基于多结点样条磨光函数的几何迭代法

Geometric Iteration Method Based on Many-Knot Spline Polishing Functions

几何迭代法在计算机辅助几何设计(CAGD)中有广泛地应用,为了提高传统的B-样条曲线插值在几何迭代中的收敛速度和迭代精度,提出了基于多结点样条磨光函数的几何迭代法,引入多结点样条磨光函数,在曲线拟合时把多结点样条磨光方法和几何迭代方法结合,经过磨光和迭代,在L-BFGS迭代算法的最优解下构造具有高逼近性的曲线拟合方法。实验结果表明,在相同精度下,该方法不仅减少了迭代次数,且提高了迭代速度,可以用于飞机、汽车等外形设计上,亦可用于文物、房屋等外形重构和重建,以及卫星图形图像的处理中。

Geometric iteration method has been widely used in computer aided geometric design(CAGD).In order to improve the convergence speed and iterative accuracy of the traditional B-spline curve interpolation in geometric iterations,this study proposes the geometric iteration method based on many-knot spline polishing functions,which introduces many-knot spline polishing functions,and combines many-knot spline polishing functions method and geometric iteration method in curve fitting.After polishing operator and iterating,the curve fitting method with high approximation under the optimal solution of L-BFGS iterative algorithm is constructed.Experimental results show that the proposed method not only reduces the times of iterations,but also improves the iterative speed under the same accuracy.The proposed geometric iteration method can be used in the shape design of airplanes,automobiles,etc.It can also be used to reconstruct and rebuild the shape of cultural relic houses and satellite image processing.