quadric

简明释义

英[ˈkwɒdrɪk]美[kwɑːdrɪk]

adj. 二次的

n. 二次曲面

英英释义

单词用法

同义词

反义词

例句

1.This paper presents a new algorithm for realtime generation of rotating paraboloid images, which can be extended into quadric surfaces.

本文提出一种全新的，可推广至一般二次曲面的旋转抛物面实时成象的等灰曲度线算法。

2.To solve the problem of quadric surface reconstruction in reverse modeling for mechanical parts, a two-step fitting algorithm was presented.

针对机械零件反求建模过程中常见二次曲面的表面重建问题，提出了曲面拟合分步计算法。

3.In order to solve the problem, this paper put forward an improved mesh simplification algorithm based on quadric error metrics.

为了解决这个问题，本文作者提出一种改进的基于二次误差测度的网格简化算法。

4.By using quadric LQR algorithm, optimal control rule was educed. According to extremum principle, control force of driver on semi-active damper was confirmed.

通过二次型最优控制LQR算法，根据极值原理导出最优控制律，以确定半主动减振器驱动器控制力。

5.In this paper, the authors expounded covariance analysis with two correlated variables and solved it with quadric form.

利用二次型解决了双协变量的方差分析方法。

6.We call this surface the stress quadric.

我们称这个曲面为应力二次曲面。

7.The planar components and straight line components of the quadric surfaces intersections are studied precisely by means of matrix algebra in this paper.

本文利用特征多项式方程使得二次曲面交线的平面曲线分支的求解简化成平面与二次曲面求交问题。

8.The quadric 二次曲面 formula helps in defining shapes like ellipsoids and hyperboloids.

quadric 二次曲面 公式有助于定义椭球体和双曲面等形状。

9.In computer graphics, rendering a quadric 二次曲面 can be achieved using specialized algorithms.

在计算机图形学中，渲染 quadric 二次曲面 可以使用专门的算法来实现。

10.When studying conic sections, we often begin with the quadric 二次曲面 equations to understand their properties.

在研究圆锥曲线时，我们通常从 quadric 二次曲面 方程开始，以理解它们的性质。

11.The intersection of two quadric 二次曲面 surfaces can create complex shapes in three-dimensional space.

两个 quadric 二次曲面 的交集可以在三维空间中形成复杂的形状。

12.In mathematics, a quadric 二次曲面 is defined as a surface that can be represented by a second-degree polynomial equation.

在数学中，quadric 二次曲面 被定义为可以通过二次多项式方程表示的曲面。

作文

In the realm of mathematics, particularly in algebra and geometry, the term quadric refers to a specific type of surface or equation that is defined by a polynomial of degree two. These surfaces can take various forms, including ellipsoids, hyperboloids, and parabolas. Understanding quadric equations is essential for students who wish to delve deeper into the field of mathematics because they serve as foundational concepts that lead to more complex topics such as calculus and analytical geometry. The general form of a quadric equation in three-dimensional space can be expressed 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. This equation describes a variety of shapes depending on the values of these coefficients. For instance, if A, B, and C are all positive, the resulting shape is an ellipsoid, which resembles a stretched sphere. On the other hand, if one of these coefficients is negative, the shape can become a hyperboloid, which has a saddle-like appearance.One interesting aspect of quadric surfaces is their application in various fields outside of pure mathematics. For example, in computer graphics, quadric surfaces are used to model smooth shapes and surfaces, such as the contours of an object. Artists and engineers often rely on these mathematical principles to create realistic renderings in video games and simulations.Moreover, the study of quadric equations extends to physics, where they can describe the trajectories of objects under the influence of gravity. For instance, the path of a thrown ball can be modeled using a quadric equation, allowing physicists to predict its motion accurately. This intersection of mathematics and physics illustrates how essential quadric equations are in understanding the world around us.In addition to their practical applications, quadric equations also hold aesthetic value in art and architecture. Many famous structures, such as the Guggenheim Museum in New York, incorporate quadric forms into their designs. The curves and surfaces created by quadric equations can evoke a sense of fluidity and elegance, making them appealing to both artists and architects alike.To fully appreciate the concept of quadric equations, one must engage with both their theoretical underpinnings and their real-world applications. Students are encouraged to explore the geometric interpretations of these equations through graphing software or physical models. By doing so, they can gain a deeper understanding of how quadric surfaces behave and interact with one another in space.In conclusion, the term quadric encompasses a wide range of mathematical surfaces that play a crucial role in various disciplines. From mathematics to physics, art, and computer graphics, quadric equations provide valuable insights and tools for understanding both abstract concepts and tangible realities. As students continue to explore these fascinating equations, they will discover the beauty and complexity of the mathematical world, ultimately enriching their knowledge and appreciation for the subject.

在数学领域，特别是在代数和几何中，术语quadric指的是由二次多项式定义的特定类型的曲面或方程。这些曲面可以采取各种形式，包括椭球体、双曲面和抛物线。理解quadric方程对于希望深入数学领域的学生至关重要，因为它们是通往更复杂主题（如微积分和解析几何）的基础概念。三维空间中quadric方程的一般形式可以表示为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，该方程描述了各种形状。例如，如果A、B和C都是正数，则生成的形状是一个椭球体，看起来像一个拉伸的球体。另一方面，如果其中一个系数为负，则形状可能变成双曲面，具有鞍状外观。quadric曲面的一个有趣方面是它们在纯数学之外的各种领域中的应用。例如，在计算机图形学中，quadric曲面用于建模平滑的形状和表面，例如物体的轮廓。艺术家和工程师通常依赖这些数学原理来创建视频游戏和模拟中的真实渲染。此外，quadric方程的研究还扩展到物理学中，它们可以描述物体在重力影响下的轨迹。例如，抛出的球的路径可以用quadric方程进行建模，从而使物理学家能够准确预测其运动。这种数学与物理的交汇展示了quadric方程在理解我们周围世界中的重要性。除了它们的实际应用，quadric方程在艺术和建筑中也具有美学价值。许多著名的建筑，如纽约的古根海姆博物馆，将quadric形态融入其设计中。quadric方程所创造的曲线和曲面可以唤起流动感和优雅感，使其对艺术家和建筑师都具有吸引力。要充分理解quadric方程的概念，必须同时参与其理论基础和现实应用。鼓励学生通过图形软件或物理模型探索这些方程的几何解释。通过这样做，他们可以更深入地理解quadric曲面在空间中的行为和相互作用。总之，术语quadric涵盖了一系列在各种学科中发挥关键作用的数学曲面。从数学到物理学、艺术和计算机图形学，quadric方程提供了宝贵的见解和工具，用于理解抽象概念和具体现实。随着学生继续探索这些迷人的方程，他们将发现数学世界的美丽和复杂性，最终丰富他们对这一学科的知识和欣赏。