A Compact Spectral Descriptor for Shape Deformations

Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply these methods, suitable data representations for components under development as well as for related design criteria have to be found. While a component's geometry is typically represented by a polygon surface mesh, it is often not clear how to parametrize critical design properties in order to enable efficient computational analysis. In the present work, we propose a novel methodology to obtain a parameterization of a component's plastic deformation behavior under stress, which is an important design criterion in many application domains, for example, when optimizing the crash behavior in the automotive context. Existing parameterizations limit computational analysis to relatively simple deformations and typically require extensive input by an expert, making the design process time intensive and costly. Hence, we propose a way to derive a compact descriptor of deformation behavior that is based on spectral mesh processing and enables a low-dimensional representation of also complex deformations. We demonstrate the descriptor's ability to represent relevant deformation behavior by applying it in a nearest-neighbor search to identify similar simulation results in a filtering task. The proposed descriptor provides a novel approach to the parametrization of geometric deformation behavior and enables the use of state-of-the-art data analysis techniques such as machine learning to engineering tasks concerned with plastic deformation behavior.