3D Printing Dimensional Calibration Shape: Clebsch Cubic

  • Janko Böhm
  • Magdaleen S. Marais
  • André F. van der Merwe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9725)

Abstract

3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Various techniques are used to validate and calibrate dimensional accuracy through the complete building envelope. The validation process involves the growing and measuring of a shape with known parameters. The measured result is compared with the intended digital model. Processes with the risk of deformation after time or post-processing may find this technique beneficial. We propose to use objects from algebraic geometry as test shapes. A cubic surface is given as the zero set of a degree 3 polynomial in 3 variables. A class of cubics in real 3D space contains exactly 27 real lines. These lines can be used for dimensional calibration. Due to the thin shape geometry the material required to produce an algebraic surface is minimal. We provide a library for the computer algebra system Singular which, from 6 given points in the plane, constructs a cubic and the lines on it.

Keywords

Clebsch cubic 3D printing Applied algebraic geometry 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Janko Böhm
    • 1
  • Magdaleen S. Marais
    • 2
  • André F. van der Merwe
    • 3
  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa
  3. 3.Department of Industrial EngineeringStellenbosch UniversityStellenboschSouth Africa

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