空间曲线

3D reconstruction is one of the most challenging problems in computer vision. This project uses CAD model to increase the accuracy,robustness and speed of 3D reconstruction and five different works are conducted: 1 research on space curve 3D reconstruction method based on high curvature point nad turning point; 2 free-form curve 3D reconstruction based on B-spline and BURBS; 3 Active surface affine reconstruction based on single frame; 4 Matching and reconstruction of 3D sparse points; Data fitting method based on the iteration of nearest point.

三维重建是计算机视觉中公认的难题，本项目使用CAD模型来提高三维重建的精度、稳健性和速度的思路，围绕着空间曲线和曲面的三维重建和匹配开展了以下五个方面的研究：1）基于高曲率点和拐点分割的空间曲线三维重建方法研究；2）基于B样条和NURBS表示的空间自由曲线三维重建方法研究；3）基于单帧图像的有源曲面仿射重建；4）三维离散数据的匹配与重建；5）基于迭代最近点的数据拟合方法。

In spatial analytic geometry,a spatial curve is an intersecting line of two curved surfaces.

在空间解析几何中，空间曲线是两曲面的交线，在空间曲线中消去一元，即得投影柱面。

Input the equation and other related parameters of space curve of driving tine by the system interface, then the equation and other parameters of space curve of the conjugate driven tine could be given by automatic design and calculation in the system.

通过系统界面输入主动轮钩杆的空间曲线方程及其他有关参数，此系统可以自动设计计算得到与其共轭的从动轮钩杆的空间曲线方程及其他参数。

The interpolation algorithm of introduced error compensation for complex parametric curve in space is proposed for the high precision interpolation of parametric curve on the basis of studying the first, second order taylor expression parametric curve interpolation algorithm and the plane parametric curves interpolation algorithm.

以一、二阶泰勒展开式参数曲线插补算法和平面参数曲线插补算法研究为基础，提出引入误差补偿值的复杂空间参数曲线高精度插补算法以实现空间曲线的高精度插补。

The paper discuss about the space curve and plane curve, and introduce the basic concept and the relations of them which we use to solve problem.

介绍了空间曲线和平面曲线的基本概念，空间曲线和平面曲线的关系，利用空间曲线与平面曲线的关系解题。

Briefly speaking, a space curve is called affinely infinite if it is intersected by every plane in the 3D real projective space; otherwise, it is called affinely finite.

简单地说，在三维实射影空间，如果一条空间曲线与射影空间中任意一个平面都相交，那么称这条曲线是仿射无限的；反之是仿射有限的。

Introduced is a kind of space uniform rational spline curve, which possesses tension parameters and is based on hyperbolic spline functions.

引入了基于双曲样条函数的、具有张力参数的空间有理等距节点样条参数曲线，给出了这种曲线在每个样条子区间上为挠曲线段的充分必要条件；分析了这种挠曲线段没有尖点、重结点和泛拐点的特性；因而在用于空间曲线几何造型时可避免奇异性。

Through research into space curve, get the equation of space curve, then reason the method of path programming according to the motion space of the manipulator.

通过空间曲线的研究，得出空间曲线方程，然后结合机械手的可达空间，得出机械手的路径规划。

Theory; the spatial meshing theory includes comparative motion, comparative differential and conjugative curved surface; and the application of meshing theory includes gear drive and worm drive. The spatial meshing theory is the main part of the course.

课程的重点讲解内容有曲线的参数方程、切线、法面、弧长、曲率、空间曲线的基本公式、挠率及平面曲线的基本公式等；曲面第一和第二基本公式，法曲率、主方向和主曲率、欧拉公式、短程挠率、欧拉公式和贝特朗公式推广、相对法曲率和相对短程挠率等；刚体的绝对和相对运动速度、相对微分和绝对微分、相对速度和相对微分、轨迹曲面的法曲率和短程挠率等；空间共轭曲面的啮合条件、诱导法曲率、两类界限点、等距共轭曲面、空间啮合的二次接触原理等；蜗杆传动的数学模型建立及啮合特性分析方法等。

However,there have been no papers which have investigated Minkowski and Minkowski slant helices and Minkowski conical geodesic curves so far as.In this paper,our major study is to give the definition of Minkowski general helix and Minkowski slant helices and Minkowski conical geodesic curves in indicators 1 in pseudo-Euclidean three-space (that is, three-dimensional Minkowski space), and study the definition of equivalence Minkowski general helix, By considering geometric invariants of these space curves, we can estimate the order of contact with those special curves for general space curves.

本篇文章主要研究在指标数为1的3维伪欧氏空间(即三维Minkowski空间)中，我们给出Minkowski一般螺线、Minkowski斜螺线和Minkowski锥面测地线的定义，研究Minkowski一般螺线的等价定义，给出Minkowski斜螺线和Minkowski锥面测地线作为三维Minkowski空间中的特殊曲线所特有的性质，并通过考虑三维Minkowski空间曲线的几何不变量，估计Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和一般Minkowski空间曲线切触的阶数。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。