In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...

A new class of single-valued curves in polar coordinates obtained by a transformation of a subset of rational B ezier curves into Cartesian coordinates has recently been presented in (SS anchez-Reyes, 1990), and independently considered by P.de Casteljau, who called these curves focal B ezier. These curves are trigonometric polynomials that can be represented by a basis similar to the Bernstein...

The geometry of curves and surfaces plays a very important role in computer-aided geometric design (CAGD). goal this paper is to construct the Frenet frames trigonometric B\'ezier Euclidean $ 2 3- $space. Especially, curvatures these are investigated at beginning ending points.

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. 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 splines in polar coordinates has been pr...

We present an algorithm for interactive display of trimmed NURBS surfaces. The algorithm converts the NURBS surfaces to B ezier surfaces and NURBS trimming curves into B ezier curves. It tessellates each trimmed B ezier surface into triangles and renders them using the triangle rendering capabilities common in current graphics systems. It makes use of tight bounds for uniform tessel-lation of B...

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...

I. Introduction Rational spline is a commonly used spline function. In many cases the rational spline curves better approximating functions than the usual spline functions. It has been observed that many simple shapes including conic section and quadric surfaces can not be represented exactly by piecewise polynomials, whereas rational polynomials can exactly represent all conic sections and qua...

We discuss a natural way to deene barycentric coordinates associated with circular arcs. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar interval case, and which has close connections to trigonometric polynomials. x1. Introduction Bernstein-B ezier (BB-) polynomials deened on an interval are useful tools for constructing piecewise functional and parametric c...

In this paper we discuss a natural way to deene barycen-tric coordinates associated with circular arcs. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar interval case, and which has close connections to trigonometric polynomials. x1. Introduction Bernstein-B ezier (BB-) polynomials deened on an interval are useful tools for constructing piecewise functional a...