Volumetric snapping: Watertight triangulation of point clouds

We propose an algorithm which constructs an interpolating triangular mesh from a closed point cloud of arbitrary genus. The algorithm first constructs an intermediate structure called a Delaunay cover, which forms a barrier between the inside and the outside of the object. This structure is used to build a boolean voxel grid, with cells intersecting the cover colored black and all other cells colored white. The outer surface of the voxel grid is snapped to the point cloud by replacing each exterior surface vertex with the closest point in the point cloud. The snapped mesh is processed such that it is manifold and consists of triangles with good aspect ratio. We show that if a fine voxel grid is used, the snapping yields Delaunay-like triangulation of the original points. High grid resolutions are possible because of the Delaunay cover and a new contouring method, which extracts the outer surface of the grid with O(n) worst case space complexity, where n is the number of voxels in one dimension.