geodesics

简明释义

英[ˌdʒiːəˈdɛsɪks]美[ˌdʒiːəˈdɛsɪks]

n. [测]测地线（geodesic 的复数）

英英释义

单词用法

同义词

反义词

例句

1.A two-dimensional model of such a universe would look like a sphere. It's impossible to have parallel geodesics (straight lines on a curved surface) — the two lines will cross at some point.

这样的2维宇宙模型就像是球体，不可能出现平行的测地线(测地线是曲面上的直线)——两直线必然在某点相交。

2.A two-dimensional model of such a universe would look like a sphere. It's impossible to have parallel geodesics (straight lines on a curved surface) — the two lines will cross at some point.

这样的2维宇宙模型就像是球体，不可能出现平行的测地线(测地线是曲面上的直线)——两直线必然在某点相交。

3.Because arc length of trajectory is regarded as the variant in geodesics based method, it possesses the advantages of non-time based trajectory planning at the same time.

本文的基于测地线的轨迹规划是以轨迹弧长作为参考变量的，因此它还具有非时间参考的机器人轨迹规划的优点。

4.We present two practical linear methods computing straightest geodesics starting from a given point and going along a special tangent direction on triangle mesh.

我们提出了两个个实际的线性时间的算法求解三角网格上一点开始沿给定切方向的最直测地线。

5.Geodesics on smooth surface have many good geometric properties and there are equivalent partial differential equations and analytical methods solving it.

测地线在光滑曲面上有很好的几何性质，也有相应的测地线偏微分方程表达以及一些解析的方法来求解。

6.Straightest geodesics are with intact differential definition and theory system, but related study and application in graphics is very few now.

最直测地线有更完整的微分几何定义和理论系统，在图形学领域内，对它的研究和应用还比较少。

7.Also, the paper discuss the existence of the infinite closed geodesics of a compact no-simply connected Riemannian manifold.

并由此讨论了紧致的非单连通黎曼流形上无穷多的闭测地线存在性问题。

8.Adopting geodesics as dividing lines, space surfaces were developed by minimal extremum method.

采用测地线划分曲面，应用最小极值法进行曲面的展开。

9.It is proved that geodesics can be produced by stretch elastic strings along a smooth surface.

可以证明，连接平滑曲面上任意两点的弹性细丝当拉紧时具有测地线的形状。

10.In 1728 Euler gave differential equations for geodesics on surfaces.

1728年，奥伊勒绘出了曲面上测地线的微方程。

11.In mathematics, geodesics 测地线 are the shortest paths between two points on a curved surface.

在数学中，geodesics 测地线 是曲面上两点之间的最短路径。

12.The study of geodesics 测地线 is crucial in fields like astronomy and navigation.

对geodesics 测地线 的研究在天文学和导航等领域至关重要。

13.When designing a GPS system, engineers must consider the geodesics 测地线 of the Earth.

在设计GPS系统时，工程师必须考虑地球的geodesics 测地线。

14.In general relativity, geodesics 测地线 represent the paths that objects follow in spacetime.

在广义相对论中，geodesics 测地线 表示物体在时空中遵循的路径。

15.The concept of geodesics 测地线 can be applied to both theoretical models and real-world applications.

geodesics 测地线 的概念可以应用于理论模型和现实世界的应用。

作文

In the realm of mathematics and physics, the concept of geodesics plays a crucial role in understanding the shortest path between two points on a curved surface. A geodesic can be thought of as the equivalent of a 'straight line' in curved space, much like how a great circle represents the shortest distance between two points on the surface of a sphere. This idea has profound implications not only in theoretical mathematics but also in practical applications such as navigation, general relativity, and even computer graphics. To grasp the significance of geodesics, one must first appreciate the nature of curved surfaces. Imagine the Earth: while we often think of distances in terms of flat maps, the reality is that our planet is a three-dimensional object. When traveling from one city to another, the most efficient route is not always a straight line on a map but rather follows the curvature of the Earth. This path, which minimizes travel distance, is a geodesic. In the context of general relativity, Albert Einstein's theory illustrates how mass and energy can curve spacetime. In this framework, objects in motion follow geodesics through the curved spacetime, which explains why planets orbit stars and why light bends around massive objects. The concept of geodesics thus provides a powerful tool for physicists to describe the motion of celestial bodies and the behavior of light in the universe. Furthermore, geodesics find applications beyond pure science. In computer graphics, for example, algorithms designed to calculate the shortest paths on complex surfaces utilize the principles of geodesics to render realistic animations and simulations. This is particularly important in virtual reality environments where accurate representations of space enhance user experience. In engineering, the study of geodesics is essential for designing structures that must account for the curvature of the Earth, such as bridges or large buildings. Architects and engineers use the principles of geodesics to ensure that their designs are both aesthetically pleasing and structurally sound. Moreover, in the field of geography, geodesics assist in mapping and navigation systems. Global Positioning Systems (GPS) rely on precise calculations of geodesics to determine locations on Earth accurately. Without understanding these concepts, the functionality of GPS would be severely compromised, affecting everything from personal navigation to global logistics. In conclusion, the term geodesics encapsulates a fundamental principle that transcends various fields of study, from mathematics to physics, engineering, and computer science. By understanding geodesics, we gain insight into the nature of space and the relationships between different points within it. This knowledge not only enriches our academic pursuits but also enhances our everyday experiences, showcasing the interconnectedness of theoretical concepts and practical applications. As we continue to explore the universe and develop new technologies, the importance of geodesics will undoubtedly remain at the forefront of scientific inquiry and innovation.

在数学和物理学领域，测地线的概念在理解曲面上两点之间的最短路径方面发挥着至关重要的作用。测地线可以被视为曲面中“直线”的等价物，就像大圆表示球面上两点之间的最短距离一样。这个思想不仅在理论数学中具有深远的意义，还在导航、广义相对论甚至计算机图形学等实际应用中具有重要影响。 要理解测地线的重要性，首先必须欣赏曲面本质。想象一下地球：虽然我们通常以平面地图来思考距离，但现实是我们的星球是一个三维物体。当从一个城市旅行到另一个城市时，最有效的路线并不总是在地图上的一条直线，而是遵循地球的曲率。这条最小化旅行距离的路径就是测地线。 在广义相对论的背景下，阿尔伯特·爱因斯坦的理论说明了质量和能量如何弯曲时空。在这个框架中，运动中的物体沿着弯曲的时空遵循测地线，这解释了行星如何围绕恒星轨道运行，以及光在大质量物体周围弯曲的原因。因此，测地线的概念为物理学家描述天体运动和光在宇宙中行为提供了一种强大的工具。 此外，测地线的应用超越了纯科学。在计算机图形学中，例如，设计用于计算复杂曲面上最短路径的算法利用了测地线的原理，以渲染逼真的动画和模拟。这在虚拟现实环境中特别重要，因为准确的空间表现增强了用户体验。 在工程学中，测地线的研究对于设计必须考虑地球曲率的结构（如桥梁或大型建筑）至关重要。建筑师和工程师利用测地线的原理来确保他们的设计既美观又结构稳固。 此外，在地理学领域，测地线有助于制图和导航系统。全球定位系统（GPS）依赖于对测地线的精确计算，以准确确定地球上的位置。如果没有对这些概念的理解，GPS的功能将受到严重影响，影响从个人导航到全球物流的方方面面。 总之，术语测地线概括了一个基本原则，该原则跨越多个研究领域，从数学到物理学、工程学和计算机科学。通过理解测地线，我们获得了对空间性质及其内部不同点之间关系的洞察。这种知识不仅丰富了我们的学术追求，还增强了我们的日常体验，展示了理论概念与实际应用之间的相互联系。随着我们继续探索宇宙并开发新技术，测地线的重要性无疑将在科学探究和创新的前沿保持不变。