Abstract: As a generalization of Voronoi diagram, Laguerre diagram has numerous import applications in computational geometry and material sciences. The incremental algorithm for the regular triangulation of a set of weighted points and the process of using the dual characteristics of regular triangulation to obtain the Laguerre diagram are described. The simulation software for parametric, automation, visualization constructed Laguerre diagram is developed by discussing the effect of Laguerre structure on the different sets of weighted points. The microstructure of polycrystalline and foam structure material is simulated by using the data information to create the geometry model. The analyses show that the results obtained by this software has good usability.

Key words: Laguerre diagram, Regular triangulation, incremental algorithm, material microstructure

摘要： Laguerre图作为Voronoi图的推广，在计算几何学、材料科学等领域中有着重要应用。重点讨论了带权点集Regular三角化的增量算法以及根据其对偶性质构造Laguerre图的实现过程；通过研究球填充带权点集对Laguerre图胞体结构特征的影响，在此基础上开发了用于参数化、自动化、可视化构造Laguerre图的软件；利用软件给出了多晶体材料与泡沫材料微结构仿真的应用实例，验证了软件的有效性。

关键词: Laguerre图, Regular三角化, 增量算法, 材料微结构