In this paper, we analyse the different parameter choices for fitting B-spline curves. New estimating criteria for data approximation are introduced in order to estimate the results. The definitions of norms correspond to a global analysis of the curve. Other criteria are based on a local analysis. We present a new method for data compression using fitting B-splines and compare it to usual ones.

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructi...

Extensions of the classical B-spline curves by shape parameters are discussed in this paper. Using a method of linear blending, first we extend the abilities of GB-splines, originally defined by uniform shape parameter, to multiple shape parameters. Then two methods, having different types of continuity, are examined in terms of their curvature behavior.

Abstract Nowadays, NURBS (Non-Uniform Rational B-Spline) method is widely used in CAD/CAM (Computer-Aided Design/Computer-Aided Manufacturing) to represent sculptured curves or surfaces. In this paper, we develop a 5-axis NURBS real-time interpolator and realize it in our developing CNC(Computer Numerical Control) system. At first, we use two NURBS curves to represent tool-tip and tool-axis pat...

There are thousands of articles published on variants of splines, including least squares cubic splines. One of the first least squares articles was de Boor and Rice [1], and a comprehensive explanatory textbook is Dierckx [2]. Unfortunately, every example in the literature and on the web of a least squares cubic spline makes use of B-splines. While B-splines have a certain elegance, they are s...

This paper presents a Bayesian method to reconstruct the centerline in noisy data using B-spline curves. The method is illustrated on simulated twoand three dimensional data and is applied to recover the centerline of the colon in single photon emission computed tomography images.

In this paper we describe two natural ways to express the first derivative of a rational B-spline curve in terms of its control points and weights. These expressions generalise the established ones for non-rational curves and offer numerically stable methods for computing the derivative. Some useful properties are derived from one of them. §

This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1(t) and C2(r) as an implicit curve F(t; r) = 0, where F(t; r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve F(t; r) = 0 has degree 4m 2, whi...

i=0 Pn n=0 bijB m i (u)B n j (v) of bi-degree (m;n) has total degree m + n, however, the class of Gmn(u; v) is a subset of polynomials of total degree m + n. G (resp G) continuity implies curve segments share the same tangent(curvature) at join points(knots). In each of the G and G constructions, we develop a spline curve family whose member satis es given interpolation conditions. Each family ...