Morse cell decomposition and parametrization of surfaces from point clouds
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Alberich Carramiñana, Maria [1] ; Amorós Torrent, Jaume [1] ; Coltraro, Franco [1] ; Torras, Carme [1] ; Verdaguer López, Miquel [1]
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[1] Institut de Robòtica i Informàtica Industrial, CSIC-UPC
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- Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 35-38
- Idioma: inglés
- Enlaces
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Resumen
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.
