barycentric

简明释义

英[ˈbæriːsntrɪk]美[bæriˈsentrɪk]

adj. 重心的

英英释义

单词用法

同义词

反义词

例句

1.The advantages of barycentric interpolation formulations in computation are small number of floating point operations (flops) and good numerical stability.

重心插值公式具有计算量小、数值计算稳定性好和增加新的插值节点不需重新计算原有插值节点基函数的优点。

2.The advantages of barycentric interpolation formulations in computation are small number of floating point operations (flops) and good numerical stability.

重心插值公式具有计算量小、数值计算稳定性好和增加新的插值节点不需重新计算原有插值节点基函数的优点。

3.Based on homogeneous barycentric coordinates, a new geometric variable, sharpness factor, is defined for measuring sharpness of independent vertexes.

基于齐次重心坐标，定义了新的网格顶点几何变量——锐度因子。

4.The barycentric coordinates of the plane view projection of a coal face are solved with a formula of geometric gravity centre.

利用平面图形几何重心公式计算回采工作面水平投影图形的重心坐标，然后根据影响传播角和开采深度计算下沉盆地中心位置的坐标。

5.At first the original data points are resampled using barycentric coordinates, followed by fitting the resampled data points.

该方法首先用重心坐标对原始的数据点进行重采样，然后对重采样得到的数据点进行拟合。

6.The differentiation matrices of unknown function are constructed by using barycentric rational interpolation.

采用重心有理插值近似未知函数，得到未知函数的各阶微分矩阵。

7.The relativistic geometric time delay of VLBI is derived in the Barycentric Reference System (BRS).

本文以太阳系质心参考系为基础推导了VLBI时延和引力延迟的后牛顿表达式；

8.Chapter 4 USES barycentric subdivision method on arbitrary discrete parametric curves net.

第四章考虑上述的重心加细方法，将之应用于任意的离散参数曲线网上。

9.In computer graphics, the use of barycentric 重心的 coordinates allows for smooth interpolation of vertex attributes across a triangle.

在计算机图形学中，使用barycentric 重心的 坐标可以实现三角形顶点属性的平滑插值。

10.The barycentric 重心的 method is often applied in finite element analysis to simplify complex geometries.

在有限元分析中，barycentric 重心的 方法常用于简化复杂几何形状。

11.Using barycentric 重心的 coordinates, we can easily determine if a point lies within a triangle.

使用barycentric 重心的 坐标，我们可以轻松判断一个点是否位于三角形内部。

12.The barycentric 重心的 approach is essential in rendering techniques that require precise color blending.

在需要精确颜色混合的渲染技术中，barycentric 重心的 方法是必不可少的。

13.In physics, barycentric 重心的 coordinates can be useful for analyzing systems with multiple bodies.

在物理学中，barycentric 重心的 坐标对于分析多体系统非常有用。

作文

In the field of mathematics and physics, the term barycentric refers to a coordinate system that is centered around the centroid of a geometric shape or a set of points. This concept is particularly useful in various applications, including computer graphics, physics simulations, and even in the analysis of complex systems. The barycentric coordinate system allows us to express points within a triangle or a simplex in relation to its vertices, which simplifies many calculations and enhances our understanding of spatial relationships. To illustrate the significance of barycentric coordinates, consider a triangle formed by three vertices A, B, and C. Any point P inside this triangle can be represented as a combination of these vertices using weights that sum up to one. The weights correspond to how much influence each vertex has on the position of point P. For instance, if point P is closer to vertex A, it will have a higher weight associated with A compared to B and C. This representation not only provides a clear geometric interpretation but also facilitates interpolation and other mathematical operations. The utility of barycentric coordinates extends beyond simple geometric shapes. In computer graphics, they are widely used for texture mapping and shading. When rendering a triangle on the screen, each pixel within the triangle can be assigned color values based on the barycentric coordinates of the corresponding vertices. This technique allows for smooth transitions and realistic visual effects, enhancing the overall quality of graphical representations. Furthermore, in physics, barycentric coordinates play a crucial role in understanding the dynamics of systems involving multiple bodies. For example, in celestial mechanics, the motion of planets and satellites can be analyzed using a barycentric approach, where the center of mass of the system serves as the reference point. This perspective simplifies the equations of motion and provides insights into gravitational interactions between bodies. Moreover, the concept of barycentric coordinates is not limited to two-dimensional spaces; it can be extended to higher dimensions as well. In three-dimensional space, for instance, a tetrahedron can be described using barycentric coordinates relative to its four vertices. This versatility makes the barycentric approach applicable in various fields, including computer-aided design (CAD), robotics, and even machine learning. In conclusion, the term barycentric encapsulates a powerful mathematical framework that enhances our ability to analyze and manipulate geometric and physical systems. By providing a means to express points in relation to a set of reference points, barycentric coordinates simplify complex calculations and enable a deeper understanding of spatial relationships. As technology continues to advance, the applications of barycentric concepts in various domains will undoubtedly expand, paving the way for innovative solutions and discoveries. Understanding this term is essential for anyone interested in mathematics, physics, or computer graphics, as it lays the foundation for numerous practical applications and theoretical explorations.

在数学和物理学领域，术语barycentric指的是围绕几何形状或一组点的质心中心的坐标系统。这个概念在各种应用中尤其有用，包括计算机图形学、物理模拟，甚至在复杂系统的分析中。质心坐标系统使我们能够根据其顶点表示三角形或单纯形内的点，这简化了许多计算并增强了我们对空间关系的理解。 为了说明barycentric坐标的重要性，考虑一个由三个顶点A、B和C形成的三角形。三角形内部的任何点P都可以表示为这些顶点的组合，其权重之和为1。权重对应于每个顶点对点P位置的影响程度。例如，如果点P更靠近顶点A，则与A相关的权重将高于与B和C相关的权重。这种表示不仅提供了清晰的几何解释，还便于插值和其他数学运算。 barycentric坐标的实用性超越了简单的几何形状。在计算机图形学中，它们广泛用于纹理映射和阴影处理。当在屏幕上渲染三角形时，三角形内的每个像素可以根据相应顶点的质心坐标分配颜色值。这种技术允许平滑过渡和逼真的视觉效果，增强了图形表示的整体质量。 此外，在物理学中，barycentric坐标在理解涉及多个物体的系统的动力学方面发挥着关键作用。例如，在天体力学中，行星和卫星的运动可以使用质心方法进行分析，其中系统的质心作为参考点。这种视角简化了运动方程，并提供了对物体之间引力相互作用的深入见解。 而且，barycentric坐标的概念不仅限于二维空间；它可以扩展到更高维度。例如，在三维空间中，一个四面体可以相对于其四个顶点用质心坐标来描述。这种多功能性使得barycentric方法在计算机辅助设计（CAD）、机器人技术甚至机器学习等多个领域都有应用。 总之，术语barycentric概括了一种强大的数学框架，增强了我们分析和操纵几何和物理系统的能力。通过提供一种相对于一组参考点表达点的方法，barycentric坐标简化了复杂的计算，并使我们对空间关系有了更深刻的理解。随着技术的不断进步，barycentric概念在各个领域的应用无疑将扩展，为创新解决方案和发现铺平道路。理解这个术语对于任何对数学、物理或计算机图形学感兴趣的人来说都是至关重要的，因为它为众多实际应用和理论探索奠定了基础。