A Class of Quasi-Quartic Trigonometric Polynomial Bézier Curves with a Shape Parameter

A class of quasi-quartic trigonometric polynomial Bezier 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 Bezier 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 Bezier 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.