6533b855fe1ef96bd12b06d7

RESEARCH PRODUCT

Two -methods to generate Bézier surfaces from the boundary

R. OsetE. MorenoP. CentellaJuan Monterde

subject

Bézier surfaceMathematical analysisAerospace EngineeringBoundary (topology)TangentGeometryMixed boundary conditionBiharmonic Bézier surfaceComputer Graphics and Computer-Aided DesignComputer Science::GraphicsModeling and SimulationAutomotive EngineeringBiharmonic equationUniquenessBoundary value problemMathematics

description

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.

yearjournalcountryeditionlanguage
2009-02-01Computer Aided Geometric Design
https://doi.org/10.1016/j.cagd.2008.07.003