曲面

The pattern of camber die-drawing are optimized. The physical innate character of drawing with camber die is analyzed thoroughly. For the first time, the periodical relation between the limit drawing coefficient and the large longitudinal stress in dangerous section is established. Furthermore, the rationale to judge limit deforming degree is developed. Then, the limit drawing coefficient of drawing with camber die is proposed. Based on the criterion that the large stress in flange is smaller than that of limit value, the formula of drawing with camber die without wrinkles is deduced.

对拉深凹模的型式进行了优化；深入地分析了曲面凹模拉深成形的物理本质，首次定量地确定了极限拉深系数与危险断面最大径向应力的关系，提出了判断极限变形程度的依据，分析了极限承载能力，建立了曲面凹模拉深的极限拉深系数的表达式；以凸缘切向最大压应力小于凸缘切向压应力临界值为准则，推导出了曲面凹模拉深不起皱的理论表达式。

Because of the condition of 〓 for two neighbour parametricspline surfaces is too strong,here,instead of it,some simple and practicableconditions of 〓 resulted from the general theorem obtained by Prof.LiuDing Yuan in Chapter 1 were proved,and three 〓 triangular splinesurfaces schemes wre presented:one is piecewise cubic spline surface patcheshaving local 〓 and whole 〓 continuity based on the refined HCTtriangulation,another is the same degree spline surface patches but based onthe refined Powell-Sabin triangulation,the third is piecewise quartic splinesurface patches having local 〓 and whole 〓 continuity based on therefined P-S triangulation.

由于对参数曲面，一阶导数连续的要求较强，我们采用第一章从刘鼎元定理导出的简单实用的几何连续条件，讨论了基于HCT加细三角剖分和P-S加细三角剖分上的两种局部达一阶导数连续而整体有一阶几何连续的分片三次样条曲面构造算法，一种局部达二阶导数连续整体有一阶几何连续的分片四次样条曲面构造方法。

The maximum spherical-head cotter radius was obtained by computing the minimum curvature radios of the cavity surface, and the finish cutter locution data were computed using the equidistant offset surface method.

通过计算型腔曲面最小曲率半径，确定精加工时球头刀的最大允许半径；应用等距偏移曲面法计算出型腔曲面数控精加工刀位数据。

It is the first time that the rational Bézier surfaces modeling problem has been proposed and approached successfully, which make it possible for us to research on minimal surface modeling of general conicoid.

在CAGD领域内首次提出了有理Bézier极小曲面造型问题并进行了成功的尝试，使得统一地研究一般二次曲面的极小曲面造型成为可能。

This paper makes the soil movement be four sections: a Cutting soil with edge; bThe soil movement along the plowshare and plow chest's below surface; c The soil movement along the plow cliff ;dThe soil movement beyond the plow in the course of farming in order to study the force of moldboard plow surface.

本文在研究犁体曲面受力时，把犁耕时土垡的运动分为四个阶段：a 用铧刃切开土垡；b 土垡沿犁铧和犁胸下部曲面运动；c 土垡沿犁壁运动；d 土壤超出犁壁曲面运动。

Estimation of the normal and curvature on meshes with good precision and rapidness is the foundation of many applications, such as characteristic detecting, partitioning, simplification, smoothing, distortion, reconstruction on mesh.

精确、快速地计算网格曲面的法向量和曲率等微分量是众多离散曲面应用的重要基础，对网格曲面的特征提取、网格分割、网格简化、网格光顺、网格变形、网格重建等处理过程均有重要的作用。

Because of the cost of computation,the order of the approximation surface usually is below four.

在对采样点构建插值曲面时，响应面法（Response Surface Method，RSM）通常是对整个曲面进行插值近似，由于计算量的原因，采用的近似曲面阶数通常不超过四阶。

Secondly, we investigate C°-flows on orientable closed surfaces having POTP, and obtain a necessary and sufficient condition of such flows.

剖析了这些轨道的邻域的轨线结构，还考虑了经过Poisson稳定点及几乎周期点的横截圈和相应的回归映射，其中本文讨论了可定向闭曲面上具有伪轨跟踪性质的C〓-流，得到了可定向闭曲面上C〓-流具有伪轨跟踪性质的较为简洁的充分必要条件；最后本文借助于从可定向的闭曲面到不可定向闭曲面的复叠投射，讨论了不可定向闭曲面上的C〓-流与其提升的轨线之间的联系，解决了不可定向闭曲面上C〓-流具有伪轨跟踪性质的判定问题。

The sculptured surface is machined with the difference method.3. In order to support sculptured surface design oriented to manufacturing,an embedded-computer-based platform was presented.

针对一个雕塑曲面零件设计实例，通过对模具分型方向和加工约束进行分析，给出了可行的分型曲面设计结果，验证了所提出的曲面可制造性分析方法的可行性。

Theorem(Stokes's Theorem) Let be a piecewise smooth oriented curve in three-space, be a piecewise smooth oriented surface with boundary curve .The surface and the curve are related by a right-hand relationship, i.e., if the fingers of the right hand are cupped in the direction of ,then the thumbpoints in the direction of orientation of .,, have continuous first partial derivatives on and ,then

定理 设为分段光滑的空间有向闭曲线，是以为边界的分片光滑的有向曲面，的正向与的侧符合右手规则(即如果右手大拇指表示曲面的方向，则弯曲四指表示曲线的方向)，函数，，在曲面上具有一阶连续偏导数，则有下述公式成立

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％。