The Quintic Bézier Approximation of Conic Curves

The conic curves cannot be accurately represented by polynomial curves. To solve this problem, this paper presents the approximation methods of conic curves by quintic Bézier curve. By analyzing the approximation error function, which is the determinant for the upper bound of the Hausdorff error, the first kind of approximation curve we got achieves G³ continuity at the endpoints, which better preserves the properties at the endpoints. The second one is G¹ continuous. And the maximum value of the error function is minimum. The last one is also G¹ continuous and the L₁ norm is minimized. The curve is further extended to tensor product surface. The tensor product quintic Bézier surface is obtained to approximate surface. Finally, the numerical example of quintic Bezier curve approximating conic curve proves that the proposed method has better approximation effect.