针对三维物体表面的描述和识别问题，从描述三维表面变化的基本参数-法向量出发，以法向量累积分布曲线NVCDC为不变量，对比较光滑的三维曲面，给出了一个描述形状的方法方法和相似性判别准则，并依法向量的方向角将三维空间分割成子空间，然后统计落入每个子空间的法向量个数，以得到法向量的分布，再将其排序后，即得到法向量累积分布曲线NVCDC，由于与不同的法向量累积分布曲线对应的三维曲面也是不同的，所以采用NVCDC之间的差异为相似性判别准则，对不同三维曲面进行了一对一的相似性判别，为检验该方法的效果，还对足底表面进行了实验，结果表明，该曲面描述方法与相似性判别则是有效的。

This paper proposes a method of representation and comparability determination of thenar surface. The method is based on the geometric feature of three-dimensional surface. It calculates the normal vector of the points on the surface. The method segments the three-dimensional space into subspaces according to the direction angle of normal vectors and counts the number of normal vectors belonging to the three-dimensional subspace. Then the distribution of normal vectors of three-dimensional surface can be obtained. And it uses the distribution of normal vectors to represent three-dimensional surface. At last the method uses the difference between two normal vector cumulative distributing curves—NVCDCs to determine the comparability of two three-dimensional surfaces. The method proposed in this paper is not sensitive to small changes of the datum plane. Experimental results show that the method is valid in the representation and comparability determination of three-dimensional surfaces.