Resumen de Morse cell decomposition and parametrization of surfaces from point clouds
Maria Alberich Carramiñana, Jaume Amorós Torrent, Franco Coltraro, Carme Torras Genís, Miquel Verdaguer López
An algorithm for the reconstruction of a surface from a point sample is presented. It proceeds directly from the point-cloud to obtain a cellular decomposition of the surface derived from a Morse function. No intermediate triangulation or local implicit equations are used, saving on computation time and reconstruction-induced artifices. No a priori knowledge of surface topology, density or regularity of its point sample is required to run the algorithm. The results are a piecewise parametrization of the surface as a union of Morse cells, suitable for tasks such as noise-filtering or mesh- independent reparametrization, and a cell complex of small rank determining the surface topology. The algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.
