In any method aimed at solving a boundary value problem using isogeometric analysis, it is imperative to find a high quality parameterization of the domain over which the partial differential equation is posed. The parameterization of the domain is an essential part of solving the problem, and the accuracy of the analysis to be performed rely heavily on the quality of the parameterization. In this thesis we introduce four different methods for parameterization of planar geometries for applications within isogeometric analysis. The methods all rely on B-splines and the isogeometric framework. We describe B-splines and isogeometric analysis in detail, and we introduce several mesh metrics to be used to check the mesh quality in our pursuit of producing superior meshes. Several illustrative examples are given, and the methods tested on several different geometries, all representing different parameterization challenges.The methods are found to produce quite different parameterizations for the same geometry. We have found that the most complex methods in general show the best overall performance, both with respect to mesh quality and perseverance.
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