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.

翻译：TPMS通常以函数表示（F-rep）格式进行描述，而现代CAD/CAM/CAE工具则建立在边界表示（B-rep）格式之上。为解决这一问题，需要将TPMS转换为STEP格式，此过程称为TPMS2STEP。本文给出了TPMS2STEP的约束矩阵与收敛性证明，从而确保在转换过程中能够维持$C^2$连续性，并使几何偏差的误差限控制在$2\epsilon$以内。