Approximate Bezier curves by cubic LN curves

作者：Huang, Wei-Xian; Jin, Cong-Jian; Wang, Guo-Jin^*

来源：Applied Mathematics and Computation, 2011, 218(7): 3083-3092.

DOI：10.1016/j.amc.2011.08.032

• Offset
• Cubic LN Bezier curves
• Bezier curves
• Hausdorff distance
• Approximation

In order to derive the offset curves by using cubic Bezier curves with a linear field of normal vectors (the so-called LN Bezier curves) more efficiently, three methods for approximating degree n Bezier curves by cubic LN Bezier curves are considered, which includes two traditional methods and one new method based on Hausdorff distance. The approximation based on shifting control points is equivalent to solving a quadratic equation, and the approximation based on L(2) norm is equivalent to solving a quartic equation. In addition, the sufficient and necessary condition of optimal approximation based on Hausdorff distance is presented, accordingly the algorithm for approximating the degree n Bezier curves based on Hausdorff distance is derived. Numerical examples show that the error of approximation based on Hausdorff distance is much smaller than that of approximation based on shifting control points and L(2) norm, furthermore, the algorithm based on Hausdorff distance is much simple and convenient.

• 出版日期2011-12-1
• 单位浙江大学