Modelling Through Trigonometric Curve and Surfaces

Abstract

A kind of Rational cubic Bezier curves by the blending of algebraic polynomials and trigonometric polynomials using weight method is presented, named WAT Rational Bezier curves. Here weight coefficients are also shape parameters, which are called weight parameters. The interval [0, 1] of weight parameter values can b e extended to [-2, 2.33] and the corresponding WAT Rational Bezier curves and surfaces are defined by the introduced base functions. The WAT Rational Bezier curves inherit most ofproperties similar to those of Cubic Bezier curves, and can be adjusted easily by using the shape parameter A. The jointing conditions of two pieces of curves with G2 and C2 continuity are discussed. With the shape parameter chosen properly, the defined curves can express exactly any plane curves or space curves defined by parametric equation based on {1, sint, cost, sint2t, cos2t} and circular helix with high degree of accuracy without using rational form. Examples are given to illustrate that the curves and surfaces can be used as an efficient new model for geometric design in the fields of CAGD. Unlike the existing techniques based on C-Bezier methods which can approximate the Bezier curves only from single side, the WAT Rational Bezier curves can approximate the Bezier curve from the both sides, and the change range of shape of the curves is wider than that of C-Bezier curves. This WAT Rational Bezier curves much closer to the control point compare to the other curves. The geometric effect of the alteration of this weight parameter is discussed.