关键词: 自由曲面, 网格平面化, 力学模拟, 优化算法, 动力松弛法, 迭代, 评价指标

Abstract: In order to obtain the planar quadrangle architectural mesh of free-form surfaces，a mesh optimization algorithm based on mechanical simulation was proposed． The spring-mass model comprised of restraint force for rod length，the restraint force for boundary fixed particle，the adsorption force for surface to particle and the force for mesh planarization，was established． First，according to the designer，mapping method or other methods were used for the initial quadrangle grid generation． Then，considering the requirements of different performance，the elastic coefficient k ij ，boundary constraint stiffness k c ，adsorption stiffness k m ，and planarity coefficient p c were calculated． The mesh spring particle model with coplanar target was established，and the coplanar mesh was ob- tained by multiple iterations through dynamic relaxation method． Then，combined with the quadrilateral planariza- tion index，the quality of the grid was evaluated comprehensively by fluency index and uniformity index，and the grid deviation index was introduced to control the shape of the grid． Finally，examples were given to verify the re- sults． Examples show that the planarity optimization algorithm can be well adapted to free-form surfaces． By adjus- ting the parameters，the allowable error limits of planarization can reach a reasonable range with fluent and uniform architectural grids under certain conditions．

Key words: free-form surfaces, planar quadrilateral grid generation, mechanical simulation, optimization algo- rithm, dynamic relaxation method, iteration, evaluation indicator