frustum

简明释义

英[ˈfrʌstəm]美[ˈfrʌstəm]

n. [数] 截头锥体；平截头体

复 数 f r u s t a 或 f r u s t u m s

英英释义

单词用法

同义词

反义词

例句

1.According to this difficulty, a kind of fast calculation method of satellite orbit-extract the orbits control points is put forward, and perspective frustum is combined to judge the orbits visibility.

针对这一难点，提出了一种卫星轨道快速计算的方法-提取轨道的控制点，结合透视裁剪体来判断轨道的可见性。

2.Time spent culling objects outside the camera frustum.

摄像机视景外剔除对象花费的时间。

3.With the feather of them, they can be used to developing visualization simulation engine. These algorithms also include the terrain texture generation algorithms and the frustum culling algorithms.

这一章还介绍了地形纹理的生成算法，视图平截头体选取算法，这些算法使得计算机可以用来处理大规模的可视化工作。

4.In addition, dynamical management of terrain dataset in view field was implemented effectively by visible detection based on the simplified view frustum and terrain data prediction strategy.

此外，简化视见体的可见性判断和数据预取策略，实现可见数据的动态管理。

5.It is necessary to consider the reasonableness of split and the quality of shadow image when drawing shadow based on the view frustum split in a large scale scenes.

采用基于视截体分层的方法进行大规模场景阴影绘制时，需要考虑分层的合理性与阴影的图像质量。

6.Since we defined the frustum, we know the Angle at which the sides of the frustum meet - this is the field of view we used to create the projection matrix in the first place.

确定好锥截体，我们就知道锥截体顶角的大小—这是我们在第一个地方用来创建投影矩阵的视场。

7.The volume of a cone can be calculated by subtracting the volume of the smaller cone from the larger cone's volume, resulting in the volume of the frustum.

通过从较大圆锥的体积中减去较小圆锥的体积，可以计算出圆锥的体积，从而得到截头体的体积。

8.In architecture, the design often incorporates a frustum shape for aesthetic appeal.

在建筑设计中，常常采用截头体形状以增强美观性。

9.The frustum of a pyramid can be used to create unique furniture designs.

金字塔的截头体可以用来创造独特的家具设计。

10.To calculate the surface area of a frustum, you need to find the areas of both circular bases and the lateral surface area.

要计算截头体的表面积，需要找出两个圆形底面的面积和侧表面积。

11.A frustum is often seen in engineering applications, such as in the design of certain types of tanks.

在工程应用中，截头体常常出现在某些类型的储罐设计中。

作文

In the world of geometry, shapes come in various forms and sizes, each with its unique properties and applications. One such shape that often finds its way into both theoretical mathematics and practical engineering is the frustum. A frustum is defined as the portion of a solid that lies between two parallel planes cutting it. More specifically, when we talk about a frustum, we are usually referring to the truncated portion of a cone or a pyramid. This fascinating geometric figure has numerous applications, from architecture to manufacturing, demonstrating its importance in both academic and real-world contexts. To better understand the frustum, let’s delve into its characteristics and how it is formed. Imagine taking a cone and slicing it horizontally through its height, resulting in two parts: the top part, which is a smaller cone, and the bottom part, which is the frustum. The frustum retains the base of the original cone while losing its apex. This process of truncation allows for a variety of useful shapes that can be employed in design and construction. One of the most common uses of the frustum is in the design of lampshades. A lampshade often resembles a frustum because it needs to be wider at the bottom to allow for light dispersion while being narrower at the top to fit onto a lamp base. Similarly, many architectural structures utilize the frustum shape, such as towers and columns, to provide stability and aesthetic appeal. The tapering design not only helps in distributing weight but also enhances the visual perspective of the building. In addition to architecture, the frustum is significant in the field of engineering. For instance, when designing certain mechanical parts, engineers often use frustums to optimize material usage while ensuring strength and durability. The concept of the frustum also extends to the creation of molds in manufacturing processes, where a frustum shape can facilitate the production of complex components with ease. Mathematically, calculating the volume of a frustum is essential for various applications. The formula for the volume of a frustum of a cone is given by V = (1/3)πh(R² + Rr + r²), where h is the height of the frustum, R is the radius of the larger base, and r is the radius of the smaller base. This formula allows architects and engineers to determine how much material is needed for construction or how much space a particular design will occupy. Moreover, the frustum appears in computer graphics, particularly in rendering three-dimensional objects. In this context, a frustum defines the visible area of a scene, helping to manage what is displayed on the screen and optimizing performance. By understanding the dimensions of the frustum, programmers can efficiently render images, ensuring that only the necessary parts of a scene are processed and displayed. In conclusion, the frustum is more than just a geometric term; it is a crucial concept that bridges the gap between mathematics and practical applications. From lampshades to architectural designs and engineering components, the frustum plays an integral role in our daily lives. Understanding its properties and applications not only enhances our knowledge of geometry but also equips us with valuable insights into the world around us. As we continue to explore the realms of mathematics and its applications, the frustum will undoubtedly remain a shape of significance.

在几何学的世界中，形状有各种形式和大小，每种形状都有其独特的属性和应用。其中一个经常出现在理论数学和实际工程中的形状是截头体。截头体被定义为位于两个平行平面之间的固体部分。更具体地说，当我们谈论截头体时，通常是指圆锥或金字塔的截断部分。这种迷人的几何图形在建筑到制造等多个领域都有许多应用，展示了它在学术和现实世界中的重要性。 为了更好地理解截头体，让我们深入探讨其特征以及它是如何形成的。想象一下，取一个圆锥并在其高度上水平切割，结果得到两个部分：顶部部分是一个较小的圆锥，底部部分则是截头体。截头体保留了原始圆锥的底面，而失去了顶点。这种截断过程允许形成多种有用的形状，可以用于设计和建造。 截头体最常见的用途之一是在灯罩的设计中。灯罩通常类似于一个截头体，因为它需要在底部更宽以便散发光线，同时在顶部更窄以适应灯座。同样，许多建筑结构利用截头体形状，例如塔楼和柱子，以提供稳定性和美观。锥形设计不仅有助于分配重量，还增强了建筑的视觉透视效果。 除了建筑，截头体在工程领域也具有重要意义。例如，在设计某些机械部件时，工程师经常使用截头体来优化材料使用，同时确保强度和耐久性。截头体的概念还扩展到制造过程中模具的创建，其中截头体形状可以方便复杂组件的生产。 在数学上，计算截头体的体积对各种应用至关重要。圆锥的截头体体积公式为V = (1/3)πh(R² + Rr + r²)，其中h是截头体的高度，R是较大底面的半径，r是较小底面的半径。这个公式使建筑师和工程师能够确定建筑所需的材料量或特定设计所占空间。 此外，截头体在计算机图形学中也出现，特别是在渲染三维物体时。在这种情况下，截头体定义了场景的可见区域，有助于管理屏幕上显示的内容并优化性能。通过理解截头体的尺寸，程序员可以有效地渲染图像，确保仅处理和显示场景的必要部分。 总之，截头体不仅仅是一个几何术语；它是一个关键概念，架起了数学与实际应用之间的桥梁。从灯罩到建筑设计再到工程部件，截头体在我们的日常生活中扮演着不可或缺的角色。理解其属性和应用不仅增强了我们对几何的认识，还为我们提供了对周围世界的宝贵见解。随着我们继续探索数学及其应用的领域，截头体无疑将继续作为一个重要的形状存在。