中文摘要：

通过对三维单纯形积分公式的分析给出了其伪代码实现,并结合具体实例描述了其求解过程,给出了任意形状多面体重心计算方法。利用上述算法,对比了中空规则形状多面体重心的计算值与理论值差异,分析了不同边长比（10^-4—104）情况下计算值与理论值的差异,讨论了计算结果的精度。通过非规则形状多面体重心计算结果的稳定性分析,讨论了单纯形积分的普适性特征。结果表明,积分和重心的计算值与理论值的相对误差约为10^-15—10^-14,图形条件对积分结果的影响极小且不存在系统性。因此,单纯形积分结果具有高度的稳定性和精确性。

英文摘要：

Based on analyzing to simplex integration formula,its algorithm written by pseudocode is given,and described the integration procedure,and illustrate the calculation algorithm of gravity centers in polyhedron with arbitrary shape.The accuracy of above algorithms through comparing the difference between theoretical and calculated results of gravity centers in regular integral region with hollow,and analyzing their difference in different edge length ratio（10^-4—104） are discussed.Then the adaptive characteristics of simplex integration algorithm are discussed through analyzing integral results in irregular integral region.The results show that the relative error between calculated results and theoretical results is about 10^-15—10^-14,and the graphics conditions have minimal impact on integral results and the impact has not systematic characteristic.In conclusion,the results of simplex integration and gravity center have high stability and accuracy.