曲面

We can perhaps forgive those who said the moons of Jupiter were produced by Galileo's spy-glass if we recall that in his day, as for centuries before, curved glass was the popular contrivance for producing not truth but illusion, untruth; and if a single curved glass would distort nature, how much more would a pair of them?

如果我们回忆一下，Galileo时代如同它的几个世纪以前一样，曲面镜不是用来产生真像而是产生幻影或假像的常用器械，那么，对于那些把木星的卫星说成用Galileo小望远镜产生出来的人们，我们或许会予以原谅的；如果一面曲面镜会歪曲大自然，那么一对曲面镜将会造成多大的歪曲呢？

We present application of this technique to generation of revolution surface .

流曲线曲面造型是一种自由曲线曲面造型技术，尝试用这种方法生成旋转曲面。

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。

After analysing functions and basic theory of Surfacer and studying key technology of object reverse engineering of complex parts, author expatiates data capture, data processing and surface reconstruction and summarizes methods and steps of surface reconstruction.

本文通过对逆向工程软件Surfacer的功能和基本原理的分析，研究了复杂曲面实物逆向工程的关键技术，对逆向工程中的数据获取、数据处理和曲面重构技术进行了详细阐述，总结了Surfacer在曲面重构中的方法、步骤和技巧。

Adopt software of Surfacer to fit curve and remodel surface, go on analysis of error and continuity, make model surface achieve rang of smooth and precision.

利用Surfacer软件对点云进行曲线拟合以及曲面重构拟合，通过对拟合曲线和自由曲面的误差分析以及连续性的分析，使构造的自由曲面光顺度和精度均满足要求，从而实现理论与实际的相结合。

Two merging methods of Bézier curves are generalized to tensor product Bé zier surfaces, we propose two methods to approximate two pieces of adjacent tensor product Bézier surfaces by a piece of tensor product Bézier surface. We offer the explicit formulas of the merged tensor product Bézier surfaces with all kinds of merging conditions.

同样，Bézier曲线的两种合并方法也被成功的推广到张量积Bézier曲面上，得到把两片相邻张量积Bézier曲面合并成一片张量积Bézier曲面的两种合并方法，并给出在各种合并条件下的合并曲面控制顶点的显示表示式。

At first, each surface is tessellated by subdividing all its bounding edges and joining the subdivision nodes with a regular array of isoparametric grids.

为使相邻曲面边界单元相容，即网格单元在相邻曲面边界处不会产生裂缝与覆盖，对多个裁剪参数曲面模型的网格剖

And then, by regarding the curve and surface as a map from differential manifold to topological manifold, we present the framework of GRPCS and discussed its basic properties in detail. GRPCS provides a unified framework for parametric curve and surface.

然后通过势函数来构造微分流形上的单位分解，将曲线曲面看作微分流形到拓扑流形的映射，给出了广义有理参数曲线曲面的整体理论框架，并对广义有理参数曲线曲面的基本性质进行了讨论。

Of, relating to, or shaped like a torus or part of a torus.

环形圆纹曲面环形圆纹曲面的或其某一部分的；形状象环形圆纹曲面的或其某一部分的；与之有关的

Testing in terrain relief, and the algorithms can optimize the structure of TIN nicely.(2) According to the smoothness of the terrain and correlation between adjacency data points, the paper studied the possibility of smooth surface constructing of DEM based on TIN. Then based on Tayor fomula, vertical normal vector, triangular decomposition, continuous and smooth of surface and so on, a new kind of interpolate model of DEM was proposed based on TIN.

2分析原始地形起伏变化的连续光滑性以及邻近数据点之间的相关性，探讨了基于TIN的DEM光滑曲面构造的可行性，并基于二元泰勒公式、三角面剖分、曲面的连续光滑性等，提出了一种TIN上的DEM表面光滑插值模型，并通过构造数学曲面进行精度评估，并对模型进行了可视化分析。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。