Minimal energy surfaces on Powell--Sabin type triangulations

Authors:
D. Barrera;M. A. Fortes;P. González;M. Pasadas
Affiliations:
Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n 18071 Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n 18071 Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n 18071 Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n 18071 Granada, Spain
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

In this paper we present a method to obtain an explicit surface on a polygonal domain D which approximates a Lagrangian data set and minimizes a certain ''energy functional''. The minimization space is the C^1-quadratic spline space constructed from an @a-triangulation over D and its Powell-Sabin subtriangulation, i.e., we obtain a C^1-polynomial with the minimal possible degree. A convergence result is established and some numerical and graphical examples are analyzed.