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A 3D shape characterization that allows establishing robust similarity measurements is presented. This characterization is based on a new extended curvature feature called cone-curvature (CC), built on top of the recent modeling wave (MW) topological organization for 3D objects modeling meshes. Through the CC feature, flexible and extended surroundings geometry knowledge for every point of the solid surface is given. In order to reduce the dimensionality of this representation and after carrying out a study of the principal components the weighted cone-curvature (WCC) concept is defined. This reduction notoriously simplifies the volume of data handled in the model without loss of information. As an application, a similarity measurement based on the WCC feature has been defined and implemented to compare and recognize 3D objects using their models. Both the principal components analysis and the similarity applications have been experimentally tested in our lab and the main results are shown.