quadrics

简明释义

英[ˈkwɒdrɪks]美[ˈkwɑːˌdrɪks]

n. 二次型；二次曲线（quadric 的复数形式）

英英释义

单词用法

同义词

反义词

例句

1.The inverse dynamic method of manipulator and the Linear Quadrics (LQ) optimum control method are employed to investigate the problems of trajectory tracking and eliminating the remaining vibration.

利用机械臂逆动力学方法和线性二次型（LQ）最优控制方法讨论刚柔性耦合机械臂的轨迹跟踪控制问题和消除残余振动的控制问题。

2.The inverse dynamic method of manipulator and the Linear Quadrics (LQ) optimum control method are employed to investigate the problems of trajectory tracking and eliminating the remaining vibration.

利用机械臂逆动力学方法和线性二次型（LQ）最优控制方法讨论刚柔性耦合机械臂的轨迹跟踪控制问题和消除残余振动的控制问题。

3.The following embarks from the system state space; the condition feedback control and quadrics optimum controls are studied.

随后又从系统的状态空间出发，研究了状态反馈控制和二次型最优控制；

4.In this thesis, we will investigate subdivision method and its application, including construction of four-point wavelets, generation of sharp features and quadrics.

本文主要研究细分方法及其应用，所做的工作包括四点小波的构造、尖锐特征造型和二次曲面造型。

5.It is known that the projection of the intersection of quadrics with common plane of symmetry on this plane is a curve of second order.

具有公共对称平面的二次曲面的交线在该平面上的投影为二次曲线。

6.Architects may model buildings using quadrics 二次曲面 for aesthetic purposes.

建筑师可能会使用quadrics 二次曲面来建模建筑，以达到美学目的。

7.The study of quadrics 二次曲面 is essential in algebraic geometry.

对quadrics 二次曲面的研究在代数几何中至关重要。

8.In physics, quadrics 二次曲面 can describe the surfaces of certain fields.

在物理学中，quadrics 二次曲面可以描述某些场的表面。

9.Mathematicians classify quadrics 二次曲面 into various types based on their properties.

数学家根据属性将quadrics 二次曲面分类为不同类型。

10.In computer graphics, we often use quadrics 二次曲面 to represent complex shapes with simple mathematical equations.

在计算机图形学中，我们常用quadrics 二次曲面来用简单的数学方程表示复杂的形状。

作文

In the realm of mathematics and geometry, the term quadrics refers to a specific class of surfaces defined by polynomial equations of degree two. These surfaces play a pivotal role in various fields, including computer graphics, engineering, and physics. Understanding quadrics is essential for anyone looking to delve deeper into the study of three-dimensional shapes and their properties.A quadric can be expressed in a canonical form as Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0, where A, B, C, D, E, F, G, H, I, and J are constants. Depending on the values of these coefficients, quadrics can take on various shapes, such as ellipsoids, hyperboloids, paraboloids, and cones. Each of these shapes has unique geometric properties that have practical applications in real-world scenarios.For instance, an ellipsoid, which is a type of quadric, resembles a stretched sphere and can be used to model objects like planets and stars in astrophysics. Hyperboloids, another form of quadrics, are often found in architectural designs due to their aesthetic appeal and structural integrity. Paraboloids, characterized by their bowl-like shape, are commonly used in satellite dishes and reflectors because they can focus parallel rays to a single point.The classification of quadrics is primarily based on their geometric properties. They can be categorized into four main types: elliptic, hyperbolic, parabolic, and degenerate. Elliptic quadrics include ellipsoids, which have a closed shape, while hyperbolic quadrics consist of hyperboloids that open outward. Parabolic quadrics represent surfaces that resemble a parabola, and degenerate quadrics refer to cases where the surface does not form a complete shape, such as intersecting lines or points.To visualize quadrics, one can use graphing software or tools that allow for three-dimensional modeling. By manipulating the coefficients in the polynomial equation, students and enthusiasts can observe how the shape of the quadric changes in response. This hands-on approach not only reinforces theoretical understanding but also enhances spatial reasoning skills.In addition to their mathematical significance, quadrics have practical implications in various technological advancements. For example, in computer graphics, quadrics are utilized to create realistic models of objects and environments. By approximating complex shapes with quadrics, graphic designers can achieve high levels of detail while maintaining computational efficiency. Similarly, in engineering, quadrics are employed in the design of structures and components, ensuring stability and functionality.In conclusion, the study of quadrics encompasses a rich interplay between mathematics, geometry, and real-world applications. Whether one is exploring the beauty of geometric shapes or applying these concepts in technology and engineering, understanding quadrics provides a foundational knowledge that is both fascinating and practical. As we continue to explore the complexities of three-dimensional spaces, quadrics will undoubtedly remain a critical area of study, revealing insights into the nature of shapes and their interactions within our universe.

在数学和几何学的领域中，术语quadrics指的是由二次多项式方程定义的一类特定表面。这些表面在计算机图形学、工程学和物理学等多个领域中发挥着关键作用。理解quadrics对于任何希望深入研究三维形状及其属性的人来说都是至关重要的。quadric可以用标准形式表示为Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0，其中A、B、C、D、E、F、G、H、I和J是常数。根据这些系数的值，quadrics可以呈现出各种形状，例如椭球体、双曲面、抛物面和圆锥体。这些形状每一种都有独特的几何属性，在现实世界中具有实际应用。例如，椭球体作为一种quadric，类似于拉伸的球体，可以用来模拟天文学中的行星和恒星。双曲面，另一种quadrics，因其美学吸引力和结构完整性而常见于建筑设计中。抛物面以其碗状形状为特征，广泛用于卫星天线和反射器，因为它们能够将平行光线聚焦到一个点上。quadrics的分类主要基于它们的几何属性。它们可以分为四种主要类型：椭圆型、双曲型、抛物型和退化型。椭圆型quadrics包括椭球体，这些体具有封闭形状，而双曲型quadrics则由向外开放的双曲面组成。抛物型quadrics表示类似于抛物线的表面，退化型quadrics指的是表面未形成完整形状的情况，例如相交的直线或点。为了可视化quadrics，人们可以使用图形软件或允许三维建模的工具。通过操纵多项式方程中的系数，学生和爱好者可以观察到quadric形状如何随之变化。这种动手实践的方法不仅强化了理论理解，还增强了空间推理能力。除了数学意义外，quadrics在各种技术进步中也具有实际意义。例如，在计算机图形学中，quadrics被用于创建真实的物体和环境模型。通过用quadrics近似复杂形状，图形设计师可以在保持计算效率的同时实现高水平的细节。同样，在工程学中，quadrics被用于结构和组件的设计，以确保稳定性和功能性。总之，quadrics的研究涵盖了数学、几何与现实世界应用之间的丰富互动。无论是探索几何形状的美丽，还是在技术和工程中应用这些概念，理解quadrics都提供了一个既迷人又实用的基础知识。随着我们继续探索三维空间的复杂性，quadrics无疑将继续成为一个关键研究领域，揭示形状及其在我们宇宙中的相互作用的深刻见解。