Circular Plot and Circular Histogram

Question

The spherical or circular data arises when we measure data in degree e.g wind direction, clock and compass etc. Then representation of such data we need to plot circular plot, circular histogram and rose diagram. How to plot this data? for example we have data

data={8,9,13,13,14,18,22,27,30,34,38,38,40,44,45,47,48,48,48,48,50,53,56,57,58,58,61,63,
64,64,64,65,65,68,70,73,78,78,78,83,83,88,88,88,90,92,92,93,95,96,98,100,103,106,113,118,138,
153,153,155,204,215,223,226,237,238,243,244,250,251,257,268,285,319,343,350}

These are the 76 directions measured in degree clockwise from north. The specimen of circular plot, circular histogram and rose diagram are given below

Circular Plot (data given above)

Circular Histogram (not above data)

Rose Diagram (not above data)

Note: Any appropriate interval is to be taken for circular histogram from the given data.

Answer 1

The function f takes as arguments the raw, unbinned data, the number of sectors, and a boolean parameter to indicate whether polar gridlines are to be drawn.

data = {8, 9, 13, 13, 14, 18, 22, 27, 30, 34, 38, 38, 40, 44, 45, 47, 48, 48, 48, 48, 50, 53, 56, 57, 58, 58, 61, 63, 64, 64, 64, 65, 65, 68, 70, 73, 78, 78, 78, 83, 83, 88, 88, 88, 90, 92, 92, 93, 95, 96, 98, 100, 103, 106, 113, 118, 138, 153, 153, 155, 204, 215, 223, 226,237, 238, 243, 244, 250, 251, 257, 268, 285, 319, 343, 350}

f[dat_,nSectors_,polarGridLinesQ_]:=Module[{binwidth=360/nSectors},
SectorChart[Thread[{ConstantArray[1,360/binwidth],BinCounts[data,binwidth]}],
PolarAxes->If[polarGridLinesQ,{True,True},{False,True}],
PolarTicks->{If[polarGridLinesQ,"Degrees",None],Automatic},
PolarGridLines->If[polarGridLinesQ,{Table[2Pi k/nSectors+Pi/4,{k,1,nSectors}],Automatic},{None,None}],
SectorOrigin->{Pi/2,"Clockwise"}]]

---

With 5 sectors

GraphicsGrid[{{f[data, 5, True], f[data, 5, False]}}, ImageSize -> Large]

---

With 25 sectors

GraphicsGrid[{{f[data, 25, True], f[data, 25, False]}}, ImageSize -> Large]

Answer 2

Here's my contribution for the first type of chart:

bins = Tally @ Ceiling[data, 5];

labelfn = Text[HoldForm[# °], 8 {Sin[# °], Cos[# °]}] &;

ptfn = Rotate[Point @ Thread @ {10 + Range@#2, 0}, Pi/2 - # °, {0, 0}] &;

linefn = Rotate[Line[{{9.5, 0}, {10, 0}}], Pi/2 - # °, {0, 0}] &;

Graphics[{
  Circle[{0, 0}, 10],
  labelfn /@ {0, 90, 180, 270},
  linefn /@ Range[0, 355, 5],
  PointSize[0.02],
  ptfn @@@ bins
}]

Sizes are hard-coded which is never the best, but it's a start.

I don't have HistogramList is v7 so I used Tally for brevity.

Kuba's V9 edit:

bins = {MovingAverage[#, 2], #2} & @@ HistogramList[data, {0, 360, 3.1}] // Transpose;
ptfn = Rotate[Point@Thread@{10 + Range@#2, 0}, Pi/2 - # °, {0, 0}] &;

linefn = Rotate[Line[{{9.5, 0}, {10, 0}}], Pi/2 - # °, {0, 0}] &;

Graphics[{Circle[{0, 0}, 10], 
          labelfn /@ {0, 90, 180, 270}, 
          linefn /@ Range[0, 355, 10], 
          PointSize[0.02], ptfn @@@ bins
        }]

Answer 3

Here's my take at replicating your circular plot. To get the ticks right isn't as easy as one might think, there is no option to put the ticks on the inside of the circle. The ticks will have to be produced manually...

CircularDotHistogram[data_, n_, clockwise_: True] := 
 Module[{hist, pts, deg2rad, angdata},
  hist = HistogramList[data, n][[2]];
  deg2rad[deg_, clock_] := 
   If[clock, (5/2) Pi - (2 Pi/n) deg, (2 Pi/n) deg];
  pts[maxval_, {degree_}] := {deg2rad[ degree, True], 10 + #} & /@ 
    Range[maxval];
  angdata = MapIndexed[pts, hist];
  ListPolarPlot[angdata,
   PlotMarkers -> Graphics[{Black, PointSize[Large], Point[{0, 0}]}],
   Axes -> False,
   PolarTicks -> None,
   PolarAxes -> {True, False},
   PolarGridLines -> False,
   PolarAxesOrigin -> {Pi, 10}
   ]
  ]
CircularDotHistogram[data, 72, True]