# Radial PolarTicks skewed when aspect ratio is not 1

In the following plots, the radial axis phi == 30 Degree has a single tick at r == 1/2. This tick is skewed (i.e. does not cross the radial axis orthogonally) unless the PlotRange is such that the aspect ratio of the plot is 1.

Table[
PolarPlot[1, {phi, 0, Pi/2}
, PolarAxes -> {False, True}
, PolarAxesOrigin -> {30 Degree, 1}
, PlotRange -> {{0, 1}, {0, yMax}}
, PolarTicks -> {{{1/2, "", 0.15}}}
, TicksStyle -> Directive[Thick, Black]
] // {HoldForm["yMax"] == yMax, #} &
, {yMax, {0.3, 0.5, 1, 2, 5}}
] // Transpose // TableForm


Is there a workaround (other than drawing the ticks manually with primitives)?

Update: A post-processing function that works more generally:

ClearAll[fixPolarTicks]
fixPolarTicks[offset_: 15][g_] :=
Module[{aspectr = (AspectRatio /. Options[g, AspectRatio]),
pr = (PlotRange /. Options[g, PlotRange]) /. {{All, All}, {All, All}} ->
RegionBounds[Quiet@DiscretizeGraphics[g]], xylengths, oo},
xylengths = -Subtract @@@ pr;
aspectr = aspectr /. Automatic -> Ratios[xylengths][[1]];
oo = offset Normalize[# {1, 1/ aspectr}  xylengths]/Norm[xylengths] &;
ReplaceAll[g, {tl : (_Line | _Text) :>
(tl /. {Offset[o_, Scaled[a_, b_]] :> Offset[o + oo[a], b],
Scaled[a_, b_] :> Offset[oo[a], b]})}]];


Examples:

arlist = {Automatic, .3, 1., 3};

grid = Labeled[Grid[Prepend[Prepend[""]@Table[ar, {ar, arlist}]]@
Table[Prepend[ymax]@
Table[PolarPlot[1, {phi, 0, Pi/2}, PolarAxes -> {False, True},
PlotRange -> If[ymax === Automatic, Automatic, {{0, 1}, {0, ymax}}],
AspectRatio -> ar, PolarAxesOrigin -> {30 Degree, 1},
PolarTicks -> {Thread[{Subdivide[4], 1. Subdivide[4], .15}]},
TicksStyle -> Directive[Thick, Black]],
{ar, arlist}], {ymax, arlist}] , Dividers -> All],
Style[#, 20] & /@ {"aspect ratio", Rotate[ "ymax", 90 Degree]},
{Top, Left}]


grid /. g_Graphics :> fixPolarTicks[][g]


Row[{pp = PolarPlot[1/Sqrt[t], {t, .1, 30}, PolarAxes -> {False, True},
PolarAxesOrigin -> {125 Degree, 2},
PolarTicks -> {Thread[{Subdivide[0, 2, 4], 1. Subdivide[0, 2, 4], .1}]},
ImageSize -> Medium],
fixPolarTicks[45] @ pp}]


Row[{pp2 = Show[pp, AspectRatio -> 3, PlotRange -> {{-2, 1}, {-1, 2}}],
fixPolarTicks[45] @ pp2}, Spacer[10]]


ClearAll[fixTicks]
fixTicks = ReplaceAll[Line[s : {__Scaled}] :>
Line[MapAt[Function[x, x/Normalize[-Subtract @@@ PlotRange[#], Min]],  s,
{All, 1}]]] @ # &;

Table[fixTicks@
PolarPlot[1, {phi, 0, Pi/2}, PolarAxes -> {False, True},
PolarAxesOrigin -> {30 Degree, 1},
PlotRange -> {{0, 1}, {0, yMax}},
PolarTicks -> {{{1/2, "", 0.15}}},
TicksStyle -> Directive[Thick, Black]] // {HoldForm["yMax"] ==
yMax, #} &, {yMax, {0.3, 0.5, 1, 2, 5}}] //
Transpose // TableForm