This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

Abstract In this paper, we present a new form of density based topology optimization where the design space is restricted to the B-spline space. An arbitrarily shaped design domain is embedded into a rectangular domain in which tensor-product B-splines are used to represent the density field. We show that, with proper choice of B-spline degrees and knot spans, the B-spline design space is free ...

This paper presents a C Pythagorean-Hodograph (PH) spline curve interpolator for contourfollowing tasks. To generate the C PH quintic spline curve, a uniform knot sequence is employed. The Scurve motion planning architecture with variable feedrate for a planar C PH quintic spline curve is also developed. In particular, C cubic feed acceleration/deceleration is imposed on the first and last PH q...

Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-s...

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.