I can run the following code without issue:
DynamicModule[{\[Alpha] = {1, 0}}, {Show[
Graphics[{{Dashed, Circle[], PointSize[0.1]},
Locator[Dynamic[\[Alpha], (\[Alpha] = Normalize[#]) &]]},
ImageSize -> Medium, PlotRange -> 1.2],
ParametricPlot[{r*Cos[t], r*Sin[t]}, {r, 0,
Sqrt[(1 - 0.25)/2]}, {t, 0, 2*\[Pi]}, PlotStyle -> {Red}]]}]
But when I introduce a dynamic to the upper limit of the radius r of the red disc using:
DynamicModule[{\[Alpha] = {1, 0}}, {Show[
Graphics[{{Dashed, Circle[], PointSize[0.1]},
Locator[Dynamic[\[Alpha], (\[Alpha] = Normalize[#]) &]]},
ImageSize -> Medium, PlotRange -> 1.2],
ParametricPlot[{r*Cos[t], r*Sin[t]}, {r, 0,
Sqrt[(1 - Dynamic[\[Alpha][[1]]])/2]}, {t, 0, 2*\[Pi]},
PlotStyle -> {Red}]]}]
I get the error:
ParametricPlot::plln: "Limiting value \!\(\*FractionBox[SqrtBox[RowBox[{\"1\", \"-\", DynamicBox[ToBoxes[Part[\$38748, 1], StandardForm],ImageSizeCache->{7., {0., 8.}}]}]], SqrtBox[\"2\"]]\) in \!\({r, 0, \*SqrtBox[FractionBox[RowBox[{\"1\", \"-\", DynamicBox[ToBoxes[Part[\$38748, 1], StandardForm],ImageSizeCache->{7., {0., 8.}}]}], \"2\"]]}\) is not a machine-sized real number. "
What is going on here? Can anyone help me sort out a dynamic as a limit in a Parametric Plot without plln error?
Any help much appreciated. Thanks.
