upper hull

简明释义

上船体

英英释义

例句

1.In computational geometry, finding the upper hull is crucial for many applications.

在计算几何中，寻找上包络线对许多应用至关重要。

2.To solve this problem, we need to identify the vertices of the upper hull.

要解决这个问题，我们需要识别上包络线的顶点。

3.The upper hull can be visualized as the outer boundary of a point cloud.

上包络线可以被视为点云的外部边界。

4.The algorithm efficiently computes the upper hull of the given set of points.

该算法高效地计算给定点集的上包络线。

5.The upper hull is often used in optimization problems involving convex shapes.

上包络线通常用于涉及凸形状的优化问题。

作文

In the field of computational geometry, the concept of the upper hull (上封闭) plays a crucial role in understanding and analyzing the shape of a set of points in a two-dimensional space. The upper hull is defined as the smallest convex polygon that can enclose all the points in a given dataset while maintaining the upper boundary. This geometric structure is not only fascinating but also has practical applications in various areas such as computer graphics, geographic information systems, and robotics.To illustrate the importance of the upper hull (上封闭), let's consider a simple example involving a set of points representing geographical locations. Imagine we have several cities plotted on a map, and we want to determine the most efficient way to connect these cities without crossing any boundaries. By calculating the upper hull, we can identify the outermost cities that form the perimeter of our connection route. This allows us to create a more effective transportation network, minimizing travel distance and time.The process of finding the upper hull (上封闭) can be achieved through various algorithms, with one of the most well-known being the Graham scan algorithm. This algorithm works by first identifying the point with the lowest y-coordinate, which serves as the starting point for constructing the upper hull. From there, it sorts the remaining points based on their polar angles relative to the starting point. As the algorithm progresses, it constructs the hull by adding points and removing those that would create a concave angle. Ultimately, this results in a convex polygon that represents the upper hull of the dataset.In addition to its theoretical significance, the upper hull (上封闭) has numerous real-world applications. For instance, in computer graphics, it is used in rendering scenes where objects overlap. By determining the upper hull, graphic designers can ensure that the correct visual elements are displayed in the foreground, enhancing the overall aesthetic quality of the image.Furthermore, in the realm of robotics, the upper hull (上封闭) assists in path planning for autonomous vehicles. By mapping out the convex boundaries of obstacles in the environment, robots can navigate efficiently and avoid collisions. This is particularly important in complex environments where multiple obstacles may be present.Moreover, the upper hull (上封闭) concept extends beyond two dimensions. In higher dimensions, the idea of an upper hull can still be applied, allowing researchers to analyze data in multidimensional spaces. This has implications in fields such as data mining, where understanding the structure of high-dimensional datasets is essential for uncovering patterns and relationships.In conclusion, the upper hull (上封闭) is a fundamental concept in computational geometry that provides valuable insights into the arrangement and relationships of points in a given space. Its applications span across various fields, including geography, computer graphics, and robotics, making it an indispensable tool for researchers and professionals alike. By mastering the principles of the upper hull, individuals can enhance their problem-solving skills and contribute to advancements in technology and science.

在计算几何领域，上封闭（upper hull）这一概念在理解和分析二维空间中一组点的形状方面发挥着至关重要的作用。上封闭被定义为可以包围给定数据集中所有点的最小凸多边形，同时保持上边界。这一几何结构不仅引人入胜，还有着在计算机图形学、地理信息系统和机器人技术等多个领域的实际应用。为了说明上封闭（upper hull）的重要性，让我们考虑一个涉及表示地理位置的一组点的简单例子。想象一下，我们有几个城市在地图上绘制出来，我们希望确定一种最有效的方式来连接这些城市而不跨越任何边界。通过计算上封闭，我们可以识别出形成连接路线周边的最外层城市。这使我们能够创建一个更有效的交通网络，最小化旅行距离和时间。寻找上封闭（upper hull）的过程可以通过多种算法实现，其中最著名的之一是格雷厄姆扫描算法（Graham scan）。该算法首先识别具有最低y坐标的点，该点作为构建上封闭的起点。接下来，它根据与起点的极角对剩余点进行排序。随着算法的推进，它通过添加点和移除那些会产生凹角的点来构建外壳。最终，这将导致一个表示数据集的上封闭的凸多边形。除了其理论意义外，上封闭（upper hull）还有许多现实世界的应用。例如，在计算机图形学中，它用于渲染重叠的场景。通过确定上封闭，图形设计师可以确保正确的视觉元素显示在前景中，从而增强图像的整体美学质量。此外，在机器人技术领域，上封闭（upper hull）有助于自主车辆的路径规划。通过绘制环境中障碍物的凸边界，机器人可以高效导航并避免碰撞。这在复杂环境中尤为重要，因为可能存在多个障碍物。此外，上封闭（upper hull）概念超越了二维。在更高维度中，上封闭的思想仍然可以应用，使研究人员能够分析多维空间中的数据。这在数据挖掘等领域具有重要意义，因为理解高维数据集的结构对于揭示模式和关系至关重要。总之，上封闭（upper hull）是计算几何中的一个基本概念，为了解给定空间中点的排列和关系提供了宝贵的见解。它的应用跨越多个领域，包括地理、计算机图形学和机器人技术，使其成为研究人员和专业人士不可或缺的工具。通过掌握上封闭的原理，个人可以增强解决问题的能力，并为科技和科学的进步做出贡献。