Learning conjugate direction fields for planar quadrilateral mesh generation

Tao, Jiong, Yang, Yong-Liang and Deng, Bailin ORCID: https://orcid.org/0000-0002-0158-7670 2026. Learning conjugate direction fields for planar quadrilateral mesh generation. Presented at: The 40th Annual AAAI Conference on Artificial Intelligence, Singapore, Republic of Singapore, 20-27 January 2026. Proceedings of the AAAI Conference on Artificial Intelligence. Proceedings of the AAAI Conference on Artificial Intelligence. , vol.40 AAAI Press, Item availability restricted.

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Abstract

Planar quadrilateral (PQ) mesh generation is a key process in computer-aided design, particularly for architectural applications where the goal is to discretize a freeform surface using planar quad faces. The conjugate direction field (CDF) defined on the freeform surface plays a significant role in generating a PQ mesh, as it largely determines the PQ mesh layout. Conventionally, a CDF is obtained by solving a complex non-linear optimization problem that incorporates user preferences, i.e., aligning the CDF with user-specified strokes on the surface. This often requires a large number of iterations that are computationally expensive, preventing the interactive CDF design process for a desirable PQ mesh. To address this challenge, we propose a data-driven approach based on neural networks for controlled CDF generation. Our approach can effectively learn and fuse features from the freeform surface and the user strokes, and efficiently generate quality CDF respecting user guidance. To enable training and testing, we also present a dataset composed of 50000+ freeform surfaces with ground-truth CDFs, as well as a set of metrics for quantitative evaluation. The effectiveness and efficiency of our work are demonstrated by extensive experiments using testing data, architectural surfaces, and general 3D shapes.

Item Type:	Conference or Workshop Item (Paper)
Status:	In Press
Schools:	Schools > Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software
Publisher:	AAAI Press
ISSN:	2159-5399
Date of First Compliant Deposit:	15 November 2025
Date of Acceptance:	7 November 2025
Last Modified:	19 Nov 2025 11:15
URI:	https://orca.cardiff.ac.uk/id/eprint/182430

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