Surface blending is a useful operation in geometric design for rounding sharp edges or corners. Meanwhile, NURBS has already become the de facto industrial standard in existing CAD/CAM systems. Therefore, it is required to study how to blend two B-spline surfaces. However, two arbitrary B-spline surfaces (called base surfaces) are hard to be blended with a B-spline surface (called blending surf...

In this paper, we present a non-uniform subdivision scheme of arbitrary degree with a variable parameter sequence. By this scheme, blending curves which are composing of different types of generalized B-spline curves including many analytic curves can be successfully reproduced. Generalized subdivision and the classical B-spline subdivision are all special cases of the proposed variable paramet...

Interpolation of a sequence of points by spline curves generally requires the solution of a large system of equations. In this paper we provide a method which requires only local computation instead of a global system of equations and works for a large class of curves. This is a generalization of a method which previously developed for Bspline, NURBS and trigonometric CB-spline curves. Moreover...

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

The objective of the paper is to continue the study of an interesting class of rational splines in polar coordinates, introduced by SS anchez-Reyes 17] and independently by de Casteljau 6]. We refer to these curves as p-splines. They are a generalization of certain analogous of B ezier curves in polar coordinates which we call p-B ezier. We present an alternative way to have an exact representa...

In this paper (part three of the trilogy) we use low degree G and G continuous regular algebraic spline curves de ned within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of in ection points. The regular algebraic spline curves considered h...

In this paper, we present an ef®cient sub-optimal algorithm for ®tting smooth planar parametric curves by G 1 arc splines. To ®t a parametric curve by an arc spline within a prescribed tolerance, we ®rst sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct...

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...

A new class of spline curves in polar coordinates has been presented in (SS anchez-Reyes, 1992) and independently considered in (de Casteljau, 1994). These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling sp...