Bezier projection: A unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis

We introduce Bezier projection as an element-based local projection methodology for B-splines, NURBS, and T-splines. This new approach relies on the concept of Bezier extraction and an associated operation introduced here, spline reconstruction, enabling the use of Bezier projection in standard finite element codes. Bezier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global L-2 projection. Bezier projection is used to develop a unified framework for spline operations including cell subdivision and merging, degree elevation and reduction, basis roughening and smoothing, and spline reparameterization. In fact, Bezier projection provides a quadrature-free approach to refinement and coarsening of splines. In this sense, Bezier projection provides the fundamental building block for hpkr-adaptivity in isogeometric analysis. (C) 2014 Elsevier B.V. All rights reserved.