曲面

But the design of complex curve and curve surface is the core in the CAD of vehicle body.

汽车车身是复杂的空间自由曲面，在汽车设计开发过程中，车身设计是直接影响设计成功与否的重要因素，而在车身的计算机辅助设计当中，复杂曲线和曲面的设计又是一个核心的问题。

Taking the converse design of automobile exhaust manifold that possesses complex free curved surfaces as the main line and by means of correlated development tools Surfacer and UG NX2 software etc.

以具有复杂自由曲面的汽车排气歧管逆向设计为主线，通过Surfacer和UG NX2软件等相关开发工具，介绍了整个开发过程的具体实施流程，并对其中的数据采集及变截面气道曲面拟合两个关键环节作了详细论述。

Moreover,the curve and surface subdivision occurs in 3D object rendering, surface approximation,wireframe displaying, finite element analysis and computing surface intersections,and so on.

随之而来的是对这些自由曲面的几何处理问题——曲线、曲面离散及裁剪等。

The changes of curvature in concavo-convex surface resulted in great non-uniform paint deposition when speed was constant.

针对表面有凹凸结构的复杂曲面，采用匀速喷涂方法，曲面上曲率的变化造成涂层厚度差较大。

Trajectory optimization method was applied to compensate coat thickness difference of complex curved surface with concavo-convex structure to improve the uniformity of coat thickens.

为提高曲面上涂层厚度的一致性，采用轨迹优化方法对表面有凹凸结构的复杂曲面的涂层厚度差进行补偿。

In Chapter 1,some elementary knowledge was introduced,such as theBernstein-Bezier representation for polynomials,conform triangulation,theconditions of convexity for Bézier spline surfaces,the funtional andgeometric continuity condition for neibour Bézier surface patches etc.,specially,based on the Liu-Ding-Yuan Theorem for geometric continuity,some simple and practical conditions were obtained.

第一章介绍一些基本知识，如多项式的Bernstein-Bézier表示，相容三角剖分的定义，Bézier三角样条曲面保凸的条件，相邻Bézier曲面片函数连续和几何连续的条件等，特别地，在刘鼎元关于几何连续条件的一般定理的基础上，导出了几个较简单的实用的一阶几何连续条件。

An image conic can be the projection of either a planar conic or silhouette of a conicoid. We show that at least three images, taken from the same position with different camera orientations, of two planar conics, or two conicoids, or one conic and one conicoid, are needed for the calibration, and a closed-form solution can be obtained. Our new conic based calibration technique requires no knowledge of camera's orientations, and relies solely on image correspondences.

在不同的方位拍摄三幅或三幅以上图像，每幅图像至少包含两个空间平面二次曲线、或两个二次曲面、或一个平面二次曲线与一个二次曲面的投影，利用图像之间的二次曲线对应关系，可以确定摄像机的内参数矩阵，同时可以获得摄像机不同方位之间的旋转矩阵。

Unlike previous approaches that use a single conic as proxy surface in the optimization phase, our method use multiple segments of conic to further reduce the error and guarantee C0 continuity between the conics in the same cone spline surface.

不同於旧有的方法利用单一的圆锥曲面，我们利用多段的圆锥曲面拟合网格以降低误差，并保证同一区块内，圆锥之间的C0连续性，因此我们的演算法可以利用较少的区块，来更精确的拟合网格。

The present thesis will adopt some of these methods to study on conjugation including the conjugate chord, Conjugate Direction and conjugate diameter of Conics as well as the Conjugate Direction, Conjugate net, Harmonic conjugate and Conjugate minimal surfaces of surfaces.

本文利用到了其中的某一些方法，讨论了这个问题，其中包括二次曲线的共轭弦、共轭方向，共轭直径。曲面上的共轭方向，共轭网，调和共轭，共轭极小曲面等。

The author not only presents pseudo sphere, ellipsoid ,conoid,uniported hyperboloid,elliptic biparted hyperboloid,paraboloid and hyperbolic paraboloid of the second elemental form,but also curve of the second elemental form.

不但给以了伪球面、椭圆面、劈锥曲面、单叶双曲面、双叶双曲面、椭圆抛物面及双曲抛物面的第二基本形式，而且给以了一般曲面的第二基本形式。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。