Efficient energy evaluations for active B-Spline/NURBS surfaces

Development of vector-parametric fifth-degree B-spline with control points incident the surface

“…Для получения сплайнов с первым, вторым, тре-тьим и четвертым порядками гладкости необходимо обеспечить условия склеивания (7), (12), (13), (14), (15), (18) …”

“…Работа является логическим продолжением иссле-дований [4][5][6][7][8][9][10][11][12][13][14][15]. Автор статьи планирует продолжить данные исследования, ввиду их очевидной полезности потребителям.…”

Inner products of box splines and their derivatives

“…This is usually the case in least-squares approximation methods and in Galerkin finite element methods. Various types of quadrature methods have been developed for this purpose, especially for univariate B-splines and NURBS, see [1,10,13,18]. On the other hand, algorithms to compute the exact values of these inner products have also been provided for multivariate simplex splines [9,15] and for multivariate polyhedral splines [5].…”