isometry

简明释义

英[aɪˈsɒmɪtri]美[aɪˈsɑːmətri]

n. 等距；等容；等高

英英释义

单词用法

同义词

反义词

例句

1.If many isometry parallel sections of samples, the ct image of every parallel section by analysing and sampling can be taken and the accurate 3d model of histology by computer can be rebuild.

若摄取样木的数十、成百个平行切片，依次逐步分析并采样得到的各平行切片的CT图象，运用计算机就可重建其组织结构的准确的三维模型。

2.Objective To explore the influence of femoral tunnel placement on the isometry of grafts in the reconstruction of posterolateral corner of the knee (PLC).

目的探讨膝关节后外侧角重建术中，股骨隧道定位的变化对移植物等距性的影响。

3.If many isometry parallel sections of samples, the ct image of every parallel section by analysing and sampling can be taken and the accurate 3d model of histology by computer can be rebuild.

若摄取样木的数十、成百个平行切片，依次逐步分析并采样得到的各平行切片的CT图象，运用计算机就可重建其组织结构的准确的三维模型。

4.After the further discussion and conduction, one can deduct out three patterns: symmetry pattern, isometry pattern and module pattern.

论文围绕高斯提出的算法，进一步讨论和归纳得到：对称式、等距式和模块式，运用这三种方式，更能直观、容易地解决实际问题。

5.In this paper, we show that the isometry between the unit spheres of certain normed space and its dual space can be extended to a real linear isometry on the whole space.

本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。

6.Furthmore and it is proved that every 2-local isometry of TUHF algebra is linear.

进一步证明了TUHF代数上满的2 -局部等距为线性。

7.The effects of 8 isometry transforms used in PIFS based fractal image coding on performance are discussed.

分析了基于部分迭代函数系统（PIFS）的传统分形图像压缩编码中8 种对称旋转变换对编码性能的影响；

8.We also prove that every 2-local isomety of UHF algebra is linear by studying the structure of the surjective isometry on UHF algebra.

对于UHF代数上满等距的结构，还证明了UHF代数上的2局部（满线性）等距是线性的。

9.In geometry, an isometry 等距变换 is a transformation that preserves distances between points.

在几何学中，isometry 等距变换 是一种保持点之间距离不变的变换。

10.An example of an isometry 等距变换 is a rotation, where the shape and size remain unchanged.

一个 isometry 等距变换 的例子是旋转，在这种情况下，形状和大小保持不变。

11.Understanding isometry 等距变换 helps in visualizing how objects can be manipulated in three-dimensional space.

理解 isometry 等距变换 有助于我们想象物体如何在三维空间中被操控。

12.The concept of isometry 等距变换 is crucial in the study of rigid motions in Euclidean space.

在欧几里得空间的刚性运动研究中，isometry 等距变换 的概念至关重要。

13.In computer graphics, isometries 等距变换 are used to model movements without distortion.

在计算机图形学中，isometries 等距变换 被用来模拟没有失真的运动。

作文

In the realm of mathematics, particularly in geometry, the concept of isometry plays a crucial role in understanding the properties of shapes and figures. An isometry is defined as a transformation that preserves distances between points, meaning that the original shape and its transformed image are congruent. This property of maintaining distances allows us to explore various geometrical transformations such as translations, rotations, and reflections without altering the fundamental characteristics of the shape involved.To illustrate this concept, let’s consider a simple example involving a triangle. Suppose we have a triangle ABC on a coordinate plane. If we perform a translation by moving each point of the triangle a certain distance in a specific direction, the resulting triangle A'B'C' will be an isometry. The lengths of the sides of triangle ABC will remain equal to the lengths of the corresponding sides in triangle A'B'C', thus demonstrating the essence of isometry.Another common transformation that exemplifies isometry is rotation. When we rotate triangle ABC around a fixed point, say point O, the distance from point O to each vertex of the triangle remains unchanged. Consequently, the shape and size of the triangle are preserved, reinforcing our understanding of isometry in geometric transformations.Reflections also provide a clear demonstration of isometry. If we reflect triangle ABC over a line, the resulting triangle A''B''C'' will be congruent to the original triangle ABC. The distances between the points are preserved, and thus, the transformation is classified as an isometry. These transformations not only help in visualizing geometric concepts but also serve as foundational tools in various branches of mathematics and physics.The significance of isometry extends beyond mere geometric transformations. In the field of computer graphics, for instance, isometries are essential for rendering images accurately. When creating three-dimensional models, designers often employ isometric projections to maintain the proportions and dimensions of objects. This technique ensures that the visual representation is true to the original dimensions, which is vital for realistic rendering.Moreover, isometry finds applications in robotics and animation. When programming a robotic arm to move from one position to another, engineers must account for isometries to ensure that the arm maintains its shape and does not distort during movement. Similarly, in animation, characters undergo various transformations, and understanding isometry helps animators create smooth and realistic movements.In conclusion, the concept of isometry is fundamental in both theoretical and practical applications across various fields. Its ability to preserve distances and congruence makes it a vital tool in understanding geometric properties, enhancing computer graphics, and facilitating motion in robotics and animation. As we continue to explore the intricacies of mathematics and its applications, the principles of isometry will undoubtedly remain a cornerstone of our understanding of spatial relationships and transformations.

在数学的领域，特别是几何学中，等距变换的概念在理解形状和图形的属性方面发挥着至关重要的作用。等距变换被定义为一种保持点之间距离的变换，这意味着原始形状及其变换后的图像是全等的。这种保持距离的特性使我们能够探索各种几何变换，例如平移、旋转和反射，而不改变所涉及形状的基本特征。为了说明这个概念，让我们考虑一个简单的例子，涉及一个三角形。假设我们在坐标平面上有一个三角形ABC。如果我们通过将三角形的每个点向某个方向移动一定的距离来进行平移，那么得到的三角形A'B'C'将是一个等距变换。三角形ABC的边长将与三角形A'B'C'中的对应边长保持相等，从而展示了等距变换的本质。另一个常见的示例是旋转。当我们围绕一个固定点（例如点O）旋转三角形ABC时，点O到三角形每个顶点的距离保持不变。因此，三角形的形状和大小得以保留，这进一步加深了我们对几何变换中等距变换的理解。反射也清楚地展示了等距变换。如果我们将三角形ABC关于一条直线反射，得到的三角形A''B''C''将与原始三角形ABC全等。点之间的距离得以保留，因此，该变换被归类为等距变换。这些变换不仅帮助我们可视化几何概念，而且还作为数学和物理学各个分支的基础工具。等距变换的重要性超越了单纯的几何变换。在计算机图形学领域，等距变换对于准确渲染图像至关重要。当创建三维模型时，设计师通常采用等距投影来保持物体的比例和尺寸。这种技术确保视觉表现真实于原始尺寸，这对逼真渲染至关重要。此外，等距变换在机器人技术和动画中也有应用。当编程一个机器人手臂从一个位置移动到另一个位置时，工程师必须考虑等距变换以确保手臂在运动过程中保持其形状而不失真。同样，在动画中，角色经历各种变换，理解等距变换帮助动画师创造平滑而逼真的运动。总之，等距变换的概念在理论和实践应用中都具有基础性意义。其保持距离和全等的能力使其成为理解几何属性、增强计算机图形学以及促进机器人技术和动画运动的重要工具。随着我们继续探索数学的复杂性及其应用，等距变换的原理无疑将继续成为我们理解空间关系和变换的基石。