平面可展曲面

In this paper,the B-spline curve is supposed as boundary curves,when they are in two paralled plane and two arbitrary plane,the condition about the control vertex of characteristic polygon when the ruled surface is developable are gained,solved the designing problem of degree and degree B-spline curve .Throughing (2,3) degree and (2,2) degree B-spline ,we haveproved the validity and utility of this method.

本文用两条B样条曲线作边界曲线，当它们位于两平行平面上和两任意平面上时，研究得到了由它们形成的直纹面为可展面时它们的特征多边形顶点满足的条件，解决了(n，n+1)次和次可展B样条曲面的设计问题，然后以(2，3)次和(2，2)次B样条曲面为构造实例，证明了该算法的正确性和实用性。

In this manner, a developable surface was designed using control planes with Bézier and B-spline basis functions.

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

Based on the important idea of duality between plane and point geometries,two direct explicit methods of computer-aided design for developable surface s were proposed,the developable surface s were represented using control planes with appropriate basis functions.

为了克服传统方法在可展曲面设计上的缺陷，方便地解决工程中经常遇到的可展曲面位置和形状难以调整和控制的问题，基于3D射影空间中点和平面间的对偶性这一重要思想，提出了两种直接、简单的可展曲面设计方法。

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。

In wire-cutting manufacturing of the top and bottom different curve,accomplishing cutting way of ellipse bias changing curved surface which between two plane curve into developable surface in order to calculate NC program of four axis ganging.

在上下异型工件的线切割加工中，宜采用椭圆偏置切割法，即将上、下两平面曲线间的曲面变成可展直纹面，进而计算四轴联动的数控程序，可保障加工的效率与效益。

Though the analysis of the convexity of the front surface, this paper gained some terse and practical results.We can control the shape of developable surface through adjusting corresponding plane curves.

本文通过对上述两种可展B样条曲面进行保凸分析，得到了一些简洁，适用的结论：只要调整相应平面曲线，就能控制可展面的形状。

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。

To solve the problems in adjusting and controlling shapes of developable surfaces, following the important idea of duality between points and planes in 3D projective space, two direct explicit and efficient methods of computer aided design for developable surfaces are proposed.

为了解决工程中可展曲面位置与形状难以调整和控制的问题，基于3D射影空间中点和平面间的对偶性这一重要思想，提出了2种直接、简单有效的可展曲面设计新方法。

I put some current in side the surface and use two planes to cut the surface, then made two Amperian loops, then do integral on Theta.

里面是电流分布，然后我是用两个面把那一堆电流切开，做两个安培环，然后在THETA角上做积分。

Toucans|for this musical revue in Brazil.

知道吗 我以前去找能唱歌的鸟|为巴西的音乐剧找巨嘴鸟