planarity

简明释义

英[/pləˈnɛr.ɪ.ti/]美[/pləˈnɛr.ɪ.ti/]

n. [数] 平面性；平面化

英英释义

单词用法

同义词

反义词

例句

1.The non-planarity of a surface post electroplating process is usually dependent on variations of key layout characteristics including line width, line spacing and metal density.

铜电镀工艺后表面的不平整度通常取决于版图关键特征，包括线宽，线间距和金属密度。

2.Nevertheless it has been shown that side-chain planarity is important in conferring high adenyl cytokinin activity.

然而已经证明，对于高的腺苷细胞激动素活性，侧链的平面性很重要。

3.Slurry performance for CMP can be determined by several output parameters including removal rate, global planarity and surface defect.

抛光液的优劣主要有抛光率，平坦性以及缺陷的数量等几个参数反应。

4.In this paper, an algorithm with its mechanicalization is given, by which one can accomplish the following tasks simultaneously: planarity testing, making and embedding.

本文给出了同时完成图的平面性判定，平面化，以及平面嵌入的一个算法。同时给出了这一算法的机器化结果。

5.It is a simple simulation or a prototype of the famous graph game "Planarity" without the solution checker.

这是一个简单的模拟或原型著名的图形游戏“平面”的办法检查。

6.Planarity testing algorithm of graphs is a quite complex process.

图的平面性判定算法是相当复杂的。

7.Nevertheless, it has been shown that side-chain planarity is important in conferring high adenyl cytokinin activity.

然而已经证明，对于高的腺苷细胞激动素活性，侧链的平面性很重要。

8.The conveyor system made through mylar rolls (from roll to roll and recoverable if necessary), assures maximum planarity and cleaning of panels.

传送系统由聚酯薄膜滚筒构成（如必需可实现卷到卷），确保板料的平整性和清洁性。

9.A new neural network algorithm for the planarity testing problem is presented.

给出了平面测试问题的一种新型的神经网络算法。

10.For the 3D model to be printed correctly, its planarity must be verified.

为了确保3D模型正确打印，必须验证其平面性。

11.The engineer checked the planarity of the metal sheet before proceeding with the assembly.

工程师在进行组装之前检查了金属板的平面性。

12.The architect emphasized the importance of planarity in the design of the building to ensure a smooth surface.

建筑师强调了在建筑设计中确保表面光滑的重要性，即平面性。

13.The mathematician proved that the graph has planarity, allowing for simpler visual representation.

数学家证明了该图具有平面性，这使得可视化表示更简单。

14.In computer graphics, planarity is crucial for rendering surfaces accurately.

在计算机图形学中，平面性对于准确渲染表面至关重要。

作文

In the realm of mathematics and geometry, the concept of planarity plays a crucial role in understanding the properties of shapes and surfaces. Planarity refers to the characteristic of a geometric figure being able to lie flat on a single plane without any part of it rising above or falling below that plane. This fundamental idea is not only essential in theoretical mathematics but also has practical applications in fields such as computer graphics, architecture, and engineering.To further illustrate the importance of planarity, let us consider the simplest geometric figure: the triangle. A triangle is a two-dimensional shape made up of three straight sides and three angles. By its very nature, a triangle is planar; it exists entirely within a single plane. This property allows mathematicians and engineers to calculate area, perimeter, and other attributes with ease. In contrast, if we were to introduce a third dimension by lifting one vertex of the triangle off the plane, we would no longer have a triangle but rather a three-dimensional shape known as a tetrahedron. This change takes us away from the notion of planarity and introduces complexities that require different mathematical tools and considerations.The significance of planarity extends beyond simple shapes. In graph theory, for instance, a graph is said to be planar if it can be drawn on a plane without any edges crossing each other. This concept is pivotal in network design, where the goal is often to minimize the number of crossings between lines to enhance clarity and efficiency. Understanding whether a graph is planar can impact everything from circuit board design to transportation networks, making the study of planarity highly relevant in real-world applications.Moreover, the concept of planarity also finds its place in the realm of computer science, particularly in algorithms that deal with spatial data. For example, when rendering 3D objects on a 2D screen, understanding the planarity of various surfaces allows for more efficient calculations and better visual representations. In this context, planarity becomes a tool for optimizing performance in graphics rendering, ensuring that complex shapes are displayed accurately and efficiently.In architecture, planarity is equally vital. Architects must consider the planarity of their designs to ensure stability and aesthetic appeal. Structures such as bridges and buildings rely on the principles of planarity to distribute weight evenly and maintain structural integrity. A failure to account for planarity can lead to catastrophic results, making it imperative for architects to have a solid understanding of this concept.In conclusion, planarity is a fundamental concept that permeates various fields of study, from mathematics to engineering and beyond. Its implications stretch far and wide, influencing how we understand shapes, design structures, and create efficient systems. As we continue to explore the intricacies of our world, the importance of planarity will undoubtedly remain a topic of interest and relevance. Understanding planarity not only enhances our comprehension of geometric principles but also equips us with the knowledge necessary to apply these principles in practical, real-world scenarios.

在数学和几何学的领域中，平面性的概念在理解形状和表面的属性方面发挥着至关重要的作用。平面性是指几何图形能够平躺在单一平面上，而没有任何部分高出或低于该平面的特征。这个基本思想不仅在理论数学中至关重要，而且在计算机图形学、建筑和工程等领域也有实际应用。为了进一步说明平面性的重要性，让我们考虑最简单的几何图形：三角形。三角形是一个由三条直边和三个角组成的二维形状。由于其本质，三角形是平面的; 它完全存在于一个平面内。这个属性使得数学家和工程师能够轻松计算面积、周长和其他属性。相反，如果我们通过将三角形的一个顶点抬离平面来引入第三维度，我们将不再拥有三角形，而是一个被称为四面体的三维形状。这种变化使我们远离了平面性的概念，并引入了需要不同数学工具和考虑的复杂性。平面性的重要性超出了简单形状的范畴。在图论中，图形如果可以在平面上绘制而不交叉，则称为平面图。这一概念在网络设计中至关重要，因为网络设计的目标通常是最小化线条之间的交叉，以增强清晰度和效率。了解一个图是否是平面的可以影响从电路板设计到交通网络的一切，使得对平面性的研究在现实应用中高度相关。此外，平面性的概念在计算机科学领域也占有一席之地，特别是在处理空间数据的算法中。例如，在将三维物体渲染到二维屏幕上时，理解各种表面的平面性可以实现更高效的计算和更好的视觉表现。在这种背景下，平面性成为优化图形渲染性能的工具，确保复杂形状被准确有效地显示。在建筑学中，平面性同样至关重要。建筑师必须考虑他们设计的平面性以确保稳定性和美观性。桥梁和建筑等结构依赖于平面性的原理来均匀分配重量并保持结构完整性。未能考虑平面性可能导致灾难性的结果，因此建筑师必须对这一概念有扎实的理解。总之，平面性是一个基本概念，渗透到各个学科，从数学到工程及其他领域。它的影响深远，影响着我们如何理解形状、设计结构和创建高效系统。随着我们继续探索世界的复杂性，平面性的重要性无疑将继续成为一个感兴趣和相关的话题。理解平面性不仅增强了我们对几何原理的理解，还使我们具备了在实际现实场景中应用这些原理所需的知识。