Interpolating 2D Data Set by Conic Spline with G² Continuity

A method for interpolating 2D data with conic spline is introduced.The conic is represented by implicit equation.First,a method for interpolating two given end points as well as two given tangents at these points and a given curvature at an end point is presented;Second,a method for interpolating an open points sequence in a plane is offered;Last,a method for interpolating a closed points sequence in a plane is given.The method is very robust for any 2D data sequences.Overall G² continuity is held whether the data set is open or closed.