空间曲线

First, the paper introduces the moving coordinate system based on the curve tangent vector and the curvature component vectors. Next, the total curvature vector is composed and the osculating plane determined in the moving coordinate system. The curve bending is then calculated and the recursion analysis made on the osculating plane.

鉴于空间曲线上曲率采集面的变化，引入了由曲线切向量和曲率分量决定的运动坐标系，接着在运动坐标系中合成曲率矢量，确定密切平面，然后在密切平面中对曲线进行弯曲计算和运动坐标系的变换分析，并对相关公式进行了推导。

Basing on the 3D image data compression and in accordance with the structure characteristics of 3DLCS scanning data that the scanning data set of 3D surface can be considered as a curve set in 3D space, the thesis extends 2D curve Splitting compressing method to the 3D space and presents a 3D curve compressing method based on the curve compression and the color information compression. The 3D compressing effect is better.

在三维图像数据压缩方面，根据3DLCS的扫描数据结构特点（即可以将三维表面扫描数据集看作一个空间曲线的集合），将平面曲线压缩中的Splitting方法推广到三维情形，提出了一种基于曲线压缩和彩色信息压缩的三维数据压缩方法，取得了较好的压缩效果。

Prove, proof 直线:straight line 曲线:curve 平面:plane 举例: any of a set of two or more numbers used to determine the position of a point, line, curve, or plane in a space of a given dimension with respect to a system of lines or other fixed reference.

由两个或多个数值组成的数组中的任一数值，用来在一个直线系统或其它固定参照数值方面决定点、直线、曲线或平面在已知范围空间内的位置。

The centerline of elastic rod or elastic filament can be abstracted as space curves to deal with them by the knowledge of the theory of space curve and differential geometry.

由于弹性杆的中心线或弹性细丝可以抽象成空间曲线，然后根据空间曲线论和微分几何的知识进行处理。

Similar formulae hold for a line integral of the second type taken over a space curve.

对于空间曲线上的第二类曲线积分也有类似的公式。

The line of curvature isn't only a curve of space, but a special and a very important curve of surface.

曲率线不仅是一条空间曲线，而且是曲面上定义的一种特殊而重要的曲线。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一，对其有效的表示是造型的基础，而特征参数化表示是其中一种包含语义信息的高层次表示，本文对空间自由曲线的特征参数化表示进行研究，建立了一种针织物线圈的特征参数化几何模型，采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系，并将该模型与能量极小化的方法相结合，得到了一种能较好地预测针织物缩水率的新模型，对随机选取的一些针织布缩水预测实验表明了算法的可行性。

This paper analyses the tangent equation of space curve and the derivation process of the curved tangent plane equation in the higher-mathematics teaching-materials, and shows another method to extract the tangent equation of space curve.

分析高等数学教材中空间曲线的切线方程和曲面的切平面方程的推导过程，给出求空间曲线的切线方程的另一种方法。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r&‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。