In this paper, we construct a matrix, which transforms a generalized C-Bézier basis into a generalized uniform algebraic-trigonometric B-spline (C-B-spline or UAT B-spline) basis. We also show that it is a totally positive matrix and give a normalized B-basis of the generalized UAT B-splines.  2005 Elsevier B.V. All rights reserved.

Abstract The $$\kappa $$ κ -curve is a recently published interpolating spline which consists of quadratic Bézier segments passing through input points at the loci local curvature extrema. We extend this representation to control magnitudes maximum in new scheme called extended- or $$\epsilon \kappa <mml:mrow...

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,...

The polygonization, or tesselation, of surfaces is a classical problem that has many practical applications in computer graphics and geometric modeling. The problem consists in computing a piecewise linear approximation for a smooth surface described either by parametric or implicit functions. A polygonal mesh is the one of the simplest forms of surface description and therefore is the represen...

the rotation curves of a sample of 46 low- and high-surface brightness galaxies are considered in the context of milgrom's modi_ed dynamics (mond) to test a new interpolating function proposed by zhao et al. (2010) [1] and compare with the results of simple interpolating function. the predicted rotation curves are calculated from the total baryonic matter based on the b-band surface photometry,...

In this paper, we present a geometric construction of control meshes of helicoids over trapezium domain. We first introduce the quasi-Bézier basis in the space spanned by {1, t, cos t, sin t, t sin t, t cos t}, with t ∈ [0, α], α ∈ [0, 2π). We denote the curves expressed by the quasi-Bézier basis as algebraic-trigonometric Bézier curves, for short ATBézier curves. Then we find out the transform...

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocatio...