A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the “ordinary” C2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C2 PH ...

in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

T-spline surfaces are a powerful tool in geometric modelling. A T-spline surface is an approximation of a T-grid data structure. T-grids support adaption operations like local refinement or merging of existing NURBS grids. Digital terrain models based on T-spline surfaces benefit from non-regular control grids. We show some exemplary application cases for T-spline based terrain modelling.

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...

The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines arbitrary orders. real parts the WPs are regular spline-based orthonormal designed in [4]. imaginary so-called complementary WPs, which, unlike symmetric they antisymmetric. Tensor products 1D provide diversity 2D oriented multiple directions. computat...