Research On A Class Of Rational Bézier Curves And Offset Curves

Offset curves, also called parallel curves, are defined as locus of points which are at constant distance d along the normal from the generator curves. Offset are widely used in various applications, such as computer graphics and industry fields. Therefore, the study of offset curves has become a hot topic of CAGD.Based on Bernstein polynomials and rational parameter transformation, a new class of rational composite functions-rational Bernstein function class is obtained and its analytical properties are discussed. Then, the method of a new class of rational Bezier curves design is introduced and the corresponding geometric properties of the curves are studied. At last, several applicable rational Bezier curves are studied and a numerical example is given.A new class of regular rational Bezier curves was constructed. The tangent vector at each point of the regular rational Bezier curve of degree n was obtained by using the improved rational de Casteljau algorithm. Then we can get the unit normal vector at each point of the original curve. This method has obvious geometric meaning. The algorithm is simple and the result is satisfactory in practice. Meanwhile, the mathematic program for drawing of rational Bezier curve and its offset curve are given, this makes the drawing exact and quick, and the practice effect is well.