Learning Conjugate Direction Fields for Planar Quadrilateral Mesh Generation

2025-11-14

AI Summary

To address the high computational cost and poor interactivity of conventional conjugate direction field (CDF) optimization methods in generating planar quadrilateral (PQ) meshes on freeform surfaces, this paper proposes a data-driven neural network approach. We construct a large-scale geometric-direction-field paired dataset comprising over 50,000 samples and design an end-to-end deep network that jointly encodes surface geometric features and user-provided stroke guidance. The method enables real-time CDF prediction and interactive editing. It achieves orders-of-magnitude speedup—tens of times faster than traditional optimization—while significantly improving CDF quality across diverse complex architectural surfaces. This work establishes the first high-fidelity, interactive CDF design loop for architectural PQ meshing. Key contributions include: (1) a learnable geometry-guided mechanism, (2) a user-intent embedding architecture, and (3) a lightweight deployment framework tailored for architectural CAD applications.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Generating planar quadrilateral meshes from freeform surfaces efficiently
• Optimizing conjugate direction fields with user guidance interactively
• Reducing computational cost in mesh generation using neural networks

Innovation

• Neural networks generate conjugate direction fields
• Learns features from surfaces and user strokes
• Efficiently creates planar quadrilateral mesh layouts