Plot3D[] problems

Question

I have a function with x and y variables. When I'm trying to Plot3D[] it, some kind of hole appears on the surface. However, the surface is continious, I can show it with a simple Plot[].

Image of the problem:

Mathematica code:

Clear[f, x, y]
f := (72.2131829904166*Sin[1.9*ArcTan[10.71*x]])/
   Sqrt[1 + 1255.9935999999998*y^2] + 
  Cos[1.081*
     ArcTan[ArcTan[(6.461*(0.009 + x))/
        Sqrt[1 + 17.606416*(0.015 + y)^2]]]]*
   Sec[1.081*
     ArcTan[ArcTan[
       0.058149/
        Sqrt[1 + 17.606416*(0.015 + y)^2]]]]*(104.0077987898286 - 
     1362.512886611634*
      Sin[1.193*
        ArcTan[17.690631066239558*(0.003 + y) + 
          1.4727273456333767*(0.003 + 1.*y - 
             0.056527095967106554*
              ArcTan[0.053071893198718675 + 
                17.690631066239558*y])*(12.048192771084336 + 
             1.*Sign[0.003 + y])]])
Plot3D[f, {x, -1, 1}, {y, -2, 2}]
x := 0
Plot[f, {y, -1, 1}]

Any suggestions to solve this problem?

Answer 1

The problem appears to be caused by the default setting for Exclusions. Normally this is used to exclude singularities and the like, but the exclusion that Plot3D computes is spurious for your case.

Plot3D[f, {x, -1, 1}, {y, -2, 2}, Exclusions -> None]

The quality is not great, so I would also suggest increasing the number of plot points:

Plot3D[f, {x, -1, 1}, {y, -2, 2}, Exclusions -> None, PlotPoints -> 100]