Abstract
AbstractDetermining connectivity between points and reconstructing their shape boundaries are long‐standing problems in computer graphics. One possible approach to solve these problems is to use a proximity graph. We propose a new proximity graph computed by intersecting the to‐date rarely used proximity‐based graph called spheres‐of‐influence graph (SIG) with the Delaunay triangulation (DT). We prove that the resulting graph, which we name SIGDT, contains the piece‐wise linear reconstruction for a set of unstructured points in the plane for a sampling condition superseding current bounds and capturing well practical point sets' properties. As an application, we apply a dual of boundary adjustment steps from the Connect2D algorithm to remove the redundant edges. We show that the resulting algorithm SIG‐Connect2D yields the best reconstruction accuracy compared to state‐of‐the‐art algorithms from a recent comprehensive benchmark, and the method offers the potential for further improvements, e.g., for surface reconstruction.
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