How to plot contours for a sparse data set?

[Geocentrix]

I am using the TContourPlot to show some data for which I have only 55 data points (data is inclued at the end of this post). On the plot below, I additionally draw small grey circles where my data points are located (i.e on a triangular pattern).

PileGroup.jpg (39.77 KiB) Viewed 803 times

The plot I am expecting to get is as follows:

Expected contours.jpg (50.12 KiB) Viewed 803 times

(I created this in Excel but had to interpolate between the data points, adding an extra point between every four circles)

However, I cannot get TChart to produce any contours for this data set.

Are there any settings within TChart that I can use to produce contours for this set?

Any suggestions would be most welcome!

Andrew

The data I have is as follows:

Code: Select all

Index	X	Y	Z
0	-8	192.4	0
1	8	192.4	0
2	2	195.3	-7
3	2	195.3	7
4	-2	195.3	-7
5	-2	195.3	7
6	-5	197.7	5.25
7	5	197.7	-5.25
8	5	197.7	5.25
9	-5	197.7	-5.25
10	7	200.4	1.75
11	-7	200.4	1.75
12	-7	200.4	-1.75
13	7	200.4	-1.75
14	-6	202.2	-3.5
15	6	202.2	-3.5
16	6	202.2	3.5
17	-6	202.2	3.5
18	-3	209.4	-5.25
19	3	209.4	5.25
20	-3	209.4	5.25
21	3	209.4	-5.25
22	-6	213.1	0
23	6	213.1	0
24	1	215	5.25
25	1	215	-5.25
26	-1	215	5.25
27	-1	215	-5.25
28	4	217.5	-3.5
29	4	217.5	3.5
30	-4	217.5	-3.5
31	-4	217.5	3.5
32	5	218.7	1.75
33	-5	218.7	-1.75
34	-5	218.7	1.75
35	5	218.7	-1.75
36	2	226.5	3.5
37	-2	226.5	-3.5
38	2	226.5	-3.5
39	-2	226.5	3.5
40	4	228.2	0
41	-4	228.2	0
42	0	229.4	3.5
43	0	229.4	-3.5
44	3	230.8	-1.75
45	-3	230.8	-1.75
46	3	230.8	1.75
47	-3	230.8	1.75
48	-1	236.8	1.75
49	1	236.8	1.75
50	1	236.8	-1.75
51	-1	236.8	-1.75
52	2	237.3	0
53	-2	237.3	0
54	0	240.3	0

The data used to produce the plot on Excel is:

Code: Select all

x	y	z
-8	189.6	0
-7	197.5	-1.75
-7	198.65	0
-7	197.5	1.75
-6	199.2	-3.5
-6	205.55	-1.75
-6	210	0
-6	205.55	1.75
-6	199.2	3.5
-5	194.8	-5.25
-5	205.95	-3.5
-5	215.5	-1.75
-5	216.475	0
-5	215.5	1.75
-5	205.95	3.5
-5	194.8	5.25
-4	205.1333333	-5.25
-4	214.3	-3.5
-4	220.525	-1.75
-4	224.9	0
-4	220.525	1.75
-4	214.3	3.5
-4	205.1333333	5.25
-3	206.3	-5.25
-3	217.8	-3.5
-3	227.4	-1.75
-3	228.375	0
-3	227.4	1.75
-3	217.8	3.5
-3	206.3	5.25
-2	192.4	-7
-2	208.45	-5.25
-2	223.2	-3.5
-2	229.45	-1.75
-2	233.8	0
-2	229.45	1.75
-2	223.2	3.5
-2	208.45	5.25
-2	192.4	7
-1	211.9	-5.25
-1	223.625	-3.5
-1	233.4	-1.75
-1	234.35	0
-1	233.4	1.75
-1	223.625	3.5
-1	211.9	5.25
0	216.6	-5.25
0	226	-3.5
0	232.4	-1.75
0	236.8	0
0	232.4	1.75
0	226	3.5
0	216.6	5.25
1	211.9	-5.25
1	223.625	-3.5
1	233.4	-1.75
1	234.35	0
1	233.4	1.75
1	223.625	3.5
1	211.9	5.25
2	192.4	-7
2	208.45	-5.25
2	223.2	-3.5
2	229.45	-1.75
2	233.8	0
2	229.45	1.75
2	223.2	3.5
2	208.45	5.25
2	192.4	7
3	206.3	-5.25
3	217.8	-3.5
3	227.4	-1.75
3	228.375	0
3	227.4	1.75
3	217.8	3.5
3	206.3	5.25
4	205.1333333	-5.25
4	214.3	-3.5
4	220.525	-1.75
4	224.9	0
4	220.525	1.75
4	214.3	3.5
4	205.1333333	5.25
5	194.8	-5.25
5	205.95	-3.5
5	215.5	-1.75
5	216.475	0
5	215.5	1.75
5	205.95	3.5
5	194.8	5.25
6	199.2	-3.5
6	205.55	-1.75
6	210	0
6	205.55	1.75
6	199.2	3.5
7	197.5	-1.75
7	198.65	0
7	197.5	1.75
8	189.6	0

[Yeray]

Hello,

I've been playing with your data and I came up with this:

contour.png (54.29 KiB) Viewed 282 times

I'm not sure if that fits your requirements.
Note the PopulateMissingPoints method helps to make sure the data follows a regular grid structure so the TContourSeries can handle it.
Note there's also a TPointSeries with the raw data I used for testing.

Code: Select all

uses System.Math.Vectors, System.Generics.Collections, System.Generics.Defaults, System.Math,
  Chart, TeEngine, TeeSurfa, Series;

var Chart1: TChart;

function PopulateMissingPoints(const AList: TList<TPoint3D>): TList<TPoint3D>;
var
  XValues, YValues: TList<Double>;
  XYDict: TDictionary<string, Boolean>;
  Point: TPoint3D;
  X, Y: Double;
  Key: string;
begin
  // Initialize collections
  XValues := TList<Double>.Create;
  YValues := TList<Double>.Create;
  XYDict := TDictionary<string, Boolean>.Create;
  Result := TList<TPoint3D>.Create;

  try
    // Collect unique X and Y values
    for Point in AList do
    begin
      if not XValues.Contains(Point.X) then
        XValues.Add(Point.X);
      if not YValues.Contains(Point.Y) then
        YValues.Add(Point.Y);

      // Populate dictionary for existence checks
      Key := Format('%.5f,%.5f', [Point.X, Point.Y]);
      XYDict.AddOrSetValue(Key, True);
    end;

    // Sort coordinates to maintain grid structure
    XValues.Sort;
    YValues.Sort;

    // Generate all possible X-Y combinations
    for X in XValues do
      for Y in YValues do
      begin
        Key := Format('%.5f,%.5f', [X, Y]);
        if not XYDict.ContainsKey(Key) then
          Result.Add(TPoint3D.Create(X, Y, 0));
      end;

    // Add original points and sort the combined list
    Result.AddRange(AList);
    Result.Sort(TComparer<TPoint3D>.Construct(
      function(const A, B: TPoint3D): Integer
      begin
        Result := CompareValue(A.Y, B.Y);
        if Result = 0 then
          Result := CompareValue(A.X, B.X);
      end
    ));
  finally
    XValues.Free;
    YValues.Free;
    XYDict.Free;
  end;
end;

procedure TForm1.FormCreate(Sender: TObject);
var MyPoint   : TPointSeries;
    MyContour : TContourSeries;

    tmpLines   : TStrings;
    tmpFields  : TStrings;
    n          : Integer;
    xx, yy, zz : Double;

    data: TList<TPoint3D>;
const AFileName='D:\Downloads\contour_data.csv';
begin
  FormatSettings.DecimalSeparator:='.';

  Chart1:=TChart.Create(Self);

  with Chart1 do
  begin
    Parent:=Self;
    Align:=alClient;
    Color:=clWhite;
    Gradient.Visible:=False;
    Walls.Hide;
    Legend.Hide;
    View3D:=False;
    Axes.Left.Grid.Hide;
    Axes.Bottom.Grid.Hide;
    Axes.Left.SetMinMax(-8, 8);
    Axes.Bottom.SetMinMax(-18, 18);
    Axes.Bottom.Increment:=2;
  end;

  MyPoint:=TPointSeries(Chart1.AddSeries(TPointSeries));
  MyPoint.Pointer.Size:=2;
  MyPoint.Pointer.Style:=psCircle;
  MyPoint.BeginUpdate;

  MyContour:=TContourSeries(Chart1.AddSeries(TContourSeries));
  with MyContour do
  begin
    IrregularGrid:=True;
    //Filled:=True;
    BeginUpdate;
  end;

  data:=TList<TPoint3D>.Create;
  tmpLines:=TStringList.Create;
  tmpLines.LoadFromFile(AFileName);

  n:=1;
  while n<tmpLines.Count do
  begin
    tmpFields:=TStringList.Create;
    tmpFields.Delimiter:=';';
    tmpFields.DelimitedText:=tmpLines[n];

    xx := StrToFloat(tmpFields[1]);
    zz := StrToFloat(tmpFields[2]);
    yy := StrToFloat(tmpFields[3]);

    data.Add(Point3D(xx, yy, zz));

    Inc(n);
  end;

  for var i:=0 to data.Count-1 do
    MyPoint.AddXY(data[i].X, data[i].Y);

  data:=PopulateMissingPoints(data);

  for var i:=0 to data.Count-1 do
    MyContour.AddXYZ(data[i].X, data[i].Z, data[i].Y);

  MyPoint.EndUpdate;
  MyContour.EndUpdate;

  MyPoint.Visible:=False;
end;