We introduce a Delaunay-based algorithm for reconstructing the underlying surface of a given set of unstructured points in 3D. The implementation is very simple, and it is designed to work in a parameter-free manner. The solution builds upon the fact that in the continuous case, a closed surface separates the set of maximal empty balls (medial balls) into an interior and exterior. Based on discrete input samples, our reconstructed surface consists of the interface between Voronoi balls, which approximate the interior and exterior medial balls. An initial set of Voronoi balls is iteratively processed, merging Voronoi-ball pairs if they fulfil an overlapping error criterion. Our complete open-source reconstruction pipeline performs up to two quick linear-time passes on the Delaunay complex to output the surface, making it an order of magnitude faster than the state of the art while being competitive in memory usage and often superior in quality. We propose two variants (local and global), which are carefully designed to target two different reconstruction scenarios for watertight surfaces from accurate or noisy samples, as well as real-world scanned data sets, exhibiting noise, outliers, and large areas of missing data. The results of the global variant are, by definition, watertight, suitable for numerical analysis and various applications (e.g., 3D printing). Compared to classical Delaunay-based reconstruction techniques, our method is highly stable and robust to noise and outliers, evidenced via various experiments, including on real-world data with challenges such as scan shadows, outliers, and noise, even without additional preprocessing.

Surface selection operations by a user are fundamental for many applications and a standard tool in mesh editing software. Unfortunately, defining a selection is only straightforward if the region is visible and on a convex model. Concave surfaces can exhibit self-occlusions, which require using multiple camera positions to obtain unobstructed views. The process thus becomes iterative and cumbersome. Our novel approach enables selections to lie under occlusions and even on the backside of objects and for arbitrary depth complexity at interactive rates. We rely on a user-drawn curve in screen space, which is projected onto the mesh and analyzed with respect to visibility to guarantee a continuous path on the surface. Our occlusion-aware surface-processing method enables a number of applications in an easy way. As examples, we show continuous painting on the surface, selecting regions for texturing, creating illustrative cutaways from nested models and animate them.