In Computer Aided Geometric Design it is often needed to produce a positivity preserving curve according to the given positive data. The main focus of this work is to visualize the positive data in such a way that its display looks smooth and pleasant. A rational quadratic trigonometric spline function with three shape parameters has been developed. In the description of the rational quadratic ...

We develop a method for interpolating scattered data on sphere-like surfaces based on a local triangular patch which is constructed from a blend of certain spherical Bernstein-B ezier polynomials introduced recently by Alfeld, Neamtu & Schumaker 2]. The method produces a C 1 interpolant which matches values and derivatives, and is a natural analog of a planar method of Foley & Opitz 6] and Good...

The shape features of planar trigonometric Bézier curves with two shape parameters are analyzed. The necessary and sufficient conditions are derived for these curves having one or two inflection points, a loop or a cusp, or be locally or globally convex. All conditions are completely characterized by the relative position of the control polygon’s side vectors. Furthermore we discussed the influ...

Shaded display is popular for displaying curved surfaces because of the realistic appearance of the images produced. In the eld of computer aided geometric design, however, line drawings are more commonly used. For accurate evaluation of the curved surfaces in these designs, the conventional method of approximating curved surfaces with polygons is insu cient. In this paper we will present a met...

The problem of interpolating scattered 3D data by a geometrically smooth surface is considered. A completely local method is proposed, based on employing degenerate triangular Bernstein{B ezier patches. An analysis of these patches is given and some numerical experiments with quartic and quintic patches are presented. Supported by the Netherlands Foundation of Mathematics (SMC) and the Netherla...

Given A spline curves and A patch surfaces that are implicitly de ned on triangles and tetrahedra we determine their NURBS representations We provide a trimmed NURBS form for A spline curves and a parametric tensor product NURBS form for A patch surfaces We concentrate on cubic A patches providing a C continuous surface that interpolates a given triangulation together with surface normals at th...

We use bivariate C 1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and suucient condition on Bernstein-B ezier polynomials, we set the convexity preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on t...

By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonometric; (b) hyperbolic; (c) hypertrigonometric. Each class is characterized by a perturbation of t...

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using derivatives are presented. The combination tension, continuity, bias control is used as a very powerful type interpolation; they applied to curves. Surface construction utilizing studied explored several examples obtained by C1 surface given show usefulness method.