Efficient quadrature rules for subdivision surfaces in isogeometric analysis

Additionally, we extend existing results on exact integration of subdivision splines. This allows us to validate our approach by computing surface areas and volumes with known exact values. We demonstrate on several examples that our quadratures use fewer quadrature points than traditional quadratures. We illustrate our approach to subdivision spline quadrature on the well-known Catmull-Clark scheme based on bicubic splines, but our ideas apply also to subdivision schemes of arbitrary bidegree, including non-uniform and hierarchical variants. Specifically, we address the problems of computing areas and volumes of Catmull-Clark subdivision surfaces, as well as solving the Laplace and Poisson PDEs defined over planar unstructured quadrilateral meshes in the context of isogeometric analysis.