曲面

There have been many good results when M is minimal sub manifold. In the first section we will introduce the context and make a general description on the recent researches. In the second we will introduce the complexion of the development for this problem. In the fourth we\'ll discuss the second gap on special conditions using similar methods when the mean curvature is constant, and find the second gap.

关于极小子流形的间隙问题已经有了很多好的结果，第一节引言中我们将介绍本文的研究背景及这些主要结果，第二节中我们来介绍具有常平均曲率情形的间隙问题的发展现状，在第四节中我们用类似的方法讨论平均曲率为常数的紧致超曲面的第二间隙问题，得到了第二间隙δ=？

We have proved that there exist only one type of cubic polynomial thermal minimal surface. Some basic properties of it have been discussed and the free-selfintersect region is given. In additional, the quartic minimal surface is discussed.

在本文中我们从等温参数化出发，利用等温参数极小曲面的调和性质讨论了参数多项式极小曲面的存在性和唯一性问题，证明了三次等温参数多项式极小曲面的唯一性，给出了高次参数多项式曲面是极小曲面的一个条件，并在此基础上给出了若干高次参数多项式极小曲面的例子。

The paper has calculated equation of the generating curve of minimal surface of revolution by the approach of analysing.

用分析的方法导出了极小旋转曲面的生成曲线的方程。

We only determined the connection points within the space and the rest is a mathematical formula, a minimal surface.

我们只确定了连接点的空间，其余的是一个数学公式，一个极小曲面。

In practical engineering, it is difficult to find out the minimal surface meeting the architecture demands and the boundary restrictions, hence, the difference in the stress distribution should be controlled in a special range.

在实际工程中，由于膜结构建筑要求和边界条件的限制，找到具有极小曲面性质的初始平衡形状较难。因此，一般把应力的差值控制在一定的范围内。

LAVA's process of optimized minimal surface design and CNC fabrication technology allows the sculpture to reveal a new dimension in sustainable design practice.

熔岩的流程优化的极小曲面设计和数控系统制造技术使雕塑揭示了一个新的层面在可持续设计的做法。

The problem control points of free-form surface are modified automatically can be reduced to the solution of energy functionals minimum under the condition of constraint.

将自由形状曲面的控制点自动修改问题归结为一个在约束条件下求解能量函数的极小值问题。

The approximation error is defined as the integral of the minimum distance between each surfel on the original model and the fitting surface.

算法中的逼近误差定义为原始模型各面元到拟合曲面最小距离的积分。

The minimum distance computation problem has wide applications in CAD/CAM and computer graphics.

曲线、曲面间距离的计算问题在CAD/CAM、计算机图形学中有着广泛的应用。

After contrasting and optimizing this paper gets a set of parameters. Then according to these parameters the paper sets up entity model, and after validating and analyzing with finite element it can save time of calculating. On the other hand, it can provide a good method of design of moldboard plow surface.

通过对这四个阶段中土垡的运动学和动力学分析研究，建立了犁体牵引阻力的数学模型；通过对比分析得到较优的一组参数，然后以该组参数为依据进行参数优化，最后以优化后的参数建立犁体实体模型，应用有限元进行分析，节省了计算时间和提高了计算效率，为今后犁体曲面设计提供了一种方法。

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。