Reconstruction from a given set of points is a process of extracting the shape hidden in the point set. The reconstructed shape is a piece-wise linear approximation preserving the geometrical and topological identity of the original object. The scope of this talk is outlined in reconstruction algorithms for 2D and 3D point sets - two algorithms (curve and shape reconstruction) in the 2D and a surface reconstruction algorithm in 3D.

The first algorithm is a unified method that works irrespective of the input point set- boundary sample or dot-pattern (boundary sample- samples only from the boundaries of the curves, dot-pattern- samples from both boundary and interior of the curves). Subsequently, an algorithmic framework for the 2D point set type discernment and its reconstruction will be presented. The point set discernment deals with determining whether the given point set is a boundary sample or not. Based on the type of the point set, shape reconstruction or curve reconstruction is performed. Finally, a feature preserving surface reconstruction algorithm, which works for the surfaces with or without boundaries to produce a high fidelity triangulated mesh from an unstructured input point set will be discussed. In practice, the three reconstruction algorithms perform well and these have been illustrated through extensive qualitative & quantitative comparative studies.