Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

Table 2

Experimental set of four bivariate functions.

Number	Test function
01	𝑓(𝑥,𝑦)=42.659{0.1+𝑥(0.05+𝑥^4−10𝑥^2𝑦^2+5𝑦^4)},𝑥=𝑥−0.5,𝑦=𝑦−0.5
02	𝑓(𝑥,𝑦)=1.3356[1.5(1−𝑥)+𝑒^(2𝑥−1)sin{3𝜋(𝑥−0.6)^2}+𝑒^(3(𝑦−0.5))sin{4𝜋(𝑦−0.9)^2}]
03	𝑓(𝑥,𝑦)=1.9[1.35+𝑒^𝑥sin{13(𝑥−0.6)^2}𝑒^−𝑦sin(7𝑦)])
04	𝑓(𝑥,𝑦)=3+2sin(2𝜋𝑥)sin(2𝜋𝑦)+𝑒^{−15(𝑥−1)2−15(𝑦−1)2}+𝑒^{−10𝑥2−15(𝑦−1)2}