Taking Log Transformation of unit circle using Presentations package

Question

<< Presentations`

circle = ComplexCircle[0.1, 1/2];
domain = Draw2D[{Opacity[0.6], circle},
   Frame -> True,
   Axes -> True,
   PlotRange -> 2,
   FrameLabel -> {Re, Im},
   PlotLabel -> z, ImageSize -> 200];
image = Draw2D[{Opacity[0.6], circle // ComplexMap[Log]},
   Frame -> True,
   Axes -> True,
   PlotRange -> 4,
   FrameLabel -> {Re, Im},
   PlotLabel -> w,
   ImageSize -> 200];
Row[{domain, image}]

The above code works, creating the following image.

However, if I change the center to the origin:

circle = ComplexCircle[0, 1/2];
domain = Draw2D[{Opacity[0.6], circle},
   Frame -> True,
   Axes -> True,
   PlotRange -> 2,
   FrameLabel -> {Re, Im},
   PlotLabel -> z, ImageSize -> 200];
image = Draw2D[{Opacity[0.6], circle // ComplexMap[Log]},
   Frame -> True,
   Axes -> True,
   PlotRange -> 4,
   FrameLabel -> {Re, Im},
   PlotLabel -> w,
   ImageSize -> 200];
Row[{domain, image}]

The code fails, giving the following error message:

Coordinate {DirectedInfinity[-1], 0} should be a pair of numbers, or a Scaled or Offset form.

But this works with center at the origin:

circle = {Red, Thickness[0.02], 
   ComplexCurve[Exp[I t], {t, 0, 2 Pi}]};
domain = Draw2D[{Opacity[0.6], circle},
   Frame -> True,
   Axes -> True,
   PlotRange -> 2,
   FrameLabel -> {Re, Im},
   PlotLabel -> z, ImageSize -> 200];
image = Draw2D[{Opacity[0.6], circle // ComplexMap[Log]},
   Frame -> True,
   Axes -> True,
   PlotRange -> 4,
   FrameLabel -> {Re, Im},
   PlotLabel -> w,
   ImageSize -> 200];
Row[{domain, image}]

Producing this image:

What's going on?