2D conforming Voronoi mesh generation by refinement algorithm

The conditions that guarantee the existence of constrained points and segments in Voronoi mesh are presented, which puts forward a novel two-dimensional conforming Voronoi mesh refinement algorithm that completes the mesh by setting up initial examining strip set and subdivision of the strip set. The algorithm is guaranteed to terminate on arbitrary input planar straight line graph conditions. The relative size and quality control method is also presented. The analysis of the efficiency is given and solid examples are shown to demonstrate the validation of the algorithm.