  Reconstructing 3D point clouds into triangle meshes is a key problem in
computational geometry and surface reconstruction. Point cloud triangulation
solves this problem by providing edge information to the input points. Since no
vertex interpolation is involved, it is beneficial to preserve sharp details on
the surface. Taking advantage of learning-based techniques in triangulation,
existing methods enumerate the complete combinations of candidate triangles,
which is both complex and inefficient. In this paper, we leverage the duality
between a triangle and its circumcenter, and introduce a deep neural network
that detects the circumcenters to achieve point cloud triangulation.
Specifically, we introduce multiple anchor priors to divide the neighborhood
space of each point. The neural network then learns to predict the presences
and locations of circumcenters under the guidance of those anchors. We extract
the triangles dual to the detected circumcenters to form a primitive mesh, from
which an edge-manifold mesh is produced via simple post-processing. Unlike
existing learning-based triangulation methods, the proposed method bypasses an
exhaustive enumeration of triangle combinations and local surface
parameterization. We validate the efficiency, generalization, and robustness of
our method on prominent datasets of both watertight and open surfaces. The code
and trained models are provided at https://github.com/EnyaHermite/CircNet.
