Many spatial statistics methods require neighbourhood structures such as the one determined by a Voronoi tessellation, so understanding statistical properties of Voronoi cells is crucial. While distributions of cell properties when data locations follow an unbounded homogeneous Poisson process have been studied, little attention has been given to how these properties change when a boundary is imposed. This is important when geographical data are gathered within a restricted study area, such as a national boundary or a coastline. We study the effects of imposing a boundary on the cell properties of a Poisson Voronoi tessellation. The area, perimeter and number of edges of individual cells with and without boundary conditions are investigated by simulation. Distributions of these properties differ substantially when boundaries are imposed, and these differences are affected by proximity to the boundary. We also investigate how changes in such properties when boundaries are imposed vary over two-dimensional space.

许多空间统计方法需要邻域结构，例如由Voronoi细分确定的邻域结构，因此了解Voronoi细胞的统计特性至关重要。虽然研究了当数据位置遵循无界齐次Poisson过程时的单元格属性的分布，但很少有人关注在施加边界时这些属性如何变化。当在受限的研究区域（例如国界或海岸线）内收集地理数据时，这一点很重要。我们研究了对Poisson Voronoi镶嵌的单元格属性施加边界的影响。通过模拟研究了带有和不带有边界条件的单个单元的面积，周长和边缘数。施加边界时，这些属性的分布会大不相同，这些差异会受到与边界的接近程度的影响。我们还研究了在二维空间上施加边界时，这些属性的变化是如何变化的。