Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). The quality of the cross field is essential for generating a quadrilateral mesh. In this paper, we propose a self-supervised neural representation of the cross field, named NeurCross, comprising two modules: one to fit the signed distance function (SDF) and another to predict the cross field. Unlike most existing approaches that operate directly on the given polygonal surface, NeurCross takes the SDF as a bridge to allow for SDF overfitting and the prediction of the cross field to proceed simultaneously. By utilizing a neural SDF, we achieve a smooth representation of the base surface, minimizing the impact of piecewise planar discretization and minor surface variations. Moreover, the principal curvatures and directions are fully encoded by the Hessian of the SDF, enabling the regularization of the overall cross field through minor adjustments to the SDF. Compared to state-of-the-art methods, NeurCross significantly improves the placement of singular points and the approximation accuracy between the input triangular surface and the output quad mesh, as demonstrated in the teaser figure.

提出一种名为NeurCross的自监督神经表示的跨域的四边形网格生成方法，通过利用神经符号距离函数(SDF)进行SDF过度拟合和跨域的预测，并通过SDF的Hessian矩阵对整体跨域进行规范化调整，显著改善奇异点的位置和输入三角面片与输出四边形网格的逼近精度。

NeurCross: 用于四边形网格生成中表示交叉字段的自监督神经方法