A New Class of Quasi-Cubic Trigonometric Bezier Curve and Surfaces

A kind of quasi-cubic Bzier curves by the blending of algebraic polynomials and trigonometric polynomials using weight method is presented, named WAT Bzier curves. Here weight coefficients are also shape parameters, which are called weight parameters. The interval [0, 1] of weight parameter values can be extended to [ 2, 2 / (2 6)] and the corresponding WAT Bzier curves and surfaces are defined by the introduced base functions. The WAT Bzier curves inherit most of properties similar to those of c Bzier curves, and can be adjusted easily by using the shape parameter. The jointing conditions of two pieces of curves with G2 and C4 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-Bzier methods which can approximate the Bzier curves only from single side, the WAT Bzier curves can approximate the Bzier curve from the both sides, and the change range of shape of the curves is wider than that of C-Bzier curves. The geometric effect of the alteration of this weight parameter is discussed.