曲面

Finally, when a 00, the limt situations for the developable modeling and surface development above are all disscussed and Compared with those on Bezier curve .

六、以上提出的C-B？zier曲线上可展曲面造型方法和曲面展开算法，均给出了当α→0时的极限，并与B？

It order to overcome the difficulties in representation of developable surface s utilizing traditional approaches,based the concept of duality between points and planes in 3D projective space, a direct explicit method of computer-aided design for developable surface s was presented.

基于三维射影空间中点和平面间的对偶性，提出了计算机辅助设计五次样条上可展曲面的一种简单且有效的方法，通过采用该方法，可利用具有B啨zier和B样条基的控制平面设计可展曲面。

First, this paper, in the field of intrinsic geometry, studies the geometric problems on garment design, as well as applies the frame and semi-geodesic coordinates to prove the fundamental theorem of being a developable surface.

文中首先在内在几何学的层次上，研究了服装设计所涉及的几何学问题，应用标架与半测地坐标方法证明了曲面成为可展面的基本定理，研究了可展面的分类及其性质，考虑到服装三维几何造型的需要，证明了组合式可展面各组成片相切连接条件的命题，作为构造可展面的理论依据，证明了单参数平面族的包络面必为可展面的命题，在此基础上发展出服装几何造型的"刮大白"方法以及相关的三种构造可展面的解析方法。3D→2D的变换是三维服装CAD的重要内容之一，其几何学实质是曲面的定长映射，文中总结了定长映射即可展面在平面上展开的基本准则，在这一准则的指导下，结合服装设计与相关领域的要求，讨论了可展面在平面上展开的解析方法与数字方法，上述内容确立了服装设计几何学的基本框架。

Techniques for the geometric design of developable surfaces herein had all the characteristics of existing approaches for curves design.

讨论了所设计可展曲面的特点和几何构造，研究结果表明，所提出的设计方法具有现有曲线设计方法的特征，现有的对于曲线的一些几何构造技术可延伸到可展曲面的设计。

It shows that some of the geometric construction algorithms that exist for curves can be also generalized to the design of developable surfaces.

基于将可展曲面作为平面单参数族包络面的思想，给出在B啨zier和B样条基下可展曲面的参数表示形式。

Surface blending in terms of geometric continuous is more practical and welcome with view of geometric interpretation which is different to the traditional differential method based on algebra.

几何连续是对参数曲面中参数连续度量进一步深刻的认识和研究。它是可微性的代数概念的几何抽象，克服了参数连续对曲面苛刻，高阶及结果失真等缺点。

Chapter 3,minimal surface is one of important surfaces in the differential geometry.

第三章，极小曲面是一类非常重要的曲面，在微分几何中具有特殊的重要地位。

The first section is descriptive geometry, including basic knowledge of cartography and projection, projections of point, beeline, plane and their interrelations, projection transformation, curve, curving plane, the projection of curving plane solids, line of section, line of intersection, section and segmentation, elevation projection, dimetric projection.

第一部分为画法几何：其中有制图基本知识，投影的基本知识，点、直线、平面的投影及它们之间的关系，投影变换，曲线、曲面及曲面立体的投影，截交线与相贯线，剖面图与断面图，标高投影，轴测投影等。

Earthworks zero line is determined by constructing the spatial gridding curved surface model of the original terrain and the field leveling design terrain by digital elevation mode. The DEM data of original terrain are obtained by actual measurement. The mathematical correlation is deducted to demonstrate the relationship between the coordinates of any point on spatial line and the direction cosine by the spatial linear equation. DEM data obtaining program is compiled by Fortran9.0 and it is applied automatically to obtain the DEM data of field leveling design terrain.

目的 利用数字高程模型(digital elevation model， DEM)构造原始地形和场平设计地形的空间网格曲面模型，确定土方工程中的零线方法通过实测提取原始地形DEM数据；依据空间直线方程，推导空间线段土任意点的坐标与方向余弦的数学关系式，采用Fortran90程序设计语言编写DEM数据提取程序，自动提取场平设计地形DEM数据；应用Surfers8.0和MapInfo软件构造规则的网格空间曲面模型并导出网格节，点数据；擦除场平设计范围外数据。

It includes an optimized curve fitting algorithm based on the least-squares method and a surface lofting algorithm in which a interpolation function is employed to provide a continuous variation of the parameter in one direction over the entire lofted surface.

基于最小二乘法，对截面数据进行均方误差下的精确优化拟合；在曲面蒙面算法中，采用插值函数确定蒙面曲面一个方向的参数。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。