本文提出了一种生成三维对称标架场的方法。和表面对称标架场不同的是，三维对称标架场的对称性无法用一个切平面的旋转角度表示。为此，本文利用球面函数来获得对称性表述，该表述对于绕任意轴旋转π/2的整数倍以及不同轴之间的复合是不变的。基于此，可获得标架场光顺程度的一个有效度量，并将该标架场用于六面体网格生成。

 

In this paper, a method for constructing a 3D cross- frame field was presented, In contrast to the surface cross-frame field, symmetry for 3D cross- frame fields cannot be formulated by simple one-parameter 2D rotations in the tangent planes. Spherical harmonics was used to represent the 3D frames, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, an efficient smoothness measure of the cross-frame field was formulated and so the 3D cross-frame field can be applied to produce hexahedron-dominant meshes for given volumes.