Dense 3D sensors in various real-world fields produce point clouds that are geometrically redundant for real-time processing. In this paper, we propose an efficient and scalable learning-based anisotropic surface approximation framework, HD-PEA, that operates directly on unstructured point clouds, integrating anisotropic optimization into reconstruction to produce compact, geometry-aligned surface representations with higher fidelity, fewer elements, and improved numerical stability compared to isotropic and adaptive meshes. Firstly, we develop a novel learning-based high-dimensional (high-d) Euclidean point embedding method to map the input point clouds into a high-d manifold embedding space. For handling large-scale point clouds without retraining and fine-tuning, a patch-based meta-embedding scheme is designed during the inference stage. Then, we develop a new tangent subspace estimation for the high-d embedding manifold approximation and anisotropic manifold reconstruction in high-d space. The main contribution of this work is to propose a scalable deep learning framework and a variety of datasets for constructing a high-d Euclidean point embedding space aimed to 3D anisotropic surface mesh approximation and Riemannian curvature tensor estimation from point clouds. We extensively evaluate our method against state-of-the-art surface reconstruction approaches using several datasets, such as Thingi10K dataset, AIM@SHAPE and Stanford 3D Scanning Repository, ScanNet dataset, and further demonstrate its generalization and usability on diverse unseen shapes and applications from these datasets.

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