Recently, shape-based matching and retrieval of 3D polygonal models has become one of the most fundamental problems in computer vision. Dealing with families of objects instead of a single one may impose further challenges on regular geometric algorithms. In this paper we focus on the classification of 3D objects based on their geodesic distance & path calculated on a mesh using an iterative algorithm for solving the Eikonal equation. For the classification process, we use both Multiclass Support Vector Machine (M-SVM) classifier,K-Nearest Neighbors (KNN), Decision Tree (DT) and Artificial Neural Networks (ANN) to better evaluate our descriptors. We illustrate the potential of extracted characteristics by two 3D benchmarks. The recognition rates achieved in all experiments show that a small number of curve between 9 and 12 can correctly categorize a family of 3D objects.