Curve Fitting with Splines

摘要: In many applications where curve fitting is used, one would like to modify parts of the without affecting other parts. We shall say that a scheme has local property if modifications do not propagate. Clearly, polynomials discussed in Section 10.2 have this feature and Bezier exhibit it only approximately. A change location or multiplicity guiding points requires recalculation whole curve, even though changes will little effect far from changed point. Piecewise polynomial functions offer direct way achieving control. discuss such first y = (x) form later parametric representations. The following general expression for piecewise function: $$ p(x) {p_i}(x)\quad {x_i} \leqslant x {x_{i + 1}}\quad i 0,1...,k - 1 $$ (11.1a) $$ {p_i}^{(j)}({x_i}) {p_i}{_{ 1}^{(j)}}({x_i})\quad j 0,1...r 1;i 1,...k $$ (11.1b)