切线曲面

The paper deals with curvature line and curvature characteristic of developable surface based on differential invariant of developable surface and it details curvature line and curvature characteristic of cone and tangent surface .

本文通过可展曲面的微分不变量，导出可展面的曲率线与曲率特征，并以锥面和切线曲面为例阐明这些特性的几何意义。

The methods of development for cones and tangent surface on C-Bézier curve and the complex surfaces are obtained.

首先，构造了C-B？zier曲线上的锥面和切线曲面，分别建立了它们到平面的等距映射，给出了C-B？

All quadrilateral mesh automatic generation for regular quadric surfaces based on Auto CAD AME;2. Represent Quadric Surfaces Using NURBS and Calculate the Control Vertecs and Weights;3. Through study,the property is found out that planes cutting edgewise quadric curve and quadric intersections from the quadric surfaces become the harmonic division.

文中采用了射影几何的方法，证明了画法几何中关于两个二次曲面相交的著名的复切定理和蒙日定理，通过研究得出了周切线平面和交线平面成调和分割的性质，同时还得出了处于复切的二次曲面必存在相公切的二次曲面的性

As the application of the methods given, involute helicoid, which is widely applied in engineering, is developed into plane. And the problem in plate metalwork, which is t he development of square-circle tie-in, is also solved by the method.

其一是钣金工中方-圆类接头的展开问题，该问题的解决是锥面展开方法的成功应用；其二是螺旋输送器的核心部件——铰龙的展开问题，它是切线曲面展开方法应用的典型实例。

First, a map between the cones and tangent surface on C-Bézier curve und two-dimensional plane is found respectively and then a ruled surface between two Bezier curves is constructed and a sufficient condition on its developablity is given.

zier曲线上锥面、切线曲面的展开方法。然后，构造两条空间B？zier曲线上的直纹面，给出了它成为可展曲面的一个充分条件，并通过保角保长原则，将其贴合到平面上。

The latter is a tangent surface with C-Bézier curve as spine curve.

四、给出了C-B？zier曲线上锥面、切线曲面以及复杂曲面的展开方法。

Based on the principle of surface development in differential geometry, the method of development for cone and tangent surface is given. Cone is developed in the unit ball way.

锥面的展开是利用单位球方法，确定直母线与平面上过定点射线之间的映射关系，进而展开曲面；切线曲面的展开则利用准线曲率在展开中的不变性，确定准线在平面上的展开曲线，再作与之相切的直母线，从而实现曲面的展开。

Transition piece ; development ; approximate tangent surface

变形接头；展开；近似切线曲面

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。

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。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。