angular transformation

简明释义

角变换;

英英释义

例句

1.In computer graphics, an angular transformation 角度变换 is used to rotate objects in a 3D space.

在计算机图形学中，angular transformation 角度变换 用于在三维空间中旋转物体。

2.Robotics often employs angular transformation 角度变换 to calculate the orientation of robotic arms.

机器人技术经常使用 angular transformation 角度变换 来计算机器手臂的方向。

3.The physics simulation requires an angular transformation 角度变换 to accurately represent the motion of spinning disks.

物理模拟需要进行 angular transformation 角度变换 来准确表示旋转盘的运动。

4.The software uses angular transformation 角度变换 algorithms to enhance the visual effects of video games.

该软件使用 angular transformation 角度变换 算法来增强视频游戏的视觉效果。

5.In animation, angular transformation 角度变换 helps create realistic movements by rotating characters smoothly.

在动画中，angular transformation 角度变换 通过平滑旋转角色来帮助创建逼真的动作。

作文

In the study of mathematics and physics, the concept of angular transformation plays a crucial role in understanding how objects rotate and change their orientation in space. An angular transformation refers to the process of changing the angle of an object or a coordinate system, which can significantly affect the object's position and the way it interacts with other objects. This transformation is not only applicable in theoretical contexts but also has practical implications in various fields such as engineering, computer graphics, and robotics.To better understand the significance of angular transformation, one must first consider the basic principles of rotation. When an object rotates around a fixed point, every point on the object moves along a circular path. The angle through which the object rotates is defined as the angular displacement. This concept is fundamental in mechanics, where the motion of rotating bodies is analyzed. For instance, in a spinning wheel, the angular transformation determines how fast the wheel turns and how far it travels over time.In addition to mechanical applications, angular transformation is essential in computer graphics, where it is used to manipulate images and models. When creating animations or rendering scenes, developers often need to rotate objects to achieve a desired perspective or effect. By applying angular transformation, they can easily adjust the orientation of the objects in a virtual environment, allowing for dynamic and visually appealing presentations.Moreover, in robotics, angular transformation is vital for controlling the movement of robotic arms and vehicles. Robots often operate in three-dimensional spaces, where precise movements are required to perform tasks effectively. By utilizing angular transformation, engineers can program robots to move at specific angles, enabling them to navigate complex environments and interact with objects accurately.The mathematical representation of angular transformation often involves matrices and vectors. In two-dimensional space, a rotation matrix can be used to represent the transformation mathematically. For example, if an object is rotated by an angle θ, the new coordinates of the object can be calculated using the rotation matrix, which incorporates the sine and cosine functions of the angle. This mathematical framework not only simplifies calculations but also provides a deeper understanding of the geometric implications of rotation.In conclusion, the concept of angular transformation is integral to various scientific and engineering disciplines. It allows for the analysis and manipulation of rotational motion, providing insights into the behavior of physical systems. Whether in mechanics, computer graphics, or robotics, mastering angular transformation is essential for anyone looking to delve into these fields. As technology continues to advance, the applications of angular transformation will only expand, making it a vital area of study for future innovations.

在数学和物理的研究中，角度变换的概念在理解物体如何旋转和改变其在空间中的方向方面起着至关重要的作用。角度变换是指改变物体或坐标系的角度的过程，这可以显著影响物体的位置以及它与其他物体的相互作用。这种变换不仅适用于理论背景，而且在工程、计算机图形学和机器人等多个领域具有实际应用。为了更好地理解角度变换的重要性，首先必须考虑旋转的基本原理。当一个物体围绕固定点旋转时，物体上的每个点沿着圆形路径移动。物体旋转的角度被定义为角位移。这个概念在力学中是基础的，其中旋转物体的运动被分析。例如，在一个旋转的轮子中，角度变换决定了轮子的转动速度以及它随时间的行进距离。除了机械应用之外，角度变换在计算机图形学中也是必不可少的，它用于操纵图像和模型。在创建动画或渲染场景时，开发人员经常需要旋转物体以实现所需的视角或效果。通过应用角度变换，他们可以轻松调整虚拟环境中物体的方向，从而实现动态和视觉上吸引人的展示。此外，在机器人技术中，角度变换对于控制机器人手臂和车辆的运动至关重要。机器人通常在三维空间中操作，需要精确的运动来有效执行任务。通过利用角度变换，工程师可以编程使机器人以特定角度移动，使它们能够准确地导航复杂环境并与物体互动。角度变换的数学表示通常涉及矩阵和向量。在二维空间中，可以使用旋转矩阵在数学上表示变换。例如，如果一个物体旋转了一个角度θ，则可以使用旋转矩阵计算物体的新坐标，该矩阵包含该角度的正弦和余弦函数。这种数学框架不仅简化了计算，还提供了对旋转几何意义的更深入理解。总之，角度变换的概念对于各种科学和工程学科至关重要。它允许分析和操纵旋转运动，为物理系统的行为提供了洞察。不论是在力学、计算机图形学还是机器人技术中，掌握角度变换都是任何希望深入这些领域的人的重要技能。随着科技的不断进步，角度变换的应用只会扩展，使其成为未来创新的重要研究领域。