曲面

The concept and algorithm for nonsingular orientation-workspace of the platform at a certain position are proposed.

提出了该机构处于给定位置时的非奇异姿态工作空间概念及其算法，并以非奇异姿态工作空间边界曲面的最小内切球作为实际姿态工作空间，以该球半径大小作为衡量机构处于给定位置时的实际姿态能力的性能指标。

Direct difference is sensitive to noisy data, so a threshold limitation is given, which can not only filter the result from noisy data but also pick edge points up according men's desire. On the other hand, artificial intelligence is used for segmentation in reverse engineering. Because the essence of segmentation is clustering similar characteristics and self-organizing feature mapping is one function of neural network, SOFM network is used for segmentation in the thesis, coordinates and normal of data points is took as the characteristics vector.

第二种方法，基于双向角度微分的边点提取法，针对三维正交模型采用基于截面线的方式组织数据，此方法比基于曲率半径方法更简洁，不用进行曲面拟合，大大提高了计算速度；计算过程中由数据点的直接差分逼近微分，但直接差分对数据误差敏感，为此，本文提出了阈值过滤的方法，一方面过滤了数据误差在计算结果中引起的噪音，另一方面可以按照设计意图控制边点的提取；来决定是否提取光滑交接的边点。

For keeping the cutting efficiency and balancing of machine tools,the method for adjustment of feed-rate is proposed based on division of normal curvature radius on surface of parts.

为保证数控加工中的切削效率和机床运动的平稳性，提出了基于曲面曲率划分的进给速度修正方法。

So the offset point position can be adjusted adaptively as the normal curvature of surface changes along the offsetting direction.

因此偏置点的位置能够随着偏置方向曲面法曲率的变化自适应地调整。

The normal and curvature are significant geometry information for 3D point clouds.

差分坐标以其相关之拉普拉斯运算子在三维数位几何模型上已有许多的研究及应用，顶点的差分坐标计算是由顶点与拓扑上之相邻点的相对位置关系所求得，因此顶点之差分坐标代表了区域曲面起伏变化情况，差分坐标其方向会近似於区域法线方向而其长度会近似予区域平均曲率，此两项资讯为点云资料重要几何资讯。

Moreover, an offset approximation with high precision is obtained by degree elevation of the direction curve of normal.

因此关于等距曲线、曲面的研究，已成为 CAGD中的一个热门课题。

Also how to calculate normal vector of the original surface is introduced.

在第三章，介绍了特征的准确定义，并介绍了特征提取算法，并在特征提取的算法中，介绍了一种计算网格曲面顶点法向量的比较好的方法。

Where 、and is the direction cosines of the normal vector of the directed surface at the point .

其中、、是有向曲面在点处的法向量的方向余弦。

Objective: To quantitatively analyze the normal acetabular subchondral surface and investigate its anatomic characteristics.

目的：定量分析人体正常髋臼软骨下骨的曲面形态，探讨其解剖形态学特征。

This paper presents a novel triangulation algorithm based on the normal information of the surface and the Delaunay triangulation algorithm.

借助于曲面上的法矢信息和三维Delaunay三角剖分算法，该文给出了一种新的散乱点三角剖分算法。

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％。