三维空间的Thiessen-多面体及其性质

Thiessen-polyhedron and its Properties in Three-dimensional Space

Thiessen-多面体是计算几何中的一个重要概念,在传统定义中,Thiessen-多面体又称为Voronoi-多面体.本研究拓展二维Thiessen-多边形的定义,给出三维Thiessen-多面体新的定义,研究发现该多面体的体积比原定义的体积更小,从而改进了原定义.本研究比较了Thiessen-多面体与Voronoi-多面体的定义与性质,得到Thiessen-多面体的表面积与体积相较于Voronoi-多面体更小.

According to the traditional definition,Thiessen-polyhedron,an important concept in computational geometry,is also called Voronoi-polyhedron.In this paper,we put forward a new definition of the three-dimensional Thiessen-polyhedron by expanding the definition of the two-dimensional Thiessen-polygon.The original definition was improved when it was found that the volume of the polyhedron is smaller than that of the original definition.When the definition and the nature of Thiessen-polyhedron were compared with those of Vorono-polyhedron,a conclusion was drawn that the surface area and volume of Thiessen-polyhedron are smaller than those of Vorono-polyhedron.