756 lines
17 KiB
ObjectPascal
756 lines
17 KiB
ObjectPascal
unit XForm;
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interface
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const
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NVARS = 23;
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EPS = 1E-10;
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type
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TCalcMethod = procedure of object;
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type
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TCPpoint = record
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x, y, c: double;
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end;
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PCPpoint = ^TCPpoint;
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TXYpoint = record
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x, y: double;
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end;
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PXYpoint = ^TXYpoint;
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type
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TXForm = class
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private
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FNrFunctions: Integer;
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FFunctionList: array[0..NVARS] of TCalcMethod;
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FTx, FTy: double;
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FPx, FPy: double;
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FAngle: double;
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FSinA: double;
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FCosA: double;
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FLength: double;
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CalculateAngle: boolean;
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CalculateLength: boolean;
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CalculateSinCos: boolean;
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procedure Linear; // var[0]
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procedure Sinusoidal; // var[1]
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procedure Spherical; // var[2]
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procedure Swirl; // var[3]
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procedure Horseshoe; // var[4]
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procedure Polar; // var[5]
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procedure FoldedHandkerchief; // var[6]
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procedure Heart; // var[7]
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procedure Disc; // var[8]
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procedure Spiral; // var[9]
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procedure hyperbolic; // var[10]
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procedure Square; // var[11]
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procedure Ex; // var[12]
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procedure Julia; // var[13]
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procedure Bent; // var[14]
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procedure Waves; // var[15]
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procedure Fisheye; // var[16]
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procedure Popcorn; // var[17]
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procedure Exponential; // var[18]
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procedure Power; // var[19]
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procedure Cosine; // var[20]
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procedure Rings; // var[21]
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procedure Fan; // var[22]
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public
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vars: array[0..NVARS - 1] of double; // normalized interp coefs between variations
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c: array[0..2, 0..1] of double; // the coefs to the affine part of the function
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density: double; // prob is this function is chosen. 0 - 1
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color: double; // color coord for this function. 0 - 1
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color2: double; // Second color coord for this function. 0 - 1
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symmetry: double;
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c00, c01, c10, c11, c20, c21: double;
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varType: integer;
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Orientationtype: integer;
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constructor Create;
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procedure Prepare;
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procedure NextPoint(var px, py, pc: double); overload;
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procedure NextPoint(var CPpoint: TCPpoint); overload;
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procedure NextPoint(var px, py, pz, pc: double); overload;
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procedure NextPointXY(var px, py: double);
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procedure NextPoint2C(var px, py, pc1, pc2: double);
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end;
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implementation
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uses
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SysUtils, Math;
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{ TXForm }
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///////////////////////////////////////////////////////////////////////////////
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constructor TXForm.Create;
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var
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i: Integer;
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begin
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density := 0;
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Color := 0;
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Vars[0] := 1;
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for i := 1 to NVARS - 1 do begin
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Vars[i] := 0;
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end;
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c[0, 0] := 1;
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c[0, 1] := 0;
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c[1, 0] := 0;
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c[1, 1] := 1;
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c[2, 0] := 0;
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c[2, 1] := 0;
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Symmetry := 0;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Prepare;
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begin
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c00 := c[0][0];
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c01 := c[0][1];
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c10 := c[1][0];
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c11 := c[1][1];
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c20 := c[2][0];
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c21 := c[2][1];
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FNrFunctions := 0;
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if (vars[0] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Linear;
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Inc(FNrFunctions);
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end;
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if (vars[1] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Sinusoidal;
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Inc(FNrFunctions);
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end;
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if (vars[2] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Spherical;
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Inc(FNrFunctions);
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end;
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if (vars[3] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Swirl;
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Inc(FNrFunctions);
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end;
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if (vars[4] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Horseshoe;
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Inc(FNrFunctions);
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end;
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if (vars[5] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Polar;
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Inc(FNrFunctions);
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end;
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if (vars[6] <> 0.0) then begin
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FFunctionList[FNrFunctions] := FoldedHandkerchief;
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Inc(FNrFunctions);
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end;
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if (vars[7] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Heart;
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Inc(FNrFunctions);
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end;
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if (vars[8] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Disc;
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Inc(FNrFunctions);
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end;
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if (vars[9] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Spiral;
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Inc(FNrFunctions);
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end;
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if (vars[10] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Hyperbolic;
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Inc(FNrFunctions);
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end;
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if (vars[11] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Square;
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Inc(FNrFunctions);
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end;
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if (vars[12] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Ex;
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Inc(FNrFunctions);
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end;
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if (vars[13] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Julia;
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Inc(FNrFunctions);
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end;
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if (vars[14] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Bent;
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Inc(FNrFunctions);
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end;
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if (vars[15] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Waves;
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Inc(FNrFunctions);
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end;
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if (vars[16] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Fisheye;
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Inc(FNrFunctions);
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end;
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if (vars[17] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Popcorn;
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Inc(FNrFunctions);
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end;
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if (vars[18] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Exponential;
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Inc(FNrFunctions);
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end;
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if (vars[19] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Power;
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Inc(FNrFunctions);
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end;
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if (vars[20] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Cosine;
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Inc(FNrFunctions);
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end;
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if (vars[21] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Rings;
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Inc(FNrFunctions);
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end;
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if (vars[22] <> 0.0) then begin
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FFunctionList[FNrFunctions] := Fan;
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Inc(FNrFunctions);
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end;
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CalculateAngle := (vars[5] <> 0.0) or (vars[6] <> 0.0) or (vars[7] <> 0.0) or (vars[8] <> 0.0) or
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(vars[12] <> 0.0) or (vars[13] <> 0.0) or (vars[21] <> 0.0) or (vars[22] <> 0.0);
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CalculateLength := False;
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CalculateSinCos := (vars[4] <> 0.0) or (vars[9] <> 0.0) or (vars[10] <> 0.0) or
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(vars[11] <> 0.0) or (vars[16] <> 0.0) or (vars[19] <> 0.0) or
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(vars[21] <> 0.0);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Linear;
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begin
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FPx := FPx + vars[0] * FTx;
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FPy := FPy + vars[0] * FTy;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Sinusoidal;
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begin
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FPx := FPx + vars[1] * sin(FTx);
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FPy := FPy + vars[1] * sin(FTy);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Spherical;
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var
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r2: double;
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begin
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r2 := FTx * FTx + FTy * FTy + 1E-6;
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FPx := FPx + vars[2] * (FTx / r2);
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FPy := FPy + vars[2] * (FTy / r2);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Swirl;
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var
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c1, c2, r2: double;
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begin
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r2 := FTx * FTx + FTy * FTy;
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c1 := sin(r2);
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c2 := cos(r2);
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FPx := FPx + vars[3] * (c1 * FTx - c2 * FTy);
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FPy := FPy + vars[3] * (c2 * FTx + c1 * FTy);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Horseshoe;
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//var
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// a, c1, c2: double;
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begin
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// if (FTx < -EPS) or (FTx > EPS) or (FTy < -EPS) or (FTy > EPS) then
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// a := arctan2(FTx, FTy)
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// else
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// a := 0.0;
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// c1 := sin(FAngle);
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// c2 := cos(FAngle);
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FPx := FPx + vars[4] * (FSinA * FTx - FCosA * FTy);
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FPy := FPy + vars[4] * (FCosA* FTx + FSinA * FTy);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Polar;
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var
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ny: double;
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begin
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ny := sqrt(FTx * FTx + FTy * FTy) - 1.0;
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FPx := FPx + vars[5] * (FAngle/PI);
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FPy := FPy + vars[5] * ny;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.FoldedHandkerchief;
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var
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r: double;
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begin
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r := sqrt(FTx * FTx + FTy * FTy);
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FPx := FPx + vars[6] * sin(FAngle + r) * r;
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FPy := FPy + vars[6] * cos(FAngle - r) * r;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Heart;
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var
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r: double;
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begin
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r := sqrt(FTx * FTx + FTy * FTy);
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FPx := FPx + vars[7] * sin(FAngle * r) * r;
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FPy := FPy + vars[7] * cos(FAngle * r) * -r;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Disc;
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var
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nx, ny, r: double;
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begin
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nx := FTx * PI;
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ny := FTy * PI;
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r := sqrt(nx * nx + ny * ny);
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FPx := FPx + vars[8] * sin(r) * FAngle / PI;
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FPy := FPy + vars[8] * cos(r) * FAngle / PI;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Spiral;
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var
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r: double;
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begin
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// r := sqrt(FTx * FTx + FTy * FTy) + 1E-6;
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r := Flength + 1E-6;
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FPx := FPx + vars[9] * (FCosA + sin(r)) / r;
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FPy := FPy + vars[9] * (FsinA - cos(r)) / r;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.hyperbolic;
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var
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r: double;
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begin
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// r := sqrt(FTx * FTx + FTy * FTy) + 1E-6;
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r := Flength + 1E-6;
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FPx := FPx + vars[10] * FSinA / r;
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FPy := FPy + vars[10] * FCosA * r;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Square;
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//var
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// r: double;
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begin
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// r := sqrt(FTx * FTx + FTy * FTy);
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FPx := FPx + vars[11] * FSinA * cos(Flength);
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FPy := FPy + vars[11] * FCosA * sin(Flength);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Ex;
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var
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r: double;
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n0,n1, m0, m1: double;
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begin
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r := sqrt(FTx * FTx + FTy * FTy);
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n0 := sin(FAngle + r);
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n1 := cos(FAngle - r);
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m0 := n0 * n0 * n0 * r;
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m1 := n1 * n1 * n1 * r;
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FPx := FPx + vars[12] * (m0 + m1);
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FPy := FPy + vars[12] * (m0 - m1);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Julia;
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var
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a,r: double;
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begin
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r := Math.power(FTx * FTx + FTy * FTy, 0.25);
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a := FAngle/2 + Trunc(random * 2) * PI;
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FPx := FPx + vars[13] * r * cos(a);
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FPy := FPy + vars[13] * r * sin(a);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Bent;
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var
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nx, ny: double;
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begin
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nx := FTx;
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ny := FTy;
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if (nx < 0) and (nx > -1E100) then
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nx := nx * 2;
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if ny < 0 then
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ny := ny / 2;
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FPx := FPx + vars[14] * nx;
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FPy := FPy + vars[14] * ny;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Waves;
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var
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dx,dy,nx,ny: double;
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begin
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dx := c20;
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dy := c21;
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nx := FTx + c10 * sin(FTy / ((dx * dx) + EPS));
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ny := FTy + c11 * sin(FTx / ((dy * dy) + EPS));
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FPx := FPx + vars[15] * nx;
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FPy := FPy + vars[15] * ny;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Fisheye;
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var
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{ a,} r: double;
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begin
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// r := sqrt(FTx * FTx + FTy * FTy);
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// a := arctan2(FTx, FTy);
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// r := 2 * r / (r + 1);
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r := 2 * Flength / (Flength + 1);
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FPx := FPx + vars[16] * r * FCosA;
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FPy := FPy + vars[16] * r * FSinA;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Popcorn;
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var
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dx, dy: double;
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nx, ny: double;
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begin
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dx := tan(3 * FTy);
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if (dx <> dx) then
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dx := 0.0; // < probably won't work in Delphi
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dy := tan(3 * FTx); // NAN will raise an exception...
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if (dy <> dy) then
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dy := 0.0; // remove for speed?
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nx := FTx + c20 * sin(dx);
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ny := FTy + c21 * sin(dy);
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FPx := FPx + vars[17] * nx;
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FPy := FPy + vars[17] * ny;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Exponential;
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var
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dx, dy: double;
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begin
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dx := exp(FTx)/ 2.718281828459045;
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dy := PI * FTy;
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FPx := FPx + vars[18] * cos(dy) * dx;
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FPy := FPy + vars[18] * sin(dy) * dx;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Power;
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var
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r: double;
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// nx, ny: double;
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begin
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// r := sqrt(FTx * FTx + FTy * FTy);
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// sa := sin(FAngle);
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r := Math.Power(FLength, FSinA);
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// nx := r * FCosA;
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// ny := r * FSinA;
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FPx := FPx + vars[19] * r * FCosA;
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FPy := FPy + vars[19] * r * FSinA;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Cosine;
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var
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nx, ny: double;
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begin
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nx := cos(FTx * PI) * cosh(FTy);
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ny := -sin(FTx * PI) * sinh(FTy);
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FPx := FPx + vars[20] * nx;
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FPy := FPy + vars[20] * ny;
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Rings;
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var
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r: double;
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dx: double;
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begin
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dx := sqr(c20) + EPS;
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r := FLength;
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r := r + dx - System.Int((r + dx)/(2 * dx)) * 2 * dx - dx + r * (1-dx);
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FPx := FPx + vars[21] * r * cos(FAngle);
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FPy := FPy + vars[21] * r * sin(FAngle);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.Fan;
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var
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r,t,a : double;
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dx, dy, dx2: double;
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begin
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dy := c21;
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dx := PI * (sqr(c20) + EPS);
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dx2 := dx/2;
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r := sqrt(FTx * FTx + FTy * FTy);
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t := FAngle+dy - System.Int((FAngle + dy)/dx) * dx;
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if (t > dx2) then
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a := FAngle - dx2
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else
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a := FAngle + dx2;
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FPx := FPx + vars[22] * r * cos(a);
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FPy := FPy + vars[22] * r * sin(a);
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end;
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///////////////////////////////////////////////////////////////////////////////
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procedure TXForm.NextPoint(var px,py,pc: double);
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var
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i: Integer;
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begin
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// first compute the color coord
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pc := (pc + color) * 0.5 * (1 - symmetry) + symmetry * pc;
|
|
|
|
FTx := c00 * px + c10 * py + c20;
|
|
FTy := c01 * px + c11 * py + c21;
|
|
|
|
if CalculateAngle then begin
|
|
if (FTx < -EPS) or (FTx > EPS) or (FTy < -EPS) or (FTy > EPS) then
|
|
FAngle := arctan2(FTx, FTy)
|
|
else
|
|
FAngle := 0.0;
|
|
end;
|
|
|
|
if CalculateSinCos then begin
|
|
Flength := sqrt(FTx * FTx + FTy * FTy);
|
|
if FLength = 0 then begin
|
|
FSinA := 0;
|
|
FCosA := 0;
|
|
end else begin
|
|
FSinA := FTx/FLength;
|
|
FCosA := FTy/FLength;
|
|
end;
|
|
end;
|
|
|
|
// if CalculateLength then begin
|
|
// FLength := sqrt(FTx * FTx + FTy * FTy);
|
|
// end;
|
|
|
|
Fpx := 0;
|
|
Fpy := 0;
|
|
|
|
for i := 0 to FNrFunctions - 1 do
|
|
FFunctionList[i];
|
|
|
|
px := FPx;
|
|
py := FPy;
|
|
end;
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
procedure TXForm.NextPoint(var CPpoint: TCPpoint);
|
|
var
|
|
i: Integer;
|
|
begin
|
|
// first compute the color coord
|
|
CPpoint.c := (CPpoint.c + color) * 0.5 * (1 - symmetry) + symmetry * CPpoint.c;
|
|
|
|
FTx := c00 * CPpoint.x + c10 * CPpoint.y + c20;
|
|
FTy := c01 * CPpoint.x + c11 * CPpoint.y + c21;
|
|
|
|
if CalculateAngle then begin
|
|
if (FTx < -EPS) or (FTx > EPS) or (FTy < -EPS) or (FTy > EPS) then
|
|
FAngle := arctan2(FTx, FTy)
|
|
else
|
|
FAngle := 0.0;
|
|
end;
|
|
|
|
if CalculateSinCos then begin
|
|
Flength := sqrt(FTx * FTx + FTy * FTy);
|
|
if FLength = 0 then begin
|
|
FSinA := 0;
|
|
FCosA := 1;
|
|
end else begin
|
|
FSinA := FTx/FLength;
|
|
FCosA := FTy/FLength;
|
|
end;
|
|
end;
|
|
|
|
// if CalculateLength then begin
|
|
// FLength := sqrt(FTx * FTx + FTy * FTy);
|
|
// end;
|
|
|
|
Fpx := 0;
|
|
Fpy := 0;
|
|
|
|
for i:= 0 to FNrFunctions-1 do
|
|
FFunctionList[i];
|
|
|
|
CPpoint.x := FPx;
|
|
CPpoint.y := FPy;
|
|
end;
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
procedure TXForm.NextPoint(var px, py, pz, pc: double);
|
|
var
|
|
i: Integer;
|
|
tpx, tpy: double;
|
|
begin
|
|
// first compute the color coord
|
|
pc := (pc + color) * 0.5 * (1 - symmetry) + symmetry * pc;
|
|
|
|
case Orientationtype of
|
|
1:
|
|
begin
|
|
tpx := px;
|
|
tpy := pz;
|
|
end;
|
|
2:
|
|
begin
|
|
tpx := py;
|
|
tpy := pz;
|
|
end;
|
|
else
|
|
tpx := px;
|
|
tpy := py;
|
|
end;
|
|
|
|
FTx := c00 * tpx + c10 * tpy + c20;
|
|
FTy := c01 * tpx + c11 * tpy + c21;
|
|
|
|
if CalculateAngle then begin
|
|
if (FTx < -EPS) or (FTx > EPS) or (FTy < -EPS) or (FTy > EPS) then
|
|
FAngle := arctan2(FTx, FTy)
|
|
else
|
|
FAngle := 0.0;
|
|
end;
|
|
if CalculateLength then begin
|
|
FLength := sqrt(FTx * FTx + FTy * FTy);
|
|
end;
|
|
|
|
Fpx := 0;
|
|
Fpy := 0;
|
|
|
|
for i:= 0 to FNrFunctions-1 do
|
|
FFunctionList[i];
|
|
|
|
case Orientationtype of
|
|
1:
|
|
begin
|
|
px := FPx;
|
|
pz := FPy;
|
|
end;
|
|
2:
|
|
begin
|
|
py := FPx;
|
|
pz := FPy;
|
|
end;
|
|
else
|
|
px := FPx;
|
|
py := FPy;
|
|
end;
|
|
end;
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
procedure TXForm.NextPoint2C(var px, py, pc1, pc2: double);
|
|
var
|
|
i: Integer;
|
|
begin
|
|
// first compute the color coord
|
|
pc1 := (pc1 + color) * 0.5 * (1 - symmetry) + symmetry * pc1;
|
|
pc2 := (pc2 + color) * 0.5 * (1 - symmetry) + symmetry * pc2;
|
|
|
|
FTx := c00 * px + c10 * py + c20;
|
|
FTy := c01 * px + c11 * py + c21;
|
|
|
|
if CalculateAngle then begin
|
|
if (FTx < -EPS) or (FTx > EPS) or (FTy < -EPS) or (FTy > EPS) then
|
|
FAngle := arctan2(FTx, FTy)
|
|
else
|
|
FAngle := 0.0;
|
|
end;
|
|
// if CalculateLength then begin
|
|
// FLength := sqrt(FTx * FTx + FTy * FTy);
|
|
// end;
|
|
|
|
Fpx := 0;
|
|
Fpy := 0;
|
|
|
|
for i:= 0 to FNrFunctions-1 do
|
|
FFunctionList[i];
|
|
|
|
px := FPx;
|
|
py := FPy;
|
|
end;
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
procedure TXForm.NextPointXY(var px, py: double);
|
|
var
|
|
i: integer;
|
|
begin
|
|
FTx := c00 * px + c10 * py + c20;
|
|
FTy := c01 * px + c11 * py + c21;
|
|
|
|
if CalculateAngle then begin
|
|
if (FTx < -EPS) or (FTx > EPS) or (FTy < -EPS) or (FTy > EPS) then
|
|
FAngle := arctan2(FTx, FTy)
|
|
else
|
|
FAngle := 0.0;
|
|
end;
|
|
|
|
if CalculateSinCos then begin
|
|
Flength := sqrt(FTx * FTx + FTy * FTy);
|
|
if FLength = 0 then begin
|
|
FSinA := 0;
|
|
FCosA := 0;
|
|
end else begin
|
|
FSinA := FTx/FLength;
|
|
FCosA := FTy/FLength;
|
|
end;
|
|
end;
|
|
|
|
Fpx := 0;
|
|
Fpy := 0;
|
|
|
|
for i:= 0 to FNrFunctions-1 do
|
|
FFunctionList[i];
|
|
|
|
px := FPx;
|
|
py := FPy;
|
|
end;
|
|
|
|
end.
|