This works (`SplineDegree->2`) ParametricPlot[BezierFunction[{{0, 0}, {1, 0.5}, {2, 2}}, SplineDegree -> 2][u], {u, 0, 1}] ![BezierFunction SplineDegree 2][1] but this does not (`SplineDegree->1`) ParametricPlot[BezierFunction[{{0, 0}, {1, 0.5}, {2, 2}}, SplineDegree -> 1][u], {u, 0, 1}] (* BezierFunction::invdeg: Value of option SplineDegree -> 1 should be a positive integer, or a list of positive integers *) I found no reference to a possible issue in [the documentation for `BezierFunction`][2]. `SplineDegree->1` works fine with `BSlineFunction` and `BezierCurve`; shouldn't it also work with `BezierFunction`? Mma 8.0.4 Mac OSX [1]: https://i.sstatic.net/8fZhz.png [2]: http://reference.wolfram.com/mathematica/ref/BezierFunction.html