First Semester in Numerical Analysis with Julia, 2020a

CHAPTER 3. INTERPOLATION 137
Then for each point she eyeballs the x and y-coordinates with the help of a graph
paper. The results are displayed in the table below.
t 1 2 3 4 5 6 7 8
x 0 0 -0.05 0.1 0.4 0.65 0.7 0.76
y 0 1.25 2.5 1 0.3 0.9 1.5 0
The next step is to fit a cubic spline to the data (t 1 ,x 1 ), ..., (t 8 ,x 8 ), and another
cubic spline to the data (t 1 ,y 1 ), ..., (t 8 ,y 8 ). Let’s call these splines xspline(t), yspline(t),
respectively, since they represent the x and y-coordinates as functions of the parameter t.
Plotting xspline(t), yspline(t) will produce the letter NUH, as we can see in the following
Julia codes.
First, load the PyPlot package, and copy and evaluate the functions CubicNatural
and CubicNaturalEval that we discussed earlier. Here is the letter NUH, obtained by
spline interpolation:
In [4]: t=[1,2,3,4,5,6,7,8]
x=[0,0,-0.05,0.1,0.4,0.65,0.7,0.76]
y=[0,1.25,2.5,1,0.3,0.9,1.5,0]
taxis=1:1/100:8
CubicNatural(t,x)
xspline=map(z->CubicNaturalEval(z,t),taxis)
CubicNatural(t,y)
yspline=map(z->CubicNaturalEval(z,t),taxis)
plot(xspline,yspline,linewidth=5);