Member Avatar for hosamath

Hi friends...
I have a series of points which are actually the points that form a circle... Can anyone help me how to get the circle image when i load these points as input... A simple code example will be helpful...
Thanks in advance....

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  • Latest Post Latest Post by pritaeas

Dani AI

Generated

— short practical plan, and a small Delphi implementation you can drop into your project.

If your points are unordered, simply connecting them will usually give a messy polygon (as hinted). Two practical choices:

  • If you want the sampled shape drawn exactly: sort points by polar angle around their centroid (use ArcTan2) and draw the polyline or a closed spline.
  • If you want the underlying circle (center + radius): compute a least‑squares circle fit and draw that circle.

The code below implements a robust algebraic least‑squares fit (Kasa style) in Delphi: it returns center (CX,CY) and radius R. It uses double precision and subtracts the centroid for better numeric stability.

type
  TMat3 = array[0..2,0..2] of Double;
  TVec3 = array[0..2] of Double;

function Solve3x3(const M: TMat3; const B: TVec3; out X: TVec3): Boolean;
var
  a: TMat3; b: TVec3; i,j,k,maxi: Integer;
  maxv,factor,tmp: Double;
begin
  a := M; b := B;
  for i := 0 to 2 do
  begin
    maxi := i; maxv := Abs(a[i,i]);
    for j := i+1 to 2 do if Abs(a[j,i]) > maxv then begin maxi := j; maxv := Abs(a[j,i]); end;
    if maxv < 1e-12 then Exit(False);
    if maxi <> i then
    begin
      for k := i to 2 do begin tmp := a[i,k]; a[i,k] := a[maxi,k]; a[maxi,k] := tmp; end;
      tmp := b[i]; b[i] := b[maxi]; b[maxi] := tmp;
    end;
    for j := i+1 to 2 do
    begin
      factor := a[j,i] / a[i,i];
      for k := i to 2 do a[j,k] := a[j,k] - factor * a[i,k];
      b[j] := b[j] - factor * b[i];
    end;
  end;
  for i := 2 downto 0 do
  begin
    if Abs(a[i,i]) < 1e-12 then Exit(False);
    X[i] := b[i];
    for j := i+1 to 2 do X[i] := X[i] - a[i,j] * X[j];
    X[i] := X[i] / a[i,i];
  end;
  Result := True;
end;

function FitCircle(const X, Y: array of Double; out CX, CY, R: Double): Boolean;
var
  n,i: Integer; meanX,meanY,xi,yi,zi: Double;
  Sx,Sy,Sz,Sxx,Sxy,Syy,Sxz,Syz: Double;
  M: TMat3; B,Sol: TVec3; cxs,cys,r2: Double;
begin
  n := Length(X); if (n <> Length(Y)) or (n < 3) then Exit(False);
  meanX := 0; meanY := 0; for i := 0 to n-1 do begin meanX := meanX + X[i]; meanY := meanY + Y[i]; end;
  meanX := meanX / n; meanY := meanY / n;
  Sx := 0; Sy := 0; Sz := 0; Sxx := 0; Sxy := 0; Syy := 0; Sxz := 0; Syz := 0;
  for i := 0 to n-1 do begin
    xi := X[i] - meanX; yi := Y[i] - meanY; zi := xi*xi + yi*yi;
    Sx := Sx + xi; Sy := Sy + yi; Sz := Sz + zi;
    Sxx := Sxx + xi*xi; Sxy := Sxy + xi*yi; Syy := Syy + yi*yi;
    Sxz := Sxz + xi*zi; Syz := Syz + yi*zi;
  end;
  M[0,0]:=Sxx; M[0,1]:=Sxy; M[0,2]:=Sx;
  M[1,0]:=Sxy; M[1,1]:=Syy; M[1,2]:=Sy;
  M[2,0]:=Sx;  M[2,1]:=Sy;  M[2,2]:=n;
  B[0]:=-Sxz; B[1]:=-Syz; B[2]:=-Sz;
  if not Solve3x3(M,B,Sol) then Exit(False);
  cxs := -Sol[0]/2; cys := -Sol[1]/2; r2 := cxs*cxs + cys*cys - Sol[2];
  if (r2 < 0) and (r2 > -1e-9) then r2 := 0;
  if r2 < 0 then Exit(False);
  CX := cxs + meanX; CY := cys + meanY; R := Sqrt(r2);
  Result := True;
end;

Use: call FitCircle with arrays of X/Y; on success draw with Canvas.Ellipse(Round(CX-R),Round(CY-R),Round(CX+R),Round(CY+R)). Troubleshooting: need >=3 non‑colinear points; if fitting fails it usually means degenerate input or strong outliers — filter bad samples or use RANSAC for robustness. Sorting by angle (ArcTan2) fixes unordered samples when you just want to connect the points.

Recommended Answers

All 8 Replies

Member Avatar for pritaeas

Do you just want to draw all points that you have ? Connect them by a line ? Or determine the actual circle ?

Member Avatar for hosamath

Actually am expecting that only...That would be great if u get me..When the points are connected it may not be a circle but some random closed figure...

Member Avatar for pritaeas

TCanvas has several drawing options, like MoveTo() and LineTo() that you can use.

Member Avatar for hosamath

Is there any example program of similar kind so that i get to know how to use Tcanvas or TBitmap etc....

Member Avatar for hosamath

Thank You very much... I appreciate your help ... It has been very helpful at this moment..

Member Avatar for hosamath

hey can you send me command that will display the co-ordinate points on the Tcanvas...

Member Avatar for pritaeas

Form.Canvas.Pixels

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