lower hull

简明释义

下船体

英英释义

例句

1.The algorithm calculates the convex shape by finding the lower hull (下半边) of the set of points.

该算法通过找到一组点的lower hull (下半边) 来计算凸形状。

2.The lower hull (下半边) is essential for understanding the boundary of the data distribution.

lower hull (下半边) 对于理解数据分布的边界至关重要。

3.When analyzing the dataset, the lower hull (下半边) provides insights into the minimum values.

在分析数据集时，lower hull (下半边) 提供了对最小值的洞察。

4.To create a visual representation, we need to draw the lower hull (下半边) of the data points.

为了创建可视化表示，我们需要绘制数据点的lower hull (下半边)。

5.In computational geometry, the lower hull (下半边) helps in optimizing the search for nearest neighbors.

在计算几何中，lower hull (下半边) 有助于优化最近邻的搜索。

作文

In computational geometry, the concept of the lower hull is essential for understanding how to organize and analyze a set of points in a two-dimensional space. The lower hull refers to the subset of points that forms the lower boundary of the convex shape created by a given set of points. This idea is not only fundamental in theoretical mathematics but also has practical applications in various fields such as computer graphics, geographic information systems, and robotics.To better illustrate the concept, imagine a scenario where we have a collection of points scattered across a plane. These points could represent various locations on a map, such as cities or landmarks. The goal is to find the convex polygon that encompasses all these points, which is often referred to as the convex hull. Within this convex hull, the lower hull specifically includes the points that are at the bottom edge of this polygon.The process of finding the lower hull can be achieved through several algorithms, one of the most famous being the Graham scan. This algorithm sorts the points based on their polar angle with respect to a reference point and then constructs the hull by iterating through the sorted points. During this iteration, points that would create a concave shape are discarded, ensuring that only those forming the lower hull remain.Understanding the lower hull is crucial for applications such as collision detection in computer graphics. When rendering 3D models, knowing the boundaries of objects helps determine how they interact with one another. For example, when two objects collide, calculating their lower hull can help in determining the exact point of contact and how to respond to that interaction. Similarly, in geographic information systems, the lower hull can be used to outline areas of interest, such as flood zones or urban development regions, providing valuable insights for planning and analysis.Moreover, the lower hull plays a significant role in optimization problems. In operations research, for instance, the lower hull can represent feasible solutions to certain types of linear programming problems. By analyzing the lower hull, researchers can identify the best possible outcomes while adhering to specific constraints, ultimately leading to more efficient decision-making processes.In conclusion, the concept of the lower hull is a vital component in the study of computational geometry, with far-reaching implications in various domains. From computer graphics to geographic information systems and optimization problems, understanding the lower hull enables professionals to tackle complex challenges effectively. As technology continues to advance, the importance of mastering such geometric concepts will only grow, paving the way for innovative solutions and applications in our increasingly data-driven world.

在计算几何中，lower hull的概念对于理解如何组织和分析二维空间中的点集至关重要。lower hull指的是形成给定点集所创建的凸形状的下边界的点子集。这个想法不仅在理论数学中是基础性的，而且在计算机图形学、地理信息系统和机器人等多个领域都有实际应用。为了更好地说明这一概念，想象一个场景，我们有一组散布在平面上的点。这些点可以代表地图上的各种位置，例如城市或地标。目标是找到一个包围所有这些点的凸多边形，这通常被称为凸包。在这个凸包中，lower hull特别包括位于该多边形底部边缘的点。寻找lower hull的过程可以通过几种算法实现，其中最著名的是Graham扫描算法。该算法根据与参考点的极角对点进行排序，然后通过迭代排序后的点来构建凸包。在这个迭代过程中，会丢弃那些会形成凹形状的点，从而确保只有形成lower hull的点保留下来。理解lower hull对于计算机图形学中的碰撞检测等应用至关重要。在渲染3D模型时，了解物体的边界有助于确定它们之间的相互作用。例如，当两个物体发生碰撞时，计算它们的lower hull可以帮助确定接触的确切点以及如何应对这种相互作用。同样，在地理信息系统中，lower hull可以用来勾勒出感兴趣区域，例如洪水区或城市发展区域，为规划和分析提供宝贵的见解。此外，lower hull在优化问题中也发挥着重要作用。例如，在运筹学中，lower hull可以表示某些线性规划问题的可行解。通过分析lower hull，研究人员可以识别在特定约束条件下的最佳可能结果，最终导致更高效的决策过程。总之，lower hull的概念是计算几何研究的重要组成部分，在多个领域具有广泛的影响。从计算机图形学到地理信息系统和优化问题，理解lower hull使专业人士能够有效应对复杂挑战。随着技术的不断进步，掌握此类几何概念的重要性只会增加，为我们日益数据驱动的世界中的创新解决方案和应用铺平道路。