Visualization, Analysis and Shape Reconstruction of Sparse Data

Abstract

In this chapter mathematical models and efficient algorithms are developed for the visualization, analysis and shape reconstruction for an arbitrary data set that can include unorganized points or continuous manifolds of any codimension, such as pieces of curves and surface patches. The distance function to the data set and its contours are used for fast visualization and analysis of the data set. A minimal surface and a convection model are used for shape reconstruction from the data set. All formulations and numerical algorithms are based on implicit representations on simple rectangular grids which extend to any number of dimensions and which also can easily be combined with the level set method for dynamic shape deformation and other manipulations.