Compare this
points = {{0, -0.5472612856615164`}, {1, -2.5034530266845003`}, {2, -1.8872659003939827`},
{3, -1.1793732412661466`}, {4, -3.068235490752336`}, {5, 3.4990177037576604`},
{6, -1.7312121463142187`}, {7, -1.6648538152327106`}, {8, -2.373301294370746`},
{9, 3.900761915519949`}, {10, -2.134289137239122`}};
Graphics[{BezierCurve[points, SplineDegree -> 6], Red, Point[points]}, Axes -> True]
with this
Graphics[{BezierCurve[points], SplineDegree -> 6, Red, Point[points]}, Axes -> True]
with this
Graphics[{BezierCurve[points], Red, Point[points]}, Axes -> True]
Those points were nothing special, I just made them up with RandomReal[{-4,4}], but included them here so that we would have a very concrete specific example to look at.
From that it appears thatif Graphics is given the SplineDegree option it silently ignores it, while if BezierCurve is given that option it does result in a different curve.
Does this solve your problem?
