loxodromic line in two-dimensional curved space is intrinsic oriental. After the differential equation of loxodromic line in revolution surface is derived from this definition,the restriction equations of those in inferior-arc revolution surface and in pseudo-sphere can obtain. Then it's easy to get the coordination of all discrete points according to the corresponding analytical or numerical solutions. The three dimension geometry is modeled by the steps of connecting adjacent points,rotating array and mirror. It can be referred to modeling other similar buildings.