<p>Recently, there has been a growing interest in learning-based explicit methods due to their ability to respect the original input and preserve details. However, the connectivity on complex structures is still difficult to infer due to the limited local shape perception, resulting in artifacts and non-watertight triangles. In this paper, we present a novel learning-based method with Delaunay triangulation to achieve high-precision reconstruction. We model the Delaunay triangulation as a dual graph, extract multi-scale geometric information from the points, and embed it into the structural representation of Delaunay triangulation in an organic way, benefiting fine-grained details reconstruction. To encourage neighborhood information interaction of edges and nodes in the graph, we introduce a Local Graph Iteration algorithm, serving as a variant of graph neural network. Benefiting from its robust local processing for dual graph, a scaling strategy is designed to enable large-scale reconstruction. Moreover, due to the complicated spatial relations between tetrahedrons and the ground truth surface, it is hard to directly generate ground truth labels of tetrahedrons for supervision. Therefore, we propose a multi-label supervision strategy, which is integrated in the loss we design for this task and allows our method to obtain robust labeling without visibility information. Experiments show that our method yields watertight and high-quality meshes. Especially for some thin structures and sharp edges, our method shows better performance than the current state-of-the-art methods. Furthermore, it has a strong adaptability to point clouds of different densities.</p>