Trigonometric curves pdf

Pottmann, H. Mainar, E. Zhang, J. Article Google Scholar. Mazure, M. Wagner, M. Laurent, P. Schumaker, L. Lane, J. Gordan, W. Morin, G. Download references. You can also search for this author in PubMed Google Scholar. Reprints and Permissions. Uniform trigonometric polynomial B-spline curves.

Sci China Ser F 45, — Download citation. Received : 10 December Issue Date : October The value of weight parameters can be extended to the interval [0, 1] to [-2, 2. The jointing conditions of two pieces of curves with the G2 and C2 continuity are discussed.

Examples are given to illustrate that the curves and surfaces, which can be used as an efficient new model for geometric design in the fields of CAGD. The geometric effect in case of shape preservation of this weight parameter is also discussed.

The significance of trigonometric spline in various areas are like in the design of tools and machinery and in the drafting and design of all types of buildings, from small residential types houses to the largest commercial and industrial structures hospitals and factories.

Computer aided geometric design CAGD studies the construction and manipulation of curves and surfaces using polynomial, rational, piecewise polynomial or piecewise rational splines. Among many generalizations of polynomial splines, the trigonometric splines are of practical importance.

In recent years, trigonometric splines with shape parameters have proposed for geometric modeling. Smooth curve representation of scientific data is also of great interest. In the field of data visualization, it is important that the graphical representation of information is clear and effective.

When data arise from a physical phenomenon or problems of industrial design and manufacturing, it is required that the interpolating curve www. In recent year, various authors have worked in the area of shape preserving splines, using trigonometric rational splines []. In the recent past, a number of authors and references have contributed to the shape-preserving interpolation and different polynomial methods, which are used to generate the shape-preserving interpolant, have been considered.

The rest of this paper is organized as follows. Section 2, defines the WAT-Bezier Base Functions and the corresponding rational curves and surfaces, also discuss their properties. In section 6, the representations of some curves are shown in figure.

Besides, some examples of shape modeling by using the WAT-rational Bezier surfaces are presented. The conclusions are given in section 7. Impact Factor JCC : 3. From the Figure 3, it can be seen that when the control polygon is fixed, by adjusting the weight parameter from -2 to 2. The weight parameters have the property of the geometry. The larger the shape parameter is, and the more approach the curves to the control polygon is. The paths of the given curves are line segments. Some transcendental curves can be represented by the WAT with the shape parameters and control points chosen properly.

These equations show that Cubic WAT- Rational Bezier Curve can be made closer to the control polygon by altering the values of shape parameters. Corollary 3. Thus, G1 continuity has transformed into C1 continuity. Then we can get following theorem 4.