Getting a graph from data

The following 5 lines illustrate how one can get from some data points a function. The reconstruction is here perfect. We plot the function we got from the data:

R:=2Random[]-1;data=Table[u=R;v=R;{u,v,u^2+v^2+u*v/2},{1000}];
f=Chop[Fit[data,{1,x,x^2,y,y^2,x*y},{x,y}]];
point[X_]:={Hue[Random[]],Sphere[X,0.04]};
S1=Graphics3D[Map[point,data],AspectRatio->1];
S2=Plot3D[f,{x,-1,1},{y,-1,1},Mesh->False];   Show[{S1,S2}]

Originally, I was wondering to reconstruct the function from worksheet 1 (the function was not given). So, I entered some data points and got back a function:

yy=0;  A00={{0.2 ,yy,3  },{0.65,yy,2.5},{1.4,yy,2.0},{5.1,yy,1.5},{5.65,yy,1.0}};
yy=0.5;A05={{0.3 ,yy,3  },{0.8 ,yy,2.5},{1.4,yy,2.0},{5.5,yy,1.5},{5.9, yy,1.0}}; 
yy=1.0;A10={{0.38,yy,3  },{0.95,yy,2.5},{5.3,yy,2.0},{5.5,yy,1.5},{5.8, yy,1.0}}; 
yy=1.5;A15={{0.4 ,yy,3  },{1.1 ,yy,2.5},{2.8,yy,2.5},{4.9,yy,2.5},{5.6, yy,2.0}}; 
yy=2.0;A20={{0.4 ,yy,3  },{1.2 ,yy,2.5},{2.5,yy,2.5},{5.3,yy,2.5},{5.8, yy,2.0}}; 
yy=2.5;A25={{0.35,yy,3  },{1.15,yy,2.5},{2.3,yy,2.5},{4.3,yy,3.0},{5.6, yy,2.5}}; 
yy=3.0;A30={{0.25,yy,3  },{0.95,yy,2.5},{2.3,yy,2.5},{3.3,yy,3.0},{4.95,yy,3.0},{5.7 ,yy,2.5}}; 
yy=3.5;A35={{0.25,yy,3  },{0.95,yy,2.5},{2.3,yy,2.5},{3.3,yy,3.0},{4.95,yy,3.0},{5.7 ,yy,2.5}}; 
yy=4.0;A40={{-0.1,yy,3  },{0.40,yy,2.5},{2.7,yy,2.5},{3.8,yy,3.0},{5.20,yy,3.0},{5.8 ,yy,2.5}}; 
yy=4.5;A45={{0.15,yy,3  },{1.0 ,yy,2.5},{2.7,yy,2.5},{4.1,yy,3.0},{5.20,yy,3.0},{5.9 ,yy,2.5}}; 
yy=5.0;A50={              {0.4 ,yy,2.0},{2.3,yy,2.0},{2.9,yy,2.5},{4.10,yy,3.0},{5.2 ,yy,3.0}}; 
yy=5.5;A55={              {0   ,yy,2.0},{2.7,yy,2.0},{3.6,yy,2.5},{5.80,yy,2.5}}; 
yy=6.0;A60={              {0.1 ,yy,2.5},{2.9,yy,2.5},{3.2,yy,2.0},{4.00,yy,2.5},{5.6 ,yy,2.4}}; 
f = Fit[Union[A00, A05, A10, A15, A20, A25, A30, A35, A40, A45, A50, 
    A55, A60], {1, x, y, x^2, y^2, x*y, x*y^2, x^2*y, x^2*y^2, x^3, y^3, x^3 y, x y^3}, {x, y}];
S=ContourPlot[f, {x, 0, 6}, {y, 0, 6}, Contours -> {1, 1.5, 2, 2.5, 3, 3.5},ColorFunction->Hue]

Here is the result:

It makes a cameo also in this video

Math 21a: section knill Fall 2022

21a Fall 2022

Getting a graph from data