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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: missing part of fourth-degree Bézier curve


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


screenshot of mathematica's help files 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.


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