  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.
