三参数异形椭球面方程、几何特征及应用前景  

Three-parameter heteromorphic ellipsoid surface equation, geometric characteristicsand application prospects

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,山东青岛266033

出　　处：《西安理工大学学报》2022年第2期295-300,共6页Journal of Xi'an University of Technology

基　　金：国家自然科学基金面上资助项目(51379097,50979036)。

摘　　要：基于二维异形椭圆方程和三维对流扩散物质的等浓度面方程,定义了半长度、半宽度和半高度3个独立参数,分别构建了三维空间的Ⅰ型和Ⅱ型异形椭球面——2种三参数闭曲面方程。在笛卡尔坐标系中,Ⅰ型异形椭球面在yOz平行面上的横截面为椭圆,在xOy和xOz坐标面上的剖面曲线均为异形椭圆;Ⅱ型异形椭球面在yOz平行面、xOy和xOz坐标面上的剖面曲线以及俯视轮廓线均为异形椭圆,关于坐标面xOz对称,上半部分与下半部分的体积比约为0.8∶1。分析表明,Ⅰ型和Ⅱ型异形椭球面可以选择整体或分段组合应用于蛋形曲面建筑、民用飞机、船舶形状优化和工艺品等设计,具有很好的科学研究和应用前景。Based on the two-dimensional heteromorphic ellipse equation and the three-dimensional constant concentration surface equation of convective diffusion material,three independent parameters of half length,half width and half height are defined,with two types of three-parameter closed-surface equations constructed respectively for type I and typeⅡheteromorphic ellipsoids in three-dimensional space.In the Cartesian coordinate system,the cross-section of the type I heteromorphic ellipsoid on the yOz parallel plane is an ellipse,and the profile curves on the xOy and xOz coordinate planes are all heteromorphic ellipses;the profile curves of the typeⅡheteromorphic ellipsoid surface on the yOz parallel plane,the xOy and xOz coordinate planes and the top view contour lines are all of heteromorphic ellipses.In terms of the symmetry of the coordinate plane xOz,the volume ratio of the upper half to the lower half is about 0.8∶1.The analysis shows that for Type I and Type II heteromorphic ellipsoids,the whole or segmented combination can be selected to be applied to the design of egg-shaped curved buildings,civil aircraft,ship shape optimization and handicrafts,which has good scientific research and application prospects.

关 键 词：异形椭圆 三参数闭曲面 异形椭球面 几何特征 曲面体设计 

分 类 号：TB113[理学—数学] TB21[理学—应用数学]