Abstract: Delaunay triangulation is an effective method for establishing digital terrain model，however，it introduces some problems such as artificial dams and local minima，which doesn’t reflect the realistic terrain.In this paper，the higher order triangulation that is an extension of the Delaunay triangulation is introduced，and the generation algorithm of the higher order triangulation is given.This method can effectively reduce the numbers of artificial dams and local minima.The algorithm has been implemented in five different terrains，showing that the method can effectively reduce the numbers of the local minima.So，it is more realistic for generating terrains model with higher order Delaunay triangulations.

摘要： Delaunay三角剖分是构建数字地形模型的有效方法，但是该方法会引起人工大坝和局部极值问题，使得地形模型不能很好地反映原始地形的真实面貌。在Delaunay三角网的基础上提出了一种高阶Delaunay三角网，并给出了高阶Delaunay三角网生成算法。实验结果表明，高阶Delaunay三角网能够有效地减少地形中局部极小的数量，因此，采用高阶Delaunay三角网建立的地形模型更接近于实际地形。