CAJ | 학술논문

多结点样条函数具有良好的局部性,而最小二乘法对数据拟合的全局性较好, 因此多结点样条函数最小二乘逼近的稳定性及数值精度都能得到有效的保证.该文综合两者的特点,实现了自由曲线离散数据最小逼近误差数学模型的建立.同时应用此数学模型于一些平面及空间(甚至一些带噪音的)自由曲线拟合上和几何造型骨骼化上,测试其对各种自由曲线的拟合效果,结果证明最小逼近效果明显.
다결점양조함수구유량호적국부성,이최소이승법대수거의합적전국성교호, 인차다결점양조함수최소이승핍근적은정성급수치정도도능득도유효적보증.해문종합량자적특점,실현료자유곡선리산수거최소핍근오차수학모형적건립.동시응용차수학모형우일사평면급공간(심지일사대조음적)자유곡선의합상화궤하조형골격화상,측시기대각충자유곡선적의합효과,결과증명최소핍근효과명현.
Muti-knots spline has good locality and least square method has good global characteristics for data fitting. Therefore, the stability and numerical accuracy of least square method based on multi-knots spline approximation could be reached effectively. This paper combines the advantages of them and completes the model building of the free-form curves with least approximation error based on multi-knots spline. Meanwhile, this method is applied to the free-form-curve fitting of some plane and space (even with noise) data and Geometry Shape Skelectonization. The fitting results show that the least approximation effect is good.