Bug introduced in 10.3 or earlier and persisting through 11.1.0 or later
Export
ing the filled Bézier curve to PDF or EPS yields
pts1 = {{3, 0}, {-1, 3}, {1, -5}, {5, -1}, {3, 0}};
test = Graphics[{{EdgeForm[Black], GrayLevel[0.8],
FilledCurve[BezierCurve[pts1, SplineDegree -> 4]]}},
PlotRange -> {{0.6, 3.6}, {-1.8, 1.}}, Frame -> False]
Export["i.pdf", test] // SystemOpen
In the notebook it renders correctly as
The export to EPS and PDF, thought, remains broken. Exporting to raster formats works correctly.
Export
, I get the broken version. $\endgroup$