Abstract:

A class of quasiquartic trigonometric polynomial Bézier curves  with a shape

parameter is presented. The curve is controlled by five points, and it has a lot of similar

characteristics with the traditional quartic Bézier curve, and its shape can be adjusted by a

parameter, which makes the curve feature  more powerful expression ability. The shape

parameter affects the property of geometry, the larger is the parameter, and the more of the

curve approaches the control polygon, therefore, the trigonometric polynomial curve with the

shape parameter can be close to the given control polygon than the quartic Bézier curve. The

new curve can represent exactly the arc of circle, arc of ellipse, arc of parabola and other

quadratic curves without using a rational form. For designing free curves, the G2 and C3

continuity condition of twopiece curves are also discussed. The modeling examples illustrate

that the new curve has a high application value for computer aided geometric design.

Key words: Bézier curves;trigonometric polynomial;quasiquartic;shape parameter;continuity