Quadratic Trigonometric Polynomial Curves with Two Shape Parameters

摘要

It Is well known that the cubic polynomial curves are suggested for the spaces {1,t,t2,t3}. However,curves also could be constructed for the spaces with trigonometric functions. A class of quasi-cubic trigonometric curves with two shape parameters is presented in this paper. The curves are constructed for the spaces {1,sinu,cosu,sin2u},named QCT-curves. Then,the properties,application and relationship between QCT-curves are also discussed. QCT-curves have plenty of properties similar to the corresponding cubic polynomial curves,and they could be converted into each other in proper condition. Furthermore the shape of QCT-curves can be adjusted by two shape parameters and they can accurately represent the arcs of circle,ellipse,parabola and other quadratic curves without using rational form.