Arctan Binning, from Plot to Histogram, the tricks?

You could use the ChartElementFunction option to position the sectors accurately. The first argument of ChartElementFunction is of the form {{angleMin, angleMax}, {rMin,rMax}} The first sector has bounds {angleMin, angleMax} = {-Pi/12, Pi/12} the second one {Pi/12, 3 Pi/12} etc. Therefore, to get the right rotation you could do something like.

You could use the ChartElementFunction option to position the sectors accurately. The first argument of ChartElementFunction is of the form {{angleMin, angleMax}, {rMin,rMax}}. The first sector has bounds {angleMin, angleMax} = {-Pi/12, Pi/12}, the second one {Pi/12, 3 Pi/12}, etc.Therefore, to get the right rotation you could do something like Module{Countz, maxScale, angleDivisions, dAng}, maxScale = 4; angleDivisions = 12; dAng = (2 \Pi)/angleDivisions; Countz = BinCounts Flatten@MapArcTan @@ (# - ScreenCenter) &, list, {1}, {-Pi, Pi, dAng}; SectorChart{ConstantArray1, LengthCountz, Countz}\Transpose, SectorOrigin -> {-\Pi/angleDivisions, "Counterclockwise"}, PolarAxes -> True, PolarGridLines -> Automatic, PolarTicks -> {Table{i \Degree + \Pi/angleDivisions, I \Degree}, {i, 0, 345, 30}, Automatic}, ChartStyle -> {DirectiveEdgeForm{Black, Thickness0.005}, Red}, BaseStyle -> {FontFamily -> "Arial", FontWeight -> Bold, FontSize -> 12}, ImageSize -> 400, ChartElementFunction -> Function{range}, Disk{0, 0}, range2, 2, - 11 Pi/12 + range1.

The moment I thought I was good I com back and see your solution and belisarius comments, thank you I did not even paid attention to the bar location this is so neat. – 500 Sep 17 at 21:20.

Just checking right now, but your first plot seems flawed: list = {{21, 16}, {16, 14}, {11, 11}, {11, 12}, {13, 15}, {18, 17}, {19, 11}, {17, 16}, {16, 19}}; ScreenCenter = {20, 15}; ShowListPlotlist, PlotStyle -> DirectivePointSizeMedium, Purple, Graphics {Red, PointSizeLarge, PointScreenCenter, CircleScreenCenter, 10}, AspectRatio -> 1, Axes -> False ListPolarPlot{ArcTanSequence @@ ##, Norm##} &/@ (#-ScreenCenter & /@ list), PolarAxes -> True, PolarGridLines -> Automatic, Joined -> False, PolarTicks -> {"Degrees", Automatic}, BaseStyle -> {FontFamily -> "Arial", FontWeight -> Bold, FontSize -> 12}, PlotStyle -> {Red, PointSize -> 0.02} Edit I did not followed all your code, but a reflection on the Screen Center seems to fix the thing: Module{Countz, maxScale, angleDivisions, dAng}, Countz = BinCounts {ArcTanSequence @@ ##} & /@ (# + ScreenCenter & /@ -list), {-Pi, Pi, Pi/6}; maxScale = 4; angleDivisions = 12; dAng = (2 Pi)/angleDivisions; SectorChart{ConstantArray1, LengthCountz, Countz}\Transpose, SectorOrigin -> {-Pi/angleDivisions, "Counterclockwise"}, PolarAxes -> True, PolarGridLines -> Automatic, PolarTicks -> {Table{i \Degree + Pi/angleDivisions, I \Degree}, {i, 0, 345, 30}, Automatic}, ChartStyle -> {DirectiveEdgeForm{Black, Thickness0.005}, Red}, BaseStyle -> {FontFamily -> "Arial", FontWeight -> Bold, FontSize -> 12}, ImageSize -> 400 Edit Here you may see the small misalignment in my code, that is solved in Heike's answer (vote for it! ) ShowModule{Countz, maxScale, angleDivisions, dAng}, Countz = BinCounts{ArcTan Sequence @@ ##} & /@ (# + ScreenCenter & /@ -list), {-\Pi, \Pi, \Pi/6}; maxScale = 4; angleDivisions = 12; dAng = (2 \Pi)/angleDivisions; SectorChart{ConstantArray1, LengthCountz, Countz}\Transpose, SectorOrigin -> {-\Pi/angleDivisions, "Counterclockwise"}, PolarAxes -> True, PolarGridLines -> Automatic, PolarTicks -> {Table{i \Degree + \Pi/angleDivisions, I \Degree}, {i, 0, 345, 30}, Automatic}, ChartStyle -> {DirectiveEdgeForm{Black, Thickness0.005}, Red}, BaseStyle -> {FontFamily -> "Arial", FontWeight -> Bold, FontSize -> 12}, ImageSize -> 400, ListPlotPlus# - ScreenCenter & /@ list/2.5, PlotMarkers -> ImageCrossMatrix10, ImageSize -> 10 .

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