Elliptic grid generation using NURBS surfaces

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Abstract

Recently, there has been a move towards NURBS-based grid generation systems, where the original geometry is given as analytically defined NURBS surfaces. The process of surface grid generation is the computation of an algebraic grid based on the NURBS surface definition and the computation of an elliptic grid based on the algebraic grid. The NURBS format provides a common mathematical representation for both standard analytic shapes and free-form curves and surfaces. The derivatives of the physical coordinates with respect to the parametric coordinates can be evaluated directly. An improved elliptic surface grid generation method for NURBS surfaces is presented. New techniques for computing the control functions and imposing boundary orthogonality are developed.

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Khamayseha, A., & Hamann, B. (1996). Elliptic grid generation using NURBS surfaces. Computer Aided Geometric Design, 13(4), 369–386. https://doi.org/10.1016/0167-8396(95)00050-X

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