Analysis of Kinematic Methods For Invariants Based Classification in the ISO/TC213 Framework

The Geometrical Product Specification (GPS) project in ISO/TC213 adopted a classification of three-dimensional surfaces based on their invariance under the action of the Lie group of rigid motions. Such high level framework is extremely concise and powerful but demand for some more manageable mathematical formulation. In the scientific literature recently appeared two methods that seem to be coherent with the above mentioned classification: the Stanford method and the Vienna method. Both of them give a classification strategy based on a kinematic description of the surface and these paper highlight their theoretical equivalence.