InterpolatePoints

procedure InterpolatePoints(const points: TPathD; tension: integer = 0): TPathD;

Performs Hermite Interpolation on a series of points that are horizontally equidistant.

The tension parameter indicates the relative weighting toward horizontality around individual points with -1 indicating less tension (less horizontal) and +1 indicating more.

uses Img32, Img32.Fmt.PNG, Img32.Draw, Img32.Extra;
...
var
  i: integer;
  img: TImage32;
  points, path: TPathD;
begin
  points := MakePathD([10,100, 60,50, 110,50, 160,10, 210,100]);
  path := InterpolatePoints(points, 0);

  img := TImage32.Create(220,320);
  DrawLine(img, path, 3, clBlue32, esSquare);
  for i := 0 to High(points) do
    DrawPoint(img, points[i], 3, clRed32);
  img.SaveToFile('interpolate.png');
  img.Free;