Unexpected behavior of BSplineFunction and BezierFunction

Question

$Version
ParametricPlot[BezierFunction[RandomInteger[100,{3,2}]][t],{t,0,1}]

10.4.1 for Microsoft Windows (64-bit) (April 17, 2016)

Crazy result.But the documentation have not any specification for this.And the BezierFunction and BSplineFunction have a same behavior in my PC.

And when I input like this

temp = RandomInteger[100, {3, 2}];
ParametricPlot[BezierFunction[temp][t], {t, 0, 1}]

We'll get the right answer.If anybody can confirm this.I'll add a bug for this post and give a support to wolfram.

You say BSplineFunction[] in the title, but BezierFunction[] in the body. Which one do you actually want? — J. M.'s missing motivation, Apr 24 '16 at 05:38
try ParametricPlot[ Evaluate@BezierFunction[RandomInteger[100, {3, 2}]][t], {t, 0, 1}]? — kglr, Apr 24 '16 at 05:41
... or ParametricPlot[ BezierFunction[RandomInteger[100, {3, 2}]][t], {t, 0, 1}, Evaluated -> True] — kglr, Apr 24 '16 at 05:42
@kglr Thanks your solution.Maybe the culprit is the attribution names HoldAll of ParametricPlot.Can you make that as an answer? — yode, Apr 24 '16 at 05:47

kglr · Accepted Answer · 2016-04-24T06:31:22.110

What is happening: For every value of t that is sampled a new triple of Randominteger pairs is generated and a new BezierFunction is constructed. So every t that is sampled is processed with a different function. This can be seen using Trace on a simpler version of the problem.

Trace[ParametricPlot[BezierFunction[RandomInteger[100, {3, 2}]][t], {t, 0, 1}, 
  PlotPoints ->3, MaxRecursion -> 0,  AspectRatio -> 1], BezierFunction| RandomInteger]

Solution: Evaluateing the first argument of ParametricPlot or using the option Evaluated->True gives the expected output.

ParametricPlot[Evaluate@BezierFunction[RandomInteger[100, {3, 2}]][t], {t, 0, 1}, 
 AspectRatio -> 1]

Mathematica graphics

ParametricPlot[BezierFunction[RandomInteger[100, {3, 2}]][t], {t, 0, 1}, 
 Evaluated -> True, AspectRatio -> 1]

Mathematica graphics

Unexpected behavior of BSplineFunction and BezierFunction

1 Answers1