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In chapter Ⅵ, we use local sampling method to approximate functions and geometric curves, and to find the solution of the Laplacian equation locally, several numerical results are presented.

第六章利用局部采样的方法来逼近函数和几何曲线以及求Laplace方程的局部解，并给出了几个具体的算例。

Besides, we also use local sampling method to approximate functions and geometric curves, and to find the solution of the Laplacian equation locally, several numerical results are presented. This PH.

此外，我们还利用局部采样的方法来逼近函数和几何曲线以及求Laplace方程的局部解，并给出了算例。

The Laplacian on Riemannian manifolds is an essential linear operator, and it is also the main object to be studied of Geometric A...

Riemann流形上的Laplace算子是一个重要的线性算子，也是流形上几何分析研究的主要对象之一。

Experiments demonstrate that the Laplacian energy is very effective in preserving geometric details and preventing unreasonable volume changes.

实验结果表明，该算法可以有效地保持输入模型的几何细节、防止明显的体积变化，得到了令人满意的结果。

It mainly displays and turns the abstract quantitative relation into the appropriate geometric figure , find connection that exist under quantity from ocular characteristic of figure, so as to take , embarrass easy abbreviating , it melts latently to be an apparent purpose, make the problem be solved simple and directly .

它主要表现在把抽象的数量关系，转化为适当的几何图形，从图形的直观特征发现数量之间存在的联系，以达到化难为易、化繁为简、化隐为显的目的，使问题简捷地得以解决。

The result shows that there is no lateralization in recognizing geometric figures.

结果表明对于几何形状的认知没有表现出偏侧化。

To examine whether it is caused by the lateralization of form cognition, the second experiment is conducted, using geometric figures.

结果表明对汉字字形的认知具有偏侧化的倾向。

He showed by using geometric construction and the law of refraction (also known as Descartes' law) that the angular radius of a rainbow is 42 degrees i.e.

他使用几何结构和折射定律显示了一次彩虹的角半径（也就是彩虹边缘的虹膜与通过彩虹中心的阳光的内角）是42度。

Based on Fermat's theorem, the law of reflection and refraction is obtained, and the geometrical ray tracing method of reflected light is introduced. In response to geometric optics rainbow theory and Airy rainbow theory, the relationship formula of the N-order rainbow angle with the refraction index and the Airy peak value position formula are derived, and the physics causation of the first order rainbow are discussed and analyzed in detail. The distribution properties of the first and second order Airy structures of spherical particles are calculated.

利用费马原理推导了反射和折射定律，以反射射线的跟踪为例介绍了几何光学射线跟踪方法的推导过程；根据几何光学彩虹理论和Airy理论，推导了N阶几何光学彩虹角与入射角和折射率的关系及Airy峰的位置表达式，详细阐述了一阶彩虹形成的物理原因，计算了球形粒子的一、二阶Airy分布。

The mechanical measurement is to use an indicator to measure the surface or the edge of the testing lens mounted in a specific holder in a contact way. The principle of the optical measurement is the geometric optics, utilizing the properties of refraction or reflection of light to detect the centering error of the testing elements in a contactless way.

机械式的测量是利用指示器配合治具对待测透镜之外缘或表面进行接触式测量；而光学式的测量原理则是利用几何光学的折射或反射性质，对待测元件进行非接触式的偏心误差量测。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。