Translating TPMS models to STEP files

TL;DR

This paper introduces a novel translation method that converts TPMS models from functional representation to STEP files, enabling better integration with standard CAD/CAM/CAE software while controlling approximation errors and preserving smoothness.

Contribution

It presents an error-controlled, $C^2$ continuity-preserving translation approach from TPMS to STEP, combining a sampling algorithm and a constrained-PIA algorithm with theoretical convergence proof.

Findings

Achieves an error bound of $2\\epsilon$ on model deviation.

Demonstrates effectiveness through examples and comparisons.

Enables integration of TPMS models into standard CAD workflows.

Abstract

Triply periodic minimal surface (TPMS) is emerging as an important way of designing microstructures. However, there has been limited use of commercial CAD/CAM/CAE software packages for TPMS design and manufacturing. This is mainly because TPMS is consistently described in the functional representation (F-rep) format, while modern CAD/CAM/CAE tools are built upon the boundary representation (B-rep) format. One possible solution to this gap is translating TPMS to STEP, which is the standard data exchange format of CAD/CAM/CAE. Following this direction, this paper proposes a new translation method with error-controlling and $C^2$ continuity-preserving features. It is based on an approximation error-driven TPMS sampling algorithm and a constrained-PIA algorithm. The sampling algorithm controls the deviation between the original and translated models. With it, an error bound of $2\epsilon$ on the deviation can be ensured if two conditions called $\epsilon$-density and $\epsilon$-approximation are satisfied. The constrained-PIA algorithm enforces $C^2$ continuity constraints during TPMS approximation, and meanwhile attaining high efficiency. A theoretical convergence proof of this algorithm is also given. The effectiveness of the translation method has been demonstrated by a series of examples and comparisons.