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Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud . The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
Efficient quadrature rules for subdivision surfaces in isogeometric analysis
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles
The quadrature rule of Hammer and Stroud  for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ...