We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider two types of singular parameterizations, domains where a part of the boundary is mapped onto one point and domains where parameter lines are mapped collinearly at the boundary. We locally map a singular tensor-product patch of arbitrary degree onto a triangular patch, thus splitting the parameterization into a singular bilinear mapping and a regular mapping on a triangular domain. This construction yields an isogeometric function space of prescribed smoothness. Generalizations to higher dimensions are also possible and are briefly discussed in the final section.

翻译：我们旨在构造几何正则性降低的域上等几何函数空间的光滑基。在此背景下，等几何函数是分段有理函数与分段有理几何参数化逆映射的复合函数。我们考虑两类奇异参数化：边界部分映射至单点的域，以及参数线在边界上共线映射的域。我们将任意次数的奇异张量积胞局部映射至三角形胞，从而将参数化分解为奇异双线性映射与三角形域上的正则映射。该构造可生成指定光滑阶的等几何函数空间。高维情形的推广亦可行，并在最后章节简要讨论。