An improved and approximate interpolation by skew axial parabola

Given two adjacent oblique axial parabolas, we propose a method to construct a Hermite curve from the tangent vector of the vertex. This method avoids extracting. Moreover, addition, substituting the direction determined by ration points for the above mentioned direction is a viable way to improve performance. The magnitudes of tangent vectors can be set to the projected length of chord in the approximate method. While gain similar shape the two algorithms are more efficient than weighted average interpolation.