二次曲面

If the profile curve has been denoted by a nonuniform rational quadratic B-spline curve, it is very convenient to represent the surface of revolution as a nonuniform rational biquadratic B-spline surface.

只要轮廓曲线用非均匀有理二次B样条曲线来表示，就可相当方便地把旋转曲面表示成非均匀有理双二次B样条曲面。

Applyingthe sufficient and necessary condition of biquadratic Bézier patch being non-negative,a method is presented to see whether two points are the closest points between twobiquadratic NURBS surfaces when the two points are respectively on the two surfaces. Based on the method, the surface split algorithm is improved while the surfaces arebiquadratic NURBS surfaces.

本文利用双二次 Bézier 曲面为非负的充要条件，提出了分别位于两张双二次 NURBS 曲面上的点是否为这两张曲面间距离最近的点的判别方法，并由此在双二次 NURBS 曲面的场合对计算最短距离的曲面分割法作了改进。

The principle of the fractal-interpolated surface was discussed. The formula and the theorem of fractal dimension of the fractal-interpolated surface were analyzed. The numerical analysis of height anomaly fit by the fractal interpolated surface and the result comparison with the quadric polynomial surface model with practical data were given.

本文论述了分形插值曲面的原理，分析了分形插值曲面的计算公式，讨论了分形插值曲面的维数估计方法和公式，用实际数据进行了分形插值曲面拟合高程异常的数值分析以及与二次多项式曲面拟合模型结果的比较。

A sufficient and necessary condition of an isothermal surface being a minimal surface is obtained.

除平面外没有其它二次多项式极小曲面，Enneper曲面是目前微分几何文献中唯一出现的三次参数多项式极小曲面，还没有出现高次多项式极小曲面的例子。

Properties of bi quadratic B spline surface are investigated by the subdivision approach, and the control mesh of bi quadratic B spline surface is constructed by employing Doo Sabin subdivision to derive the parametric representation of interpolation surface.

文中利用子分曲面理论研究双二次 B样条曲面的性质，在此基础上利用 Doo- Sabin子分模式构造插值顶点位置和法向的双二次 B样条曲面控制网格，得到插值曲面的参数表示。

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。

Either of two quadric surfaces generated by rotating a hyperbola about either of its main axes and having a finite center with certain plane sections that are hyperbolas and others that are ellipses or circles.

双曲面两个二次曲面的任何一个，通过使一个双曲线绕其任何一根中轴旋转而成，而且旋转时有一个有一定双曲线平面切面的中心，而其他切面是椭圆或圆周

Either of two quadric surfaces generated by rotating a hyperbola about either of its main ax es and having a finite center with certain plane sections that are hyperbolas and others that are ellipses or circles.

双曲面两个二次曲面的任何一个，通过使一个双曲线绕其任何一根中轴旋转而成，而且旋转时有一个有一定双曲线平面切面的中心，而其他切面是椭圆或圆周

Based on the scatted data , a suitable method has been proposed in this paper , in which the least eigenvector of covariance matrix for the local data points is used as the normal vector of the data .

这里针对散乱测量数据点云，以局部数据点协方差矩的最小特征向量作为数据点的方向矢量，并根据实际测量情况，对基于二次曲面拟合的数据点曲率估算算法进行了改进。

First, sequential tomograms of the hip are obtained from a CT scan; secondly, an accurate and automatic method is used to extract the profile of the acetabulum; thirdly, a hybrid method is utilized to gather fiducial marks on the acetabulum; fourthly, bulky error sampling points are removed. Finally, an ellipsoid fitting method is used to fit the ellipsoid model of the femoral head. Two male sufferers with different necrosis extents are chosen as experimental subjects for contrastive simulation.

首先利用一种精确的自动分割方法在髋骨部位CT序列图像中提取髋臼轮廓；然后使用基于等距栅格采样法与辐条式采样法相结合的混合采样法得到髋臼凹面的空间坐标点集，并剔除其中的误差采样点；最后采用基于二次曲面一般方程的方法拟合原始股骨头椭球面模型。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。