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Minimization, Constraints and Composite Bézier Surfaces
Keywords
bézier surface, offset surface, surface fitting, offset surface, approximate conversion, surface approximation, surface simplification, variational problem formulation, Finite-Element Method (FEM), FEM’s hp-method, Lagrange Multipliers Formulation
Abstract
This paper presents a global method for approximation and/or construction of surfaces using constraints. The method is based on a min max problem which describes approximation and differential geometric characteristics, constrained in order to achieve desired geometrical effects. The numerical solution of the problem takes full advantage of the Finite-Elements method and of constrained optimization algorithms.