二维Delaunay三角划分的平均形态比最大性质

MAXIMUM AVERAGE ASPECT RATIO PROPERTY OF THE 2D DELAUNAY TRIANGULATION

本文提出了三角划分的一种新的准则：平均形态比最大准则，证明了二维Ｄｅｌａｕｎａｙ三角划分具有最大的平均形态比，从而证明了平均形态比最大准则、最小角最大准则、Ｃｉｒｃｌｅ准则的等价性．这个性质在理论上进一步说明了Ｄｅｌａｕｎａｙ三角划分的最优性，为有限元网格划分的质量评估提供了理论依据，并为寻求三维三角划分的最优准则提供了线索．

A new criterion, the max-AAR criterion(i.e.the maximum average an pet ratio criterion) of triangulation is presented in this paper.The property of maxi mum average aspeCt ratio of the 2D Delaunay triangulation is proved, which turns out that the circle criterion, the max-min angle criterion and the max-AAR criterion are equivalent. This approach further Perfects the optimality theory Of the 2D Delaunay triangulation and forms the theoretical basis of the quality evaluation of finite element mesh.It perhaps can lead to the finding Of optimal criterion Of 3D triangulation.