Two C1-methods to generate Bézier surfaces from the boundary

Authors:
P. Centella;J. Monterde;E. Moreno;R. Oset
Affiliations:
Dep. d'Algebra, Universitat de València, Avd. Vicent Andrés Estellés, 1, E-46100-Burjassot (València), Spain and Dep. de Geometria i Topologia, Universitat de València, Av ...;Dep. de Geometria i Topologia, Universitat de València, Avd. Vicent Andrés Estellés, 1, E-46100-Burjassot (València), Spain;Dep. de Geometria i Topologia, Universitat de València, Avd. Vicent Andrés Estellés, 1, E-46100-Burjassot (València), Spain;Dep. de Geometria i Topologia, Universitat de València, Avd. Vicent Andrés Estellés, 1, E-46100-Burjassot (València), Spain
Venue:
Computer Aided Geometric Design
Year:
2009

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Abstract

Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x-=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x-=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.