Voronoi-based Feature Curves Extraction and Surface Reconstruction for Singular Surfaces

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The detection and reconstruction of feature curves in surfaces from a point cloud data is a challenging problem because most of the known theories for smooth surfaces break down at these places. The features such as boundaries, sharp ridges and corners, and curves where multiple surface patches intersect creating non-manifold points are often considered important geometries for further processing. Here we provide SingularCocone, a software able to extract feature curves and reconstruct sampled singular surfaces based on the following paper.  Paper: 1. Tamal K. Dey and Lei Wang. Voronoi-based Feature Curves Extraction for Sampled Singular Surfaces. SMI 2013, Computers & Graphics, To appear. This work uses WeightCocone to reconstruct the surface introduced in the following paper:            2. Tamal K. Dey, Xiaoyin Ge, Qichao Que, Issam Safa, Lei Wang and Yusu Wang. Feature-Preserving Reconstruction of Singular Surfaces. Computer Graphics Forum, Vol. 31 (5), 1787--1796, special issue of Eurographics Sympos. Geometry Processing (SGP 2012). This work have been supported by NSF grants CCF 1116258 and CCF 0915996 Software: SingularCocone software SingularCoconr has two parts: FeatureRecon extracts feature curves of a singular surface which could be composed by a collection of piecewise smooth surface patches. The input is a point cloud sampled on the singular surface. The output is the set of feature curves of the surface. WeightCocone is a method akin to the well known Cocone reconstruction, but with weighted Delaunay triangulation that allows protecting the feature samples with balls. WeightCocone accptes output of FeatureRecon or other feature extracting algorithms to reconstruct surfaces with singularites. Workflow of SingularCocone FeatureRecon (a) takes a point cloud as the input. It (b) detects feature points (magenta ones are those located near corners where feature curves intersect) and (c) filters feature points to get a subset from which (d) feature curves are extracted by modified NNCrust. (e) WeightCocone reconstructs the singular surface with extracted feature curves properly preserved. (a) (b) (c) (d) (e) More Results Carved Object: Detected Feature Points Carved Object: Extracted Feature Curves Sharp Sphere: Detected Feature Points Sharp Sphere: Extracted Feature Curves Noisy Sphere Cube: Detected Feature Points Noisy Sphere Cube: Extracted Feature Points Note that WeightCocone is sensitive to noise. Noisy point cloud should be smoothed before given to WeightCocone. Work with Other Feature Extraction Algorithm WeightCocone preserves singularities covered by weighted sampling. It is able to work with other feature extraction algorith. Following images show how WeightCocone preserves sharp edges identified by the method of Dey et al. The SingularCocone software based on this result is available.