A geometric characterization of Powell-Sabin triangulations allowing the construction of C-2 quartic splines Barrera Rosillo, Domingo Eddargani, Salah Ibáñez Pérez, María José Lamnii, Abdellah Powell-Sabin triangulation Quartic splines Bernstein basis Blending functions The authors wish to thank the anonymous referees for their very pertinent and useful comments which helped them to improve the original manuscript. The first and third authors are members of the research group FQM 191 Matem?tica Aplicada funded by the PAIDI programme of the Junta de Andaluc?a. The second author would like to thank the University of Granada for the financial support for the research stay during which this work was carried out. The authors wish to thank the anonymous referees for their very pertinent and useful comments which helped them to improve the original manuscript. The first and third authors are members of the research group FQM 191 Matemática Aplicada funded by the PAIDI programme of the Junta de Andalucía. The second author would like to thank the University of Granada for the financial support for the research stay during which this work was carried out. The paper deals with the characterization of Powell-Sabin triangulations allowing the construction of bivariate quartic splines of class C-2. The result is established by relating the triangle and edge split points provided by the refinement of each triangle. For a triangulation fulfilling the characterization obtained, a normalized representation of the splines in the C-2 space is given. 2021-11-03T08:47:57Z 2021-11-03T08:47:57Z 2021-10-15 info:eu-repo/semantics/article D. Barrera, S. Eddargani, M.J. Ibáñez et al. A geometric characterization of Powell-Sabin triangulations allowing the construction of C-2 quartic splines. Computers and Mathematics with Applications 100 (2021) 30–40. [https://doi.org/10.1016/j.camwa.2021.08.028] http://hdl.handle.net/10481/71243 10.1016/j.camwa.2021.08.028 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Pergamon- Elsevier Science