几种新型异形椭球面方程、几何特征及其应用前景  

Equations,Geometric Characteristics and Application Prospects of Several New Types of Heteromorphic Ellipsoid Surfaces

作　　者：武周虎[1] Wu Zhouhu(School of Environmental and Municipal Engineering,Qingdao University of Technology,Qingdao 266033,China)

机构地区：[1]青岛理工大学环境与市政工程学院,青岛266033

出　　处：《土木建筑工程信息技术》2023年第6期39-45,共7页Journal of Information Technology in Civil Engineering and Architecture

基　　金：国家自然科学基金面上项目(编号:51379097)。

摘　　要：以异形椭圆和椭圆为基本图形,定义了半长度、半宽度和半高度共3个独立参数,设定了5种新型异形椭球面的构建条件和定义区间。采用解析几何方法,分别构建了Ⅲ~Ⅶ型异形椭球面方程。5种类型异形椭球面的几何特性为:在平行于yOz上的剖面线均为异形椭圆,俯视轮廓投影线为椭圆或异形椭圆,xOz剖面线为椭圆或半异形椭圆或半椭圆。分析表明,Ⅲ、Ⅴ和Ⅶ型异形椭球面均具有双对称平面,Ⅳ和Ⅵ型异形椭球面均具有单对称平面;Ⅵ和Ⅶ型异形椭球面的俯视轮廓线与xOy剖面线重合;Ⅲ~Ⅶ型异形椭球体在俯视轮廓线以上部分的体积占各自总体积60.83%。新型异形椭球面在特殊建设工程、浮体和景观造型等设计中,具有广阔的应用前景。Taking the heteromorphic ellipse and the ellipse as basic figures,this paper defines three independent parameters,i.e.the half-length,half-width,and half-height to establish conditions and definition intervals for five new types of heteromorphic ellipsoid surfaces.The equations of typesⅢ–Ⅶheteromorphic ellipsoid surfaces are established through the analytic geometrical method.The geometric characteristics of the five types of heteromorphic ellipsoid surfaces are as follows:the cross-sections on the parallel plane yOz form a heteromorphic ellipse,the contours in the top view form an ellipse or a heteromorphic ellipse,and curves of the profile on the coordinate plane xOz form an ellipse,a semiheteromorphic ellipse,or a semi-ellipse.The analysis showed that typesⅢ,Ⅴ,andⅦheteromorphic ellipsoid surfaces have double-symmetry planes,while typesⅣand typeⅥhave single-symmetry planes.The contours of the top view of typesⅥandⅦof the heteromorphic ellipsoid surfaces coincides with the xOy profile.The volumes of parts above the contours in the top views of typesⅢ–Ⅶheteromorphic ellipsoids accounted for 60.83%of their respective total volumes.These new types of heteromorphic ellipsoid surfaces can be used broad application prospects in the design of special construction projects,floating bodies and landscape modeling.

关 键 词：3参数闭曲面 异形椭球面 数学方程 几何特征 曲面体设计 

分 类 号：TU17[建筑科学—建筑理论] TU205