It is well known that a cardinal B-spline of order m,m ∈ N, is a piecewise polynomial function. In this note we propose an effective method for calculating the coefficients of polynomials which constitute a cardinal B-spline. © 2010 Elsevier Ltd. All rights reserved.

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

In this paper we intend to generate some set of optimal trajectories according to the number of control points has been applied for parameterizing those using B-spline curves. The trajectories are used to generate an optimal locomotion gait in a crawling worm-like robot. Due to gait design considerations it is desired to minimize the required torques in a cycle of gait. Similar to caterpillars,...

Recently, a novel laser data based SLAM algorithm using B-Spline as features has been developed in [Pedraza et al., 2007]. EKF is used in the proposed BS-SLAM algorithm and the state vector contains the current robot pose together with the control points of the splines. The obervation model used for the EKF update is the intersections of the laser beams with the splines contained in the map. In...

In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular perturbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spl...

Every curve or surface can be defined by a set of parametric functions. For instance, (x,y,z) coordinates of the points of the curve can be given by:) (), (), (t Z z t Y y t X x = = = t being the parameter and X, Y, Z being polynomial functions in t. If X, Y and Z are 1 st degree polynomials, a line segment will be defined. In that case, two knowns only (i.e. two points or a point and a slope) ...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

Non-uniform basis functions for construction of interpolating and approximating spline curves and surfaces are presented. The construction is based on the theory of B-splines and enables a continuous change from interpolation to approximation of given data. It is also possible to change the tension of the curves and surfaces.