Measuring machines gives a more and more accurate number of points in order to describe a surface. In a design process, we need to have a better description of geometry in order to assess all the behaviours involving interactions between material and it's environment. Focussing at the same time the infinite complexity of real objects and the simplification needed to make simple choices is a main goal of a metrologist. This is possible by the use of adapted geometric languages. A geometry parameterization has the challenge to have the following properties: - Unicity-inversibility: a unique set of parameters gives a unique shape. - Stability: continuous parameters. - Invariance: decoupling of parameters - Efficiency: ability to represent the measurement with a minimum number of parameters. - Exhaustiveness: to describe the complete measurement. - Complexity sorting: the first parameters are associated to the simplest shape. We had the idea to think about the natural vibrations of shapes in order to use all their very interesting properties corresponding to those properties. They form an automatic, natural, geometric vector space of shape descriptors. Fourier series that we all know is very useful, but limited to very simple shapes (line, circle for single Fourier series and square for double Fourier decomposition). If you remember that Fourier series are the modal solution of a vibrating rope, you understand that nature has given us a way to generalise what Fourier has discovered. We propose to use the modal eigen shapes of surfaces in order to describe them and we adapted this method called Discrete Modal Decomposition (DMD) to discrete surfaces. Recently we have made possible to compute this method to a huge number of points making possible to assess measurements of topographic machines. Now we can simplify the complexity of a measurement to different levels of geometry from the simplest one given by the global shape, through the "middle level" given by undulation to the finest level of roughness or a very local "geometric accident" using this new (but old, because natural) method of geometric filtering.