Example (Using InputForm[ ])
Example (Using InputForm[ ])
In[114]:=
g={{1,2},{2,3},{3,6},{4,12}}
Out[114]=
{{1, 2}, {2, 3}, {3, 6}, {4, 12}}
In[115]:=
fitg=SplineFit[g,Cubic]
Out[115]=
SplineFunction[Cubic,{0., 3.},<>]
In[116]:=
plot1=ParametricPlot[fitg[x],{x,0,3},PlotRange->All,
Compiled->False];
In[117]:=
InputForm[fitg]
Out[117]=
SplineFunction[Cubic, {0., 3.},
{{1, 2}, {2, 3}, {3, 6}, {4, 12}},
{{{1, 1, 0, 0}, {2, 2/3, 0, 1/3}},
{{2, 1, 0, 0}, {3, 5/3, 1, 1/3}},
{{3, 1, 0, 0}, {6, 14/3, 2, -2/3}}}]
Notice how the coefficients and variables (x-h)/a work.
The form is {{h, a, 0, 0}, {c0, c1, c2, c3}}
c0+c1((x-h)/a)+c2((x-h)/a)^2+c3((x-h)/a)^3.
For example, {{2, 1, 0, 0}, {3, 5/3, 1, 1/3}} means that the cubic between x=2
ands x=3 is
3+5/3 ((x-2)/1) + 1((x-2)/1)^2 + 1/3 ((x-2)/1)^3.
In[118]:=
g1[x_]:=2+2/3 (x-1)+1/3 (x-1)^3
g2[x_]:=3+5/3 (x-2)+(x-2)^2+1/3 (x-2)^2
g3[x_]:=6+14/3 (x-3)+2 (x-3)^2-2/3 (x-3)^3
In[119]:=
gspl[x_]:=If[x<=2,g1[x],
If[x<=3,g2[x],
If[x<=4,g3[x]]
]
]
In[120]:=
plot2=Plot[gspl[x],{x,1,4}];
In[121]:=
Show[plot1,plot2];
