3D printing dimensional calibration shape: Clebsch cubic. 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.

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  1. Böhm, Janko; Marais, Magdaleen S.; van der Merwe, André F.: 3D printing dimensional calibration shape: Clebsch cubic (2016)