摘要:随着数字技术在建筑设计中的深入运用，国内外出现了许多用经典曲面和自由曲面^[1]造型的建筑。椭球面是一种重要的经典曲面，可用于建筑造型的场合比球面更为广泛。实际工程中却还是较多的选择球面进行几何造型。如何在椭球面上进行优美的网格剖分，国内相关文献与图形都难以见到。原因是椭球面上的几何量的计算、几何性质分析较为复杂。椭球面斜驶线微分方程求解较为困难。本文采用内蕴几何的观点和方法建立三种不同情况椭球面的斜驶线微分方程。并进行了求解，分别获得解析解、级数解及数值解。讨论了椭球面与平面的共形对应，椭球面的等距面方程。通过具体的算例，在犀牛平台采用NURBS技术进行了三维演示。

Abstract: With the deepening application of digital technology on architectural design, many buildings using techniques of classical and free curved surfaces appear at home and abroad.As an important classical surface, the ellipsoidal surface can be used more widely than the spherical surface.However, the practical engineering employs more spherical surfaces in the geometric modeling.Discussions about how to mesh the ellipsoidal surface elegantly are rarely seen in domestic literatures, for geometric calculation and analysis of ellipsoidal surfaces are relatively complicated.Besides, it is difficult to solve the differential equation of inclined path of the ellipsoidal surface.This paper adopts the viewpoint of the intrinsic geometry to establish and solve three different differential equations of inclined path of the ellipsoidal surface.Then the analytical solution, the series solution and the numerical solution are obtained.The conformal correspond of the rotational ellipsoid and the plane is discussed and the equidistant-surface equations are presented.Using the method of NURBS and the Rhinoceros-Platform, the process is presented in three-dimensional view through specific examples.