Fundamentals of Computer Aided Geometric Design

TL;DR: A modification scheme for the test function space to regain regularity is introduced for the isogeometric method for singularly parameterized domains in this case the underlying function space may not be sufficiently regular.

TL;DR: It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials and the convolution with general rational surfaces yields rational surfaces.

TL;DR: It is demonstrated that the linear reconstruction system can be solved fast enough to guarantee interactive response time thanks to a precomputed factorization of the coefficient matrix and enables to edit complex meshes while retaining the shape of the details in their natural orientation.

TL;DR: This paper reviews and analyze existing least squares orthogonal distance fitting techniques in a general numerical optimization framework and proposes two new geometric variant methods (GTDM and CDM).