Tensor Lines in Engineering: Success, Failure, and Open Questions

  • Marc Schöneich
  • Andrea Kratz
  • Valentin Zobel
  • Gerik Scheuermann
  • Markus Stommel
  • Ingrid HotzEmail author
Part of the Mathematics and Visualization book series (MATHVISUAL)


Today, product development processes in mechanical engineering are almost entirely carried out via computer-aided simulations. One essential output of these simulations are stress tensors, which are the basis for the dimensioning of the technical parts. The tensors contain information about the strength of internal stresses as well as their principal directions. However, for the analysis they are mostly reduced to scalar key metrics. The motivation of this work is to put the tensorial data more into focus of the analysis and demonstrate its potential for the product development process. In this context we resume a visualization method that has been introduced many years ago, tensor lines. Since tensor lines have been rarely used in visualization applications, they are mostly considered as physically not relevant in the visualization community. In this paper we challenge this point of view by reporting two case studies where tensor lines have been applied in the process of the design of a technical part. While the first case was a real success, we could not reach similar results for the second case. It became clear that the first case cannot be fully generalized to arbitrary settings and there are many more questions to be answered before the full potential of tensor lines can be realized. In this chapter, we review our success story and our failure case and discuss some directions of further research.


Principal Stress Design Space Rapid Prototype Product Development Process Technical Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marc Schöneich
    • 1
  • Andrea Kratz
    • 2
  • Valentin Zobel
    • 5
  • Gerik Scheuermann
    • 3
  • Markus Stommel
    • 4
  • Ingrid Hotz
    • 6
    Email author
  1. 1.University SaarbrückenSaarbrückenGermany
  2. 2.Zuse Institute BerlinBerlinGermany
  3. 3.University LeipzigLeipzigGermany
  4. 4.University DortmundDortmundGermany
  5. 5.Universität LeipzigLeipzigGermany
  6. 6.Linköping UniversityNorrköpingSweden

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