Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their capacity to leverage the anisotropic information within the point cloud. In this work, we propose a novel anisotropic formulation by introducing a convection term in the original Laplace operator. By choosing different velocity vectors, the anisotropic feature can be exploited to construct more effective linear equations. Moreover, an adaptive selection strategy is introduced for the velocity vector to further enhance the orientation and reconstruction performance of thin structures. Extensive experiments demonstrate that our method achieves state-of-the-art performance and manages various challenging situations, especially for models with thin structures or small holes. The source code will be released on GitHub.

翻译：基于高斯公式的无定向表面重建方法因其优雅的数学表达与卓越的性能而备受关注。然而，该公式的各向同性特性限制了其利用点云内部各向异性信息的能力。本研究通过在原始拉普拉斯算子中引入对流项，提出了一种新颖的各向异性公式。通过选择不同的速度矢量，可以充分利用各向异性特征构建更有效的线性方程组。此外，本文引入了速度矢量的自适应选择策略，以进一步提升薄壁结构的定向与重建性能。大量实验表明，本方法实现了最先进的性能，并能处理各种具有挑战性的情况，尤其适用于具有薄壁结构或细小孔洞的模型。源代码将在GitHub平台发布。