等距曲面

To obtain the parts surfaces' constant scallop height after machining, a new toolpath generation algorithm named as curved surface mapping approach for 3D equidistant path-interval and conto.

曲面映射法是依据加工后零件表面材料余量呈现"等残留高度"的要求，设计的一种生成空间等距环切加工刀具轨迹的新方法。

Based on that,the problem of reconstruction is studied according whether the axis-track surface is developable or not,and some valuable conclusions are derived.

在得出包络面、轴迹曲面、等效轴迹曲面互为等距曲面的结论的基础上，研究了轴迹曲面可展与不可展两种情况下的非等径包络重构问题，得到了一些有价值的结论。

Establish geometry model of hyperboloid clutch with rollers with differential geometry. We know that the line of tangent is beeline and validate it with Matlab.

利用微分几何相关知识建立了内外环的双曲面等距曲面及滚柱的几何模型，求解出其接触线为直线并用MATLAB进行了理论验证。

The main difference between the proposed method and the existing methods is that the new one embeds objects into the parametric space of the base surface by isometric or locally isometric mapping using the planar development of the base surface as the intermediate medium, thus the object to be deformed can follow the shape of the base surface homogeneously.

新方法中，变形控制曲面首先以等距或局部等距的方式展开为平面，然后经由平面的线性映射，将待变形物体嵌入控制曲面的参数空间中，从而产生符合控制曲面形状的局部均匀变形。

After introducing the primary approximation approaches for curve and surface offset, we give an optimal approximation approach for offsetting curve based on shifting control points, which relies on approximating the normal by Legendre polynomial approximation.

在全面介绍了等距曲线曲面逼近的主要方法以后，作者首先利用Legendre多项式得到基曲线法矢曲线的最佳平方逼近，由此给出了基于控制顶点偏移的等距曲线最优逼近的算法，它在算法效果和效率上都远优于其他同类算法。

The maximum spherical-head cotter radius was obtained by computing the minimum curvature radios of the cavity surface, and the finish cutter locution data were computed using the equidistant offset surface method.

通过计算型腔曲面最小曲率半径，确定精加工时球头刀的最大允许半径；应用等距偏移曲面法计算出型腔曲面数控精加工刀位数据。

We analyze and compare the advantage and the weakness of these two algorithms, and apply the second method to the approximation of tensor product offset surface.

文中分析和比较了这两种算法的优缺点，并将第二种方法推广应用于求张量积等距曲面的逼近。

Its principle is based on that there are some rdationships between curvatures of the theoretical profile surface and the real profile surface Curvatures of theoretical profile surface,which is a ruled surface,are easy to get.

该方法利用等距曲面间的曲率关系进行凸轮廓面曲率的解析计算。由于理论廓面是直纹面，其廓面曲率容易求得。

ABSTRACT This paper summarizes our researches on two key techniques in curve and surface modeling-the geometric approximation techniques and the geometric interpolation techniques. The former includes three types of geometric approximation techniques: Hybrid polynomial approximation to rational curves and surfaces, offset curves and surfaces approximation, interval Bézier curves and surfaces approximation. The latter includes a series of algorithms for shape blending modeling: the MSI algorithm for shape blending between space polylines or trees, the MSI algorithm for shape blending between triangular meshes, and skeleton-based shape blending algorithms using triangular decomposition and star-shape decomposition.

本文是作者对曲线曲面造型中两类核心技术几何逼近技术和几何插值技术的研究成果的总结，其中前者包括有理曲线曲面的Hybrid多项式逼近、等距曲线曲面逼近和区间曲线曲面逼近等三类几何逼近方法；后者包括用于形状混合造型的几何插值方法的一系列算法：空间多边形形状混合的MSI插值算法、三角网格形状混合的MSI插值算法、树的形状混合的MSI插值算法以及基于骨架树形状混合的三角剖分算法和星形剖分算法。

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。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。