Constraints Matrices and Convergence Proof of TPMS2STEP

TL;DR

This paper introduces a method with constraint matrices and a convergence proof for translating triply periodic minimal surfaces (TPMS) from functional to boundary representations, ensuring smoothness and bounded error during conversion.

Contribution

It provides the first formal convergence proof and constraint matrices for the TPMS2STEP translation process, ensuring geometric continuity and error bounds.

Findings

Ensures $C^2$ continuity during TPMS to STEP translation.

Provides a formal convergence proof for the translation process.

Establishes an error bound of $2\epsilon$ on deviation.

Abstract

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. To solve this issue, translating TPMS to STEP is needed, called TPMS2STEP. This paper provides constraint matrices and convergence proof of TPMS2STEP so that $C^2$ continuity and an error bound of $2\epsilon$ on the deviation can be ensured during the translation.