Answered
Try plotting b(x,y)=(1)/(2) (x+sqrt(x^(2)+4 y)) in 3D graphing mode
There are lots of interesting missing polygons!
(the weird brackets are directly copy-pasted from Geogebra's parsing of what I typed in, which didn't have the brackets)
Files:
geogebra-export...
The same question 
have you tried style--->quality in settings of graph?
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