凸包：曲面映射到球面
Convex Hulls: Surface Mapping onto a Sphere
AI总结：
针对三维凸包算法在共面、数值精度及退化点云等方面的实现挑战，提出一种基于支撑映射和曲面投影的全新迭代方法，构建简单且鲁棒的2d和3d凸包算法。
摘要：
编写一个简单、鲁棒且可扩展的三维凸包算法充满挑战且问题重重。这包括共面和共线问题、数值精度、性能与复杂性的权衡。虽然有许多基于几何计算（如点之间的距离）寻找凸包的方法，但它们并未解决实现可用方案时的技术挑战（例如数值问题和退化点云）。我们解释了一些常见的算法陷阱以及克服和解决这些限制的工程修改。我们提出了一种使用支撑映射和曲面投影的全新迭代方法，以创建简单且鲁棒的2d和3d凸包算法。
英文摘要：
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are a number of methods available for finding the convex hull based on geometric calculations, such as, the distance between points, but do not address the technical challenges when implementing a usable solution (e.g., numerical issues and degenerate cloud points). We explain some common algorithm pitfalls and engineering modifications to overcome and solve these limitations. We present a novel iterative method using support mapping and surface projection to create an uncomplicated and robust 2d and 3d convex hull algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
