Bézier-type curve of 5 order and its applications

To represent some quadric curves and transcendental curves,such as elliptic arc,circular arc,cycloid and helix,a new kind of Bezier-type basis functions of 5 order in the non-polynomial space { 1,t,sint,cost,sin2 t } are constructed. They share the most properties with Bernstein basis,such as non-negative,normative,symmetry,and endpoints nature. The Bezier-type curve of 5 order based on the new basis functions have similar properties as the Bezier curve,such as convex hull,symmetry,geometric invariance and endpoint interpolation and end edge tangent property. C1 and G1link conditions of the curve and an example in surface of revolution modeling are presented. The result of experimentation shows that the modeling method is effective and enriches modeling theories.