Computational Geometry

New submissions

• New submissions
• Replacements

New submissions for Tue, 14 May 24

[1]  arXiv:2405.07946 [pdf, other]

Title: TPMS2STEP: error-controlled and C2 continuity-preserving translation of TPMS models to STEP files based on constrained-PIA

Authors: Yaonaiming Zhao, Qiang Zou, Guoyue Luo, Jiayu Wu, Sifan Chen

Subjects: Computational Geometry (cs.CG)

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.

Replacements for Tue, 14 May 24

[2]  arXiv:2307.09214 (replaced) [pdf, other]

Title: Patrolling Grids with a Bit of Memory

Authors: Michael Amir, Dmitry Rabinovich, Alfred M. Bruckstein

Subjects: Robotics (cs.RO); Computational Geometry (cs.CG); Discrete Mathematics (cs.DM); Multiagent Systems (cs.MA); Combinatorics (math.CO)

[3]  arXiv:2402.12797 (replaced) [pdf, other]

Title: A Geometric Algorithm for Tubular Shape Reconstruction from Skeletal Representation

Authors: Guoqing Zhang, Yang Li

Comments: 9 pages (without reference), 6 figures

Subjects: Computer Vision and Pattern Recognition (cs.CV); Computational Geometry (cs.CG)

• New submissions
• Replacements