摘要
采用函数三次样条光顺曲线,证明在样条曲线局部转角小,总转角不超过120°情况下,曲线的光顺指示函数y″(1+y′2)3/2可以简化为二阶导数曲线y″(x).由于y″(x)对x是分段折线函数,对y是线性泛函,因而定出不光顺之处及用叠加原理计算调整公式均变得很简单.此样条函数曲线光顺能够采用电脑自动化进行.
It is proved that,when the local turning angles are small and the total turning angle of a functional spline is not greater than 120°,for the indicator y″(1+y′\+2)\+\{3/2\} of spline fairing, y″(x) can be used instead.\;Since y″(x) is sectionally linear on x and linear on y ,it is convenient to use it to find the unfair place and to calculate the adjustment quantities by superposition principle.Fairing the spline curves can be carried out automatically with computer and the mathematical ship lofting will be done quickly.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2003年第4期377-382,共6页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(69972045)
