Wolfram Technology Guide: Automated Computational Aesthetics  previous | next 
Asymptote Rendering
Mathematica can identify arbitrary jumps and singularities in curves and surfaces.
In[1]:=

Click for copyable input
Plot[Tan[x], {x, 0, 20}, Exclusions -> Cos[x] == 0, 

 ExclusionsStyle -> Directive[Red, Dashed]]
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In[2]:=

Click for copyable input
Plot3D[1/(y^2 - x^3 + 3 x - 3), {x, -3, 3}, {y, -3, 3}, 

 Exclusions -> y^2 - x^3 + 3 x - 3 == 0, MaxRecursion -> 3, 

 Mesh -> None]
Out[2]=