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.

翻译：平面四边形（PQ）网格生成是计算机辅助设计中的关键过程，尤其在建筑应用中，其目标是将自由曲面离散化为平面四边形面。定义在自由曲面上的共轭方向场（CDF）在生成PQ网格中起着重要作用，因为它很大程度上决定了PQ网格的布局。传统上，CDF通过求解复杂的非线性优化问题获得，该问题融合了用户偏好，即将CDF与用户在曲面上指定的笔触对齐。这通常需要大量计算成本高昂的迭代，阻碍了为理想PQ网格进行交互式CDF设计的过程。为解决这一挑战，我们提出了一种基于神经网络的数据驱动方法，用于可控CDF生成。我们的方法能够有效学习并融合来自自由曲面和用户笔触的特征，并高效生成符合用户指导的高质量CDF。为支持训练和测试，我们还提出了一个包含50000多个自由曲面及其真实CDF的数据集，以及一套用于定量评估的指标。通过使用测试数据、建筑曲面和通用三维形状进行的大量实验，验证了我们工作的有效性和高效性。