Abstract Unoriented surface reconstruction is an important task in computer graphics. Recently, methods based on the Gauss formula or winding number have achieved state‐of‐the‐art performance in both orientation and surface reconstruction. The Gauss formula or winding number, derived from the fundamental solution of the Laplace equation, initially found applications in calculating potentials in electromagnetism. Inspired by the practical necessity of calculating potentials in diverse electromagnetic media, we consider the anisotropic Laplace equation to derive the anisotropic Gauss formula and apply it to surface reconstruction, called “anisotropic Gauss reconstruction”. By leveraging the flexibility of anisotropic coefficients, additional constraints can be introduced to the indicator function. This results in a stable linear system, eliminating the need for any artificial regularization. In addition, the oriented normals can be refined by computing the gradient of the indicator function, ultimately producing high‐quality normals and surfaces. Regarding the space/time complexity, we propose an octree‐based acceleration algorithm to achieve a space complexity of O(N) and a time complexity of O(NlogN). Our method can reconstruct ultra‐large‐scale models (exceeding 5 million points) within 4 minutes on an NVIDIA RTX 4090 GPU. Extensive experiments demonstrate that our method achieves state‐of‐the‐art performance in both orientation and reconstruction, particularly for models with thin structures, small holes, or high genus. Both CuPy‐based and CUDA‐accelerated implementations are made publicly available at https://github.com/mayueji/AGR .

Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their mathematical formulation and good experimental performance. However, the formula’s isotropy limits its capacity to leverage the directional features of point clouds. In this study, we introduce a convection augmentation term to extend the classic Gauss formula. This new term allows our method to leverage point clouds’ directional characteristics effectively. With the proper choice of the velocity field, this method could construct more equations to calculate a more precise indicator function. Furthermore, an adaptive selection strategy of the velocity field is proposed. For large-scale point clouds, we propose a CUDA-and-octree-based acceleration algorithm with O(N) space complexity and O(N log N) time complexity. Our method can complete the orientation and reconstruction tasks of point clouds with up to 500K within a few seconds. 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 is publicly available at https://github.com/mayueji/CAGR .