针对表面法向存在的姿态敏感问题，提出了以法向和极半径构造旋转不变的径向夹角几何特征。在此基础上，结合模型极半径定义径向夹角直方图应用于3维模型检索。算法首先对模型采用一系列同心球进行分解。对落入每个球环的点，计算径向夹角用于描述其局部几何属性。最后结合极半径和径向夹角构造旋转不变直方图特征。此外，针对网格表面点随机采样存在的分布不均匀问题，采用了体素化使采样点在表面分布更为均匀。实验结果表明，径向夹角直方图在检索准确率和检索效率方面要优于其他类似的直方图。

Generally, normal based shape histogram feature，such as Complex Extend Gaussian Image, is rotation variant for 3D shape. This paper proposed a new kind of normal based shape signature, namely Radius Angle, which can remain invariant under rotation. Then, the Radius Angle Histogram(RAH) is constructed to describe shape contents and used for 3D shape retrievals. The RAH shape descriptor first uses a series of concentric spheres to capture the point distribution information of the given model. Then for points in each concentric sphere, the Radian Normal Angle is computed to extract the local geometry features. Finally, the Radius Normal Histogram is constructed by using the extracted shape signatures. The proposed shape representation remains invariant under rotations. It can be generated from the given 3D model efficiently and easily as well. In addition, this paper discusses the point sampling result’s affect on the final retrieving precision. The voxelization is used to make the sampled point more even over the surface, and better retrieving precision can be achieved by this process. the performance comparisons for the shape benchmark database have proven that the proposed algorithm can achieve better retrieving performance than other similar histogram based shape representations.