平移曲面

This dissertation addresses a practical data processing method of free-form surface for the coordinate measuring machine, including fitting algorithm, probe radius compensation and surface matching .

以坐标变换理论和最优化算法为基础，提出了应用单纯形法，对原始测量点进行坐标平移和旋转变换，将理论坐标与实际坐标统一起来，在此基础上进行误差处理，从而较好的解决了曲面匹配问题。

Then, the first and second fundamental forms, Gaussian curvature and mean curvature of the surfaces are directly calculated according to the principles of differential geometry.

首先，根据微分几何中的基本知识，得到了该种度量形式下的平移曲面的第一、第二基本形式以及高斯曲率和平均曲率；然后，主要利用高斯曲率和平均曲率之间的线性关系和平方关系，得到了这类平移曲面的分类定理。

The error compensation is introduced in the interpolation algorithm to increase the interpolation point's solution precision in the cutting direction of the parametric curved surface. The reasonable simplification of the computed result of the interpolation point's parameter value is carried in the operation process by focusing on the character that curvature of slow-varying parametric curved surface changed slowly and the feature that the scanned profile of translational scanned curved surface is parallel along the scanned line.

通过引入误差补偿值以提高参数曲面在走刀方向上插补点的计算精度，针对缓变参数曲面曲率缓变和平移扫描曲面扫描轮廓沿扫描线平行的特点在运算过程中对插补点参数值的计算结果进行合理简化。

Because there exists a high randomness an easier weighted method is used to establish Grid-format data to approximately describe 3-D space topography, 3-D topography is constructed for Grid-format data by using OpenGL technology, and a free transform of the space curved surface is realized, including parallel move, zoom, circumgyrate. Simultaneously, an algorithm of random incision of 3-D space curved surface containing most six sides is provided, in comhination of geologic evolution, element.

由于存在很大的随机性，采用较为简单的加权方法来建立规则网格Grid格式数据体对三维空间地形进行近似描述，利用OpenGL技术构造Grid数据体三维地形，并对构造出的三维空间曲面进行平移、缩放、旋转等自由变换，提供最多6个切面对三维空间曲面进行任意切割的算法，结合地质演化需要，利用双缓存技术实现了地质要素三维曲面动态演化过程。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。