trilinear

简明释义

英[traɪˈlɪnɪə(r)]美[traɪˈlɪnɪər]

adj. 三线的，包含三条线的，以三条线为边界的

英英释义

单词用法

同义词

反义词

例句

1.In the experiment of trilinear pendulum, the influence of the approximation used in the deduction to the result of measurement is analysed, and the way to reduce this influence is pointed out.

讨论了在推导转动惯量的测量公式时采用的近似方法对测量结果带来的影响，指出了减小其影响的途径。

2.Based on test results, a trilinear material property model is proposed, it permits the fire response analysis of steel structures to be made more accurately.

基于对试验结果的分析，提出了便于应用的钢材三折线高温材性模型，为较精确地进行结构火灾反应分析奠定了基础。

3.The trilinear coefficients derived from this calculation formula basically agree well with those obtained from field survey method.

采用该公式计算的三线系数与现场调查分析法所得结果基本一致。

4.Based on the theory of encounter probability, the formula for calculating trilinear coefficients is deduced.

基于遭遇概率理论，推导三线系数的计算公式。

5.Assuming a trilinear geometrical spreading model, we obtained the attenuation function in Guangdong region.

采用三段几何衰减模型拟合，得到了广东地区的几何衰减函数。

6.In elastoplastic dynamic analysis, the trilinear loop for RC wall (or tube) and the bilinear loop for steel frame are adopted.

进行弹塑性分析时，钢筋砼部分采用三线性滞回线，钢结构部分采用双线性滞回线。

7.The trilinear equation can be used to find points in a three-dimensional space.

可以使用trilinear 方程在三维空间中找到点。

8.To improve image quality, many video games utilize trilinear filtering for texture mapping.

为了提高图像质量，许多视频游戏利用trilinear 过滤进行纹理映射。

9.In architecture, a trilinear approach can help visualize complex structures.

在建筑设计中，trilinear 方法可以帮助可视化复杂结构。

10.The trilinear method is often applied in 3D modeling to enhance the realism of surfaces.

在3D建模中，通常应用trilinear 方法来增强表面的真实感。

11.In computer graphics, a trilinear interpolation is used to create smoother transitions between textures.

在计算机图形学中，trilinear 插值用于创建纹理之间更平滑的过渡。

作文

In the field of geometry, the term trilinear refers to a specific type of coordinate system that is particularly useful in triangle geometry. A trilinear coordinate system is defined by the distances from a point to the sides of a triangle. This concept allows mathematicians and students alike to explore various properties of triangles in a more nuanced manner. Understanding trilinear coordinates can greatly enhance one's grasp of triangle centers, such as the centroid, orthocenter, and circumcenter.To illustrate the importance of trilinear coordinates, consider a triangle ABC. Each side of the triangle can be assigned a length, and the distances from any point within or outside the triangle to these sides can be measured. For instance, if we have a point P, the distances from P to sides BC, CA, and AB can be denoted as d_a, d_b, and d_c respectively. The trilinear coordinates of point P are then expressed as (d_a : d_b : d_c). This representation provides a powerful tool for analyzing the relationships between points and lines within the triangle.One of the key advantages of using trilinear coordinates is that they simplify many geometric problems. For example, when dealing with concurrency of lines or the collinearity of points, trilinear coordinates can provide a straightforward approach to finding solutions. By converting complex relationships into simpler ratios, one can often derive results that would be difficult to obtain using traditional Cartesian coordinates.Moreover, trilinear coordinates are not only limited to theoretical mathematics; they also have practical applications in fields such as computer graphics and engineering. In computer graphics, understanding the properties of triangles is essential for rendering images accurately. By employing trilinear interpolation techniques, graphics programmers can create smooth transitions and realistic textures in 3D models. Similarly, engineers may use trilinear methods to analyze forces acting on triangular structures, ensuring stability and safety in their designs.In conclusion, the concept of trilinear coordinates plays a significant role in both theoretical and applied mathematics. Its utility in simplifying complex geometric relationships makes it an indispensable tool for anyone studying triangles. As we continue to explore the vast world of geometry, embracing concepts like trilinear coordinates will undoubtedly lead to deeper insights and greater understanding. Whether you are a student, a teacher, or a professional in a related field, mastering the idea of trilinear coordinates will enhance your mathematical toolkit and improve your problem-solving capabilities.

在几何学领域，术语trilinear指的是一种特定类型的坐标系统，这在三角形几何中尤为有用。trilinear坐标系统由点到三角形边的距离定义。这一概念使得数学家和学生能够以更细致的方式探索三角形的各种性质。理解trilinear坐标可以极大地增强人们对三角形中心（如重心、正交心和外心）的理解。为了说明trilinear坐标的重要性，考虑一个三角形ABC。三角形的每一条边都可以分配一个长度，从三角形内部或外部的任一点到这些边的距离都可以被测量。例如，如果我们有一个点P，那么从P到边BC、CA和AB的距离可以分别记为d_a、d_b和d_c。点P的trilinear坐标则表示为(d_a : d_b : d_c)。这种表示法为分析三角形内外点与线之间的关系提供了强大的工具。使用trilinear坐标的一个主要优点是它简化了许多几何问题。例如，在处理线的共轭性或点的共线性时，trilinear坐标可以提供找到解决方案的直接方法。通过将复杂的关系转换为更简单的比率，人们通常可以得出结论，而这些结论在传统的笛卡尔坐标系下可能很难获得。此外，trilinear坐标不仅限于理论数学；它们在计算机图形学和工程等领域也具有实际应用。在计算机图形学中，了解三角形的性质对于准确渲染图像至关重要。通过采用trilinear插值技术，图形程序员可以在3D模型中创建平滑过渡和逼真的纹理。同样，工程师可以使用trilinear方法分析作用于三角形结构的力，确保其设计的稳定性和安全性。总之，trilinear坐标的概念在理论和应用数学中扮演着重要角色。它在简化复杂几何关系方面的实用性使其成为任何研究三角形的人不可或缺的工具。当我们继续探索几何的广阔世界时，接受像trilinear坐标这样的概念无疑会带来更深刻的洞察和更大的理解。无论你是学生、教师还是相关领域的专业人士，掌握trilinear坐标的理念将增强你的数学工具箱，提高你的问题解决能力。