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The ability to identify similarities between shapes is important for applications such as medical diagnosis, object registration and alignment, and shape retrieval. This paper focuses on handling this issue using one of the well-known features that describe the local intrinsic properties of the shape. This feature is the principle curvatures (k1, k2) of the 3D shape. We introduce a framework of stable mathematical calculations to approximate these geometric properties. Once the principle curvatures are calculated, we can construct, for each shape, a matrix that represents two dimensional distribution of these curvatures as a shape descriptor for further searching operation. This descriptor is invariant to shape orientation and reflects the geometric properties of the surface. Experimental results are presented and it proves the robustness of the descriptor.