曲面的法线

In this paper,singularity is used to study the classification of singularities of the binormal curves and focal surfaces of a spacelike in Minkowski 3-space,and also establish the relationships between singularities of these and geometric invariants of curves under the action of Lorentzian group.

应用奇点理论方法对三维Minkowski空间内由空间型曲线生成的副法线标型和可展焦曲面的奇点进行了分类，并且研究了在Lorenzian群作用下的空间型曲线的几何学不变量同这些奇点之间的关系。

This paper proposes a robust filter function, called trilateral filter function, to filter the noises in the domains of surface curvature, normal and position at each sample point while the local surface is fitted in a quadratic form. By optimizing the filtering result of curvature tensor, our approach is capable of preserving the feature on the target model.

通过在扫描模型每个采样点处拟合一个二次型曲面，设计了一个鲁棒的滤波函数--三边滤波函数；应用该函数分别对模型表面上每个点的法线、曲率和位置进行滤波；通过对曲率的滤波结果进行优化，可有效地保持三维模型表面上的特征。

The shape-form analysis and load analysis were done by nonlinear FEM. On the basis of surface FEM grid nodes, geometry property research of structure curved surface was progressed, including normal vector, GAUSS curvature, mean curvature and principal direction vector. In this process, the approximate expression of surface didn't need to he known.

采用非线性有限元法进行了膜结构的形态分析和荷载分析，得到了曲面有限元网格；通过离散微分几何方法，研究了薄膜结构曲面的几何性质，包括曲面的法线向量、高斯曲率、平均曲率和主方向矢量，避免了复杂的曲面拟合过程。

The governing equations of laminate-faced sandwich cylindrical shallow shells based on the first-order shear theory with large deflection are high-order partial differential equations. Four dependent functions are involved.

大挠度剪切理论下复合材料夹层圆柱扁壳的稳定性控制方程是一组非线性高阶常系数偏微分方程，其中包含四个独立的函数，它们分别为横向挠度w、参考曲面的法线转角Φx、Φy和应力函数F。

According to the equation of asymptotic curves, a family of nonlinear asymptotic curves are given to the principal normal surface.

根据渐近曲线的方程，具体给出主法线曲面的一族非直线的渐近曲线。

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

Making use of the inverse surface equation of wave normals and the boundary condition about the continuity of electromagnetic field tangential component at the surface of crystal, expressions about wave normal and ray direction, wave normal and ray refractive indexes were obtained.

论文建立了以光线入射方向和晶体光轴方向为基准的入射坐标系，利用波法线反曲面方程和电磁场在晶体折射界面处切向分量连续性的边界条件，得到了晶体中波法线方向、射线方向、波法线折射率和射线折射率的表达式。

In this paper, a new method for aspheric conicoid machining is offered by using normal equidistance line offsetting methods.1、Obtain ecumenic equation of normal equidistance offsetting line methods for aspheric conicoid machining induced from mathematical equations of paraboloid, hyperboloid and ellipsoid surface; reason the conditions for avoiding of tool intervening.2、Bring forward the general design project for machining tool together with some primary components based on the conception of non-sphere conicoid machining by using normal equidistance line offsetting.

其主要内容有： 1、进行了二次旋转曲面法线等距离线加工方法的理论研究，分别建立了抛物面、椭球面和双曲面的法线等距离线模型，得出了避免加工过程中刀具干涉的必要条件。 2、根据法线等距离线加工法的理论，确定了二次旋转曲面加工机床的总体设计方案，并进行了零部件的选择。

The triangulating algorithm for discrete surface is presented.

在空间离散点曲面的三角划分方面，提出了限定相邻三角片的法线夹角的空间离散点曲面三角网格划分方法。

They only serve as a means to compute surface normals for use with dynamic lighting.

他们只是给电脑一种方法来计算曲面法线当使用动态灯光的时候。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。