USING PYTHON

One important application of spline interpolation is the construction of smooth curves that are not necessarily the graph of a function but that have a parametric representation I = (1 ) and y = 10) for the In 6) . Hence one needs to determine two splines interpolating ( , I ) and ( 1 9 ) ( = 0 .. ) The are length of the curve is a natural choice for the parameter t . However . this is not known a prion and instead the I s are usually chosen as the distances of consecutive points to = 0 . 6 , = 1 1 + V ( I , - 2 1 1 2 + ( 4 ; - 3 - 1 ) 2 1 2 1 ( 1 ) Use the values in Table I to construct a smooth parametric representation of a curve passing through the points ( I . " ) ) . j = 0 1 8 by finding the two natural cubic splines interpolating ( I ) and ( 1 41) . = 0 1 8 respectively . Tabulate the coefficients of the splines and plot the resulting ( parametric ) curve 01 0 150 / 0.TO 10618/ 090 090 20935060 10 0 31. 265 0.35 0.80 1 1636 0.20 0.45 5 /1905 0.10 0.20 6 / 2 317 0.50 0.10 2827 100 0.20 3.330 150 0.25