plotting - Where is the other half of my fourth degree Bézier curve?

Bug introduced in 10.0.0 and fixed in 10.2

When I enter the following command, half of the fourth-degree spline is missing from the graph (i.e. it doesn't touch the last point). Is this a bug in Mathematica or am I fundamentally misunderstanding something about Bézier curves?

Manipulate[

 Graphics[{BezierCurve[pts, SplineDegree -> 4], Dashed, Green, 
 Line[pts]}, PlotRange -> {{-.5, 1.5}, {-.5, 1.5}}, 
 Frame -> True], {{pts, {{0, 0}, {.5, 0}, {.5, .5}, {1, .5}, {1, 
 1}}}, Locator, LocatorAutoCreate -> True}]

Here's a screenshot of the output:

What makes me suspicious is that the same behavior shows up in Mathematica's own help file on BezierCurve.

Answer

Since there is really something wrong with the BezierCurve, I made this work-around:

Clear[bezierCurve];

bezierCurve[pts_] := 
 First@ParametricPlot[
   BezierFunction[pts, SplineDegree -> Length[pts] - 1][t], {t, 0, 1}]

Manipulate[
 Graphics[{bezierCurve[pts], Dashed, Green, Line[pts]}, 
  PlotRange -> {{-.5, 1.5}, {-.5, 1.5}}, 
  Frame -> True], {{pts, {{0, 0}, {.5, 0}, {.5, .5}, {1, .5}, {1, 

     1}}}, Locator, LocatorAutoCreate -> True}]

Since the spline degree is always one less than the length of the point list, I didn't adhere to the built-in syntax where the degree is specified separately through an option. I just let the function bezierCurve compute the appropriate degree automatically, to reduce the potential for error.

Comments

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