oblique coordinates

简明释义

斜座标

英英释义

例句

1.The mathematical model was easier to solve when expressed in oblique coordinates 斜坐标系, leading to faster computations.

当用oblique coordinates 斜坐标系表达时，数学模型更容易求解，从而加快了计算速度。

2.In computer graphics, transformations are often easier to perform in oblique coordinates 斜坐标系 to achieve perspective effects.

在计算机图形学中，变换通常在oblique coordinates 斜坐标系中更容易执行，以实现透视效果。

3.The engineer decided to represent the structure's dimensions in oblique coordinates 斜坐标系 to better visualize the angles.

工程师决定用oblique coordinates 斜坐标系表示结构的尺寸，以更好地可视化角度。

4.When analyzing forces in physics, using oblique coordinates 斜坐标系 can simplify the calculations of resultant vectors.

在物理学中分析力时，使用oblique coordinates 斜坐标系可以简化合力的计算。

5.In robotics, motion planning can benefit from oblique coordinates 斜坐标系 to navigate complex environments more effectively.

在机器人技术中，运动规划可以利用oblique coordinates 斜坐标系更有效地导航复杂环境。

作文

In the study of geometry and physics, the concept of oblique coordinates plays a significant role. Unlike the traditional Cartesian coordinate system, which utilizes perpendicular axes to define positions in space, oblique coordinates allow for a more versatile framework that can adapt to various geometrical configurations. This flexibility is particularly useful in fields such as engineering, computer graphics, and even in certain areas of mathematics where non-orthogonal systems provide advantages in problem-solving.To understand oblique coordinates, one must first grasp the basic principles of coordinate systems. In a Cartesian system, points are defined by their distance from two or three mutually perpendicular axes. For instance, in two dimensions, a point is represented by its x and y coordinates, while in three dimensions, it is represented by x, y, and z coordinates. However, this rigid structure can sometimes limit the representation of certain shapes or phenomena, especially when dealing with angles that are not right angles.This is where oblique coordinates come into play. By allowing the axes to be at arbitrary angles to each other, oblique coordinates enable the representation of more complex relationships between points. For example, in a system where the axes are inclined at an angle to one another, the coordinates of a point can be expressed in terms of these oblique axes, which may simplify calculations involving certain geometric figures.One practical application of oblique coordinates can be found in the field of computer graphics. When rendering images, especially those involving perspective, using oblique coordinates can help in accurately depicting objects that are not aligned with the standard axes. This method allows for more natural representations of scenes, making it easier for artists and designers to create visually appealing graphics.Moreover, in physics, oblique coordinates are often utilized in problems involving forces and motion. For instance, when analyzing the motion of an object on an inclined plane, it can be beneficial to use oblique coordinates aligned with the incline rather than the standard Cartesian coordinates. This alignment simplifies the equations of motion, making it easier to calculate the forces acting on the object and predict its trajectory.In addition to these applications, oblique coordinates also have theoretical significance in advanced mathematics. They are often employed in the study of vector spaces and transformations, where understanding the relationships between different coordinate systems is crucial. By expressing vectors in oblique coordinates, mathematicians can gain insights into their properties and behaviors that may not be apparent in a standard Cartesian framework.In conclusion, the concept of oblique coordinates offers a powerful tool for representing and analyzing various geometrical and physical phenomena. By moving beyond the constraints of traditional coordinate systems, oblique coordinates provide a flexible alternative that can enhance our understanding of complex relationships in both theoretical and applied contexts. As we continue to explore new frontiers in science and technology, the utility of oblique coordinates will undoubtedly remain an important area of focus, paving the way for innovative solutions and deeper insights into the nature of space and form.

在几何和物理学的研究中，斜坐标的概念起着重要作用。与传统的笛卡尔坐标系统不同，后者利用垂直轴来定义空间中的位置，斜坐标则允许更灵活的框架，可以适应各种几何配置。这种灵活性在工程、计算机图形学甚至某些数学领域中尤其有用，因为非正交系统在解决问题时提供了优势。要理解斜坐标，首先必须掌握坐标系统的基本原理。在笛卡尔系统中，点是通过其距离两个或三个互相垂直的轴来定义的。例如，在二维中，一个点由其x和y坐标表示，而在三维中，则由x、y和z坐标表示。然而，这种刚性的结构有时会限制某些形状或现象的表示，特别是在处理不是直角的角度时。这就是斜坐标发挥作用的地方。通过允许轴以任意角度相互倾斜，斜坐标使得可以表示点之间更复杂的关系。例如，在一个轴以一定角度倾斜的系统中，点的坐标可以用这些斜轴来表达，这可能简化涉及某些几何图形的计算。斜坐标的一个实际应用可以在计算机图形学领域找到。在渲染图像时，尤其是涉及透视的图像，使用斜坐标可以帮助准确描绘那些不与标准轴对齐的物体。这种方法允许更自然地表示场景，使艺术家和设计师更容易创建视觉上吸引人的图形。此外，在物理学中，斜坐标通常用于涉及力和运动的问题。例如，在分析物体在倾斜平面上的运动时，使用与倾斜面对齐的斜坐标可能是有益的。这种对齐简化了运动方程，使得计算作用于物体的力并预测其轨迹变得更加容易。除了这些应用外，斜坐标在高等数学中也具有理论意义。它们常常被用于研究向量空间和变换，其中理解不同坐标系统之间的关系至关重要。通过在斜坐标中表示向量，数学家可以获得关于它们的性质和行为的洞察，这在标准笛卡尔框架中可能并不明显。总之，斜坐标的概念为表示和分析各种几何和物理现象提供了一种强大的工具。通过超越传统坐标系统的限制，斜坐标提供了一种灵活的替代方案，可以增强我们对复杂关系的理解，无论是在理论还是应用的背景下。随着我们继续探索科学和技术的新前沿，斜坐标的实用性无疑将仍然是一个重要的关注领域，为创新解决方案和对空间及形式本质的深入洞察铺平道路。