http://stackoverflow.com/questions/17641308

// data point it TRectF
// all y values are >= 0
// http://stackoverflow.com/questions/17641308

// very generic framework - suboptimal in many many senses.
// in other words - no "premature optimization" :-)

// and not testing - just drafting

type
  PropagationConfig = record
     x_delta, y_delta: single;
     poly_coeff: array of single; // p[0]*x^0 + p[1]*x^2 + p[2]*x^4 + ...
  end;
// the programmer should fill those values to his tastes of what is beautiful or purposeful

  function EnrichData(const Input: any stream of TRectF): same as input stream of TRectF;
  begin
     for every pair of data points in Input
     do emit into Result ( EnrichPair( datapoint 1, datapoint 2, propagation config ) );
  end;

 function EnrichPair( dp1, dp2: TRectF; const config: propagationconfig): array of TRectF;
 var tempDP: TRectF;
 begin
    if dp1.x = dp2.x then begin
       SetLength(Result,1);
       Result[0].x := dp1.x;
       Result[0].y := Max(dp1.y, dp2.y);
       Exit;
    end;

    if dp1.x > dp2.x then begin
       tempDP := dp1; dp1 := dp2; dp2 := tempDP;
    end;

    if dp2.x - dp1.x <= config.x_delta then begin
       SetLength(Result,2);
       Result[0] := dp1;
       Result[1] := dp2;
       Exit;
    end;

    SetLength(Result, 1 + Ceil(dp2.x - dp1.x) );

    Result[Low(Result)] := dp1; Result[High(Result)] := dp2;

    for i := Low(Result) + 1 to High(Result) - 1 do begin
        Result[i].x  := Result [i-1].x + config.x_delta;
        Result[i].y := 0;
    end;

    for i := Low(Result) + 1 to High(Result) - 1 do begin
        Result[i].y := Estimate(dp1, Result[i].x, config);
        if Result[i].y < config.y_delta then break; // too far from peak - no more traces
    end;

    for i := High(Result) - 1 downto Low(Result) + 1 do begin
        y := Estimate(dp2, Result[i].x, config);
        if Result[i].y > y then break; // adjacent peak has more influence here
        Result[i].y := y;
        if Result[i].y < config.y_delta then break; // too far from peak - no more traces
    end;
 end;

 function Estimate(const peak: TRectF; const place: single; const config: PropagationConfig): single;
 var delta: single; i: integer;
 begin
     delta := abs(place - peak.x);
     if delta = 0 then Exit(peak.y);

     Result := 0;
     for i := Low(config.poly_coeff) to High(config.poly_coeff) do
         Result := Result + config.poly_coeff[i - Low(config.poly_coeff)] *
                         Power(1 + delta , 2 * ( i - Low(config.poly_coeff) ) );

     Result := peak.y / Result; // fall down from peak to the sides
 end;