发表机构
Centro de Investigación y de Estudios Avanzados (CINVESTAV-IPN)（高级研究与教育学院中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出算法计算三角形平铺中数字对象的最小周长多边形，利用可见性锥和规范边界路径，并给出边界追踪方法，实现相对凸包的求解。
AI 中文摘要
本文提出了一种算法及其正确性证明，用于确定在三角形平面平铺中作为正则复形给出的数字对象的最小周长多边形（MPP）。此类对象是由三角形瓦片组成的边邻接连通集合，没有端瓦片，且所有瓦片的点集并集构成一个简单多边形。然而，对象的边界路径并不假定为简单的。因此，MPP是一个弱简单多边形，它对应于集合$A$相对于简单多边形$B$的相对凸包（即测地线凸包），其中$A\subset B$，但$A$不一定是多边形，实际上它通常是不连通的。我们的MPP算法依赖于通过后续边界瓦片构造并迭代约束可见性锥，它利用规范边界路径的结构，MPP前沿是沿此路径的最短多边形曲线。我们还提出了一种边界追踪算法，以从对象中获取此类路径。
英文摘要
This work presents an algorithm, together with its correctness proof, to determine the minimum perimeter polygon (MPP) for digital objects given as regular complexes in the triangular plane tiling. Such objects are edge-adjacency-connected sets of triangle tiles that have no end tiles, and the point set union of all their tiles forms a simple polygon. Nevertheless, the boundary paths of the objects are not assumed to be simple. Then the MPP is a weakly simple polygon that coincides with the relative convex hull (i.e., geodesic hull) of a set $A$ with respect to a simple polygon $B$, where $A\subset B$, but $A$ is not necessarily a polygon, in fact it is generally not connected. Our MPP algorithm relies on constructing and iteratively constraining cones of visibility through forthcoming boundary tiles, it uses the structure of the canonical boundary path, the MPP frontier is the shortest polygonal curve following this path. We also propose a boundary tracing algorithm to obtain such paths from the objects.
CommentsPreprint from November 11, 2024
Journal refDiscrete Applied Mathematics, Volume 363, Pages 27-44, 2025
