The Main-Chain Divide-and-Conquer Algorithm and the Area Computation Lemma for Voronoi Cell
基链分治算法与Voronoi区的面积计算定理研究

Based on the object-oriented data structure of Voronoi diagram for normal curvilinear polygon, an improved Divide-and-Conquer algorithm is presented in this paper for Voronoi diagram generation called Main-Chain Divide-and-Conquer algorithm. It is easier to implement compared with the classical one. Meanwhile, because the boundary of a Voronoi cell contains parabolic or hyperbolic curves in the Euclidean metric, it is difficult to compute the Voronoi cell area in practice. For this reason, an area computation lemma of the Voronoi cell is presented. The lemma proof and an example are also given. Thus, a way is provided for the area calculation in some engineering applications.