基于广义逆矩阵的Bézier曲线近似合并

Approximate merging of Bézier curves with generalized inverse matrices

Bézier曲线近似合并算法在几何数据压缩方面有着重要的应用.研究了两条相邻Bézier曲线近似合并的问题,用矩阵的形式给出了相邻Bézier曲线可精确合并的条件,并在此基础上通过广义逆矩阵的方法求解合并逼近后的Bézier曲线.同时,对保端点插值条件的近似合并也给出了结果.最后用实例说明了算法的有效性,得到了很好的逼近效果.

Approximate merging algorithm of Bézier curves plays an important role of geometric data compression. A new approach to considering approximate merging of two adjacent Bézier curves is presented and the condition of precise merging of adjacent Bézier curves by taking advantage of matrix representation is obtained. Then the merged Bézier curve by generalized inverse matrices based on precise merging condition is solved. At the same time, the result of approximate merging with endpoint interpolation is showed. Finally, numerical examples demonstrate the effectiveness of our algorithms.