Translating TPMS models to STEP files

2024-05-13

AI Summary

To address the engineering applicability bottleneck of triply periodic minimal surfaces (TPMS) arising from incompatibility between their functional representation (F-rep) and the boundary representation (B-rep) format required by industrial CAD/CAM/CAE systems, this paper proposes a TPMS-to-STEP conversion method with guaranteed geometric error control and preserved C² continuity. The method introduces a unified discrete approximation and surface fitting framework integrating a provable two-sided error bound (2ε) and explicit C² continuity constraints. A constrained progressive-iterative approximation (constrained-PIA) algorithm is designed, supported by theoretical convergence analysis, and coupled with an error-driven adaptive sampling strategy. The resulting STEP models strictly satisfy both ε-density and ε-approximation criteria, with a global deviation upper bound of 2ε. Experimental results demonstrate superior performance over state-of-the-art approaches in accuracy, C² smoothness, and computational efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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 $2epsilon$ 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.

Problem

• Translates TPMS models to STEP format
• Ensures error control in model translation
• Preserves C^2 continuity in TPMS approximation

Innovation

• TPMS to STEP translation
• error-controlling algorithm
• C^2 continuity-preserving