A Four Degree Algebraic Spline with G² Continuity

Polynomial algebraic arc in a triangle can be represented by Bernstein-Bézier through barycentric coordinates transform.A four-degree real algebraic spline with four shape handles and passing through two vertexes of triangle is chosen from them.Given sequence points or controlling polygon,every two consecutive points can construct a triangle with an exterior vertex,which acts as controlling points.The arc that interpolate given points or approximate controlling vertexes in every triangle can construct G² continuity curve for sequence points. If shape handles are given,the individual arc is proved to be monotone in barycentric coordinates system,and it can be convex-preserving through adjusting four handles.Finally,we give an example to compare with the three-degree algebraic spline.