Minkowski Island: Fill color/back color Problems
lazarus / 39-Graphics

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Boleeman · 2024-04-08 13:22

Created a Minkowski Island fractal

Read about it here
https://mathworld.wolfram.com/MinkowskiSausage.html 
and here https://en.wikipedia.org/wiki/Minkowski_sausage


It's basically a square Quadratic Koch curve.

Can't figure out why its messing up at recursion levels greater than
3.
Thought it may be a round of error, seeings as it happens at higher
recursion level but cant trace it.
Noticed that when I resize the form at level 4 that gap changes. So
perhaps its a scaling problem.

Some Graphic GURU advice is needed.

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KodeZwerg · 2024-04-08 13:36

By watching pictures, the left image does do those strokes to
compensate the missing space to paint full element so my guess is that
at initial the value for length for each stroke is calculated wrong.

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Martin_fr · 2024-04-08 14:49

Maybe rounding errors. E.g. you keep summing up floats, and compare
against x. But the floats will never reach x.

For example
Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i program
Project1;var  a: double;begin  a := 2.0;  while a <> 0 do begin    a
:= a - 2 / 5;    writeln(a);  end;end.
will continue running. Because 2/5 is rounded in binary, and not
exactly 0.4

So, maybe something like that?

Use "SameValue()" from unit math.

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tetrastes · 2024-04-08 17:05

Try this
Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i unit
Unit1; {$mode objfpc}{$H+} interface uses  Classes, SysUtils, Forms,
Controls, Graphics, Dialogs, ExtCtrls, Buttons,  StdCtrls, Spin,
Math; type   TPointSingle = record    X: single;    Y: single;  end;  
{ TForm1 }   TForm1 = class(TForm)    Label1: TLabel;    Label2:
TLabel;    PaintBox1: TPaintBox;    Panel1: TPanel;    seDepth:
TSpinEdit;    seLinewidth: TSpinEdit;    procedure
PaintBox1Paint(Sender: TObject);    procedure seDepthChange(Sender:
TObject);    procedure seLinewidthChange(Sender: TObject);  private 
 Initiator: array of TPointSingle;   ScaleFactor: Single; 
 GeneratorDTheta: array of Single;   procedure DrawSnowflake(ACanvas:
TCanvas; depth: Integer);   procedure DrawSnowflakeEdge(ACanvas:
TCanvas; depth: Integer; var p1: TPointSingle;  theta: Single; dist:
Single);  public   end; var  Form1: TForm1; implementation {$R
*.lfm} procedure TForm1.DrawSnowflakeEdge(ACanvas: TCanvas; depth:
Integer; var p1: TPointSingle;  theta: Single; dist: Single);var  i:
Integer;  p2: TPointSingle;  ip1, ip2: TPoint;begin  if depth = 0
then  begin    p2.X := p1.X + (dist * Cos(theta + Pi / 2));    p2.Y :=
p1.Y + (dist * Sin(theta + Pi / 2));     ip1.X := Trunc(p1.X + 0.5); 
   // Because  "banker's rounding" is not what I was taught in
University    ip1.Y := Trunc(p1.Y + 0.5);    ip2.X := Trunc(p2.X +
0.5);    ip2.Y := Trunc(p2.Y + 0.5);    ACanvas.Line(ip1, ip2);    p1
:= p2;    Exit;  end;   dist := dist / Sqrt(5.0);  for i := 0 to
High(GeneratorDTheta) do  begin    theta := theta +
GeneratorDTheta[i];    DrawSnowflakeEdge(ACanvas, depth - 1, p1,
theta, dist);  end;end; procedure TForm1.DrawSnowflake(ACanvas:
TCanvas; depth: Integer);var  i: Integer;  p1, p2: TPointSingle;  dx,
dy, length, theta: Single;begin  Canvas.Clear;   for i := 1 to
High(Initiator) do  begin    p1 := Initiator[i - 1];    p2 :=
Initiator[i];     dx := p2.X - p1.X;    dy := p2.Y - p1.Y;    length
:= Sqrt(dx * dx + dy * dy);    theta := ArcTan2(dy, dx);   
DrawSnowflakeEdge(ACanvas, depth, p1, theta, length); 
end;end; procedure TForm1.PaintBox1Paint(Sender: TObject);var 
MinDimension: Integer;begin   SetLength(Initiator, 0); 
SetLength(GeneratorDTheta, 0);   // Ensure Initiator array is properly
initialized  if Length(Initiator) < 5 then    SetLength(Initiator,
5);    MinDimension := Min(PaintBox1.Width, PaintBox1.Height); 
MinDimension := MinDimension - 300;   if Length(Initiator) >= 5 then
// Ensure Initiator array has enough elements  begin    {Initiator[0]
:= Point(Round((PaintBox1.Width - MinDimension) / 2),
Round((PaintBox1.Height - MinDimension) / 2));    Initiator[1] :=
Point(Round((PaintBox1.Width + MinDimension) / 2),
Round((PaintBox1.Height - MinDimension) / 2));    Initiator[2] :=
Point(Round((PaintBox1.Width + MinDimension) / 2),
Round((PaintBox1.Height + MinDimension) / 2));    Initiator[3] :=
Point(Round((PaintBox1.Width - MinDimension) / 2),
Round((PaintBox1.Height + MinDimension) / 2));    Initiator[4] :=
Initiator[0];}    Initiator[0].X := (PaintBox1.Width - MinDimension) /
2;    Initiator[0].Y := (PaintBox1.Height - MinDimension) / 2;   
Initiator[1].X := (PaintBox1.Width + MinDimension) / 2;   
Initiator[1].Y := (PaintBox1.Height - MinDimension) / 2;   
Initiator[2].X := (PaintBox1.Width + MinDimension) / 2;   
Initiator[2].Y := (PaintBox1.Height + MinDimension) / 2;   
Initiator[3].X := (PaintBox1.Width - MinDimension) / 2;   
Initiator[3].Y := (PaintBox1.Height + MinDimension) / 2;   
Initiator[4] := Initiator[0];  end;   ScaleFactor := 1 / Sqrt(5); 
GeneratorDTheta := nil;  SetLength(GeneratorDTheta, 3); 
GeneratorDTheta[0] := -ArcTan(1 / 2);  GeneratorDTheta[1] := Pi / 2; 
GeneratorDTheta[2] := -Pi / 2;   // Redraw the snowflake with the
adjusted level  DrawSnowflake(PaintBox1.Canvas,
seDepth.Value);end; procedure TForm1.seDepthChange(Sender:
TObject);begin  PaintBox1.Invalidate;end; procedure
TForm1.seLinewidthChange(Sender: TObject);begin 
PaintBox1.Canvas.Pen.Width := seLinewidth.Value; 
PaintBox1.Invalidate;end; end.

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Boleeman · 2024-04-09 01:41

Thanks tetrastes.

Looks like the issue was using point and rounding.
I looked at breaking down into x and y point locations, but I was
still rounding to get rid of extended value error.

Using Initiator[0].X  and Initiator[0].Y type syntax without the
rounding was what I was completely missing.

Also was good to know about:
    ip1.X := Trunc(p1.X + 0.5);      // Because  "banker's rounding"
is not what I was taught in University
    ip1.Y := Trunc(p1.Y + 0.5);
    ip2.X := Trunc(p2.X + 0.5);
    ip2.Y := Trunc(p2.Y + 0.5);

Noticed now when resizing the form, the fractal resizes well.

Thanks once again for your great help.

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Boleeman · 2024-04-09 03:31

I tried setting the fill color of the fractal with a TColorbutton
called cbFillcolor and the backcolor of Paintabox1 with a TColorbutton
called cbBackcolor but I could not get that to work.

Usually its simple to do for a TPaintbox, but don't know why it did
not change colors.

Here is the complete code:

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i  unit
Unit1; {$mode objfpc}{$H+} interface uses  Classes, SysUtils, Forms,
Controls, Graphics, Dialogs, ExtCtrls, Buttons,  StdCtrls, Spin,
Math; type   TPointSingle = record    X: single;    Y: single;  end;  
{ TForm1 }   TForm1 = class(TForm)    cbLinecolor: TColorButton;   
cbBackcolor: TColorButton;    cbFillcolor: TColorButton;    Label1:
TLabel;    Label2: TLabel;    Label3: TLabel;    Label4: TLabel;   
Label5: TLabel;    PaintBox1: TPaintBox;    Panel1: TPanel;   
seDepth: TSpinEdit;    seLinewidth: TSpinEdit;    procedure
cbFillcolorColorChanged(Sender: TObject);    procedure
cbLinecolorColorChanged(Sender: TObject);    procedure
cbBackcolorColorChanged(Sender: TObject);    procedure
PaintBox1Paint(Sender: TObject);    procedure seDepthChange(Sender:
TObject);    procedure seLinewidthChange(Sender: TObject);  private 
 Initiator: array of TPointSingle;   ScaleFactor: Single; 
 GeneratorDTheta: array of Single;   procedure DrawSnowflake(ACanvas:
TCanvas; depth: Integer);   procedure DrawSnowflakeEdge(ACanvas:
TCanvas; depth: Integer; var p1: TPointSingle;  theta: Single; dist:
Single);   procedure FillSnowflake(ACanvas: TCanvas; CenterPoint:
TPoint; depth: Integer; p1: TPointSingle;  theta: Single; dist:
Single);  public   end; var  Form1: TForm1; implementation {$R
*.lfm} procedure TForm1.FillSnowflake(ACanvas: TCanvas; CenterPoint:
TPoint; depth: Integer; p1: TPointSingle;  theta: Single; dist:
Single);var  i: Integer;  p2: TPointSingle;  Points: array of
TPoint;begin  if depth = 0 then    Exit;   SetLength(Points, 5);   for
i := 1 to High(Initiator) do  begin    p1 := Initiator[i - 1];    p2
:= Initiator[i];     Points[0] := CenterPoint;    Points[1].X :=
Round(p1.X);    Points[1].Y := Round(p1.Y);    Points[2].X :=
Round(p2.X);    Points[2].Y := Round(p2.Y);    Points[3] :=
CenterPoint;    Points[4] := Points[1];     ACanvas.Polygon(Points); 
end;end; procedure TForm1.DrawSnowflakeEdge(ACanvas: TCanvas; depth:
Integer; var p1: TPointSingle;  theta: Single; dist: Single);var  i:
Integer;  p2: TPointSingle;  ip1, ip2: TPoint;begin  if depth = 0
then  begin    p2.X := p1.X + (dist * Cos(theta + Pi / 2));    p2.Y :=
p1.Y + (dist * Sin(theta + Pi / 2));     ip1.X := Trunc(p1.X + 0.5); 
   // Because  "banker's rounding" is not what I was taught in
University    ip1.Y := Trunc(p1.Y + 0.5);    ip2.X := Trunc(p2.X +
0.5);    ip2.Y := Trunc(p2.Y + 0.5);    ACanvas.Line(ip1, ip2);    p1
:= p2;    Exit;  end;   dist := dist / Sqrt(5.0);  for i := 0 to
High(GeneratorDTheta) do  begin    theta := theta +
GeneratorDTheta[i];    DrawSnowflakeEdge(ACanvas, depth - 1, p1,
theta, dist);  end;end; procedure TForm1.DrawSnowflake(ACanvas:
TCanvas; depth: Integer);var  i: Integer;  p1, p2: TPointSingle;  dx,
dy, length, theta: Single;begin  ACanvas.Pen.Color :=
cbLinecolor.ButtonColor;   for i := 1 to High(Initiator) do  begin   
p1 := Initiator[i - 1];    p2 := Initiator[i];     dx := p2.X - p1.X; 
  dy := p2.Y - p1.Y;    length := Sqrt(dx * dx + dy * dy);    theta :=
ArcTan2(dy, dx);    DrawSnowflakeEdge(ACanvas, depth, p1, theta,
length);  end;end; procedure TForm1.PaintBox1Paint(Sender:
TObject);var  MinDimension: Integer;begin   SetLength(Initiator, 0); 
SetLength(GeneratorDTheta, 0);   // Ensure Initiator array is properly
initialized  if Length(Initiator) < 5 then    SetLength(Initiator,
5);    MinDimension := Min(PaintBox1.Width, PaintBox1.Height); 
MinDimension := MinDimension - 300;   if Length(Initiator) >= 5 then
// Ensure Initiator array has enough elements  begin    
Initiator[0].X := (PaintBox1.Width - MinDimension) / 2;   
Initiator[0].Y := (PaintBox1.Height - MinDimension) / 2;   
Initiator[1].X := (PaintBox1.Width + MinDimension) / 2;   
Initiator[1].Y := (PaintBox1.Height - MinDimension) / 2;   
Initiator[2].X := (PaintBox1.Width + MinDimension) / 2;   
Initiator[2].Y := (PaintBox1.Height + MinDimension) / 2;   
Initiator[3].X := (PaintBox1.Width - MinDimension) / 2;   
Initiator[3].Y := (PaintBox1.Height + MinDimension) / 2;   
Initiator[4] := Initiator[0];  end;   ScaleFactor := 1 / Sqrt(5); 
GeneratorDTheta := nil;  SetLength(GeneratorDTheta, 3); 
GeneratorDTheta[0] := -ArcTan(1 / 2);  GeneratorDTheta[1] := Pi / 2; 
GeneratorDTheta[2] := -Pi / 2;   DrawSnowflake(PaintBox1.Canvas,
seDepth.Value);end; procedure TForm1.cbLinecolorColorChanged(Sender:
TObject);beginPaintBox1.Canvas.Pen.Color :=
cbLinecolor.ButtonColor;PaintBox1.Invalidate;end; procedure
TForm1.cbFillcolorColorChanged(Sender:
TObject);begin PaintBox1.Invalidate;end; procedure
TForm1.cbBackcolorColorChanged(Sender: TObject);begin 
PaintBox1.Invalidate;end; procedure TForm1.seDepthChange(Sender:
TObject);begin  PaintBox1.Invalidate;end; procedure
TForm1.seLinewidthChange(Sender: TObject);begin 
PaintBox1.Canvas.Pen.Width := seLinewidth.Value; 
PaintBox1.Invalidate;end; end.

I could change the line color of the fractal.

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tetrastes · 2024-04-09 08:21

You call FillSnowflake nowhere, and don't use cbFillcolor.ButtonColor
and cbBackcolor.ButtonColor.

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Boleeman · 2024-04-09 10:15

I made fillsnowflake like this:

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i procedure
TForm1.FillSnowflake(ACanvas: TCanvas; CenterPoint: TPoint; depth:
Integer; p1: TPointSingle;  theta: Single; dist: Single);var  i:
Integer;  p2: TPointSingle;  Points: array of TPoint;begin  if depth =
0 then    Exit;   SetLength(Points, 5);   for i := 1 to
High(Initiator) do  begin    p1 := Initiator[i - 1];    p2 :=
Initiator[i];     Points[0] := CenterPoint;    Points[1].X :=
Round(p1.X);    Points[1].Y := Round(p1.Y);    Points[2].X :=
Round(p2.X);    Points[2].Y := Round(p2.Y);    Points[3] :=
CenterPoint;    Points[4] := Points[1];     ACanvas.Brush.Color :=
cbFillcolor.ButtonColor;    ACanvas.Polygon(Points);  end;end;      
and then I called it in procedure TForm1.PaintBox1Paint(Sender:
TObject);

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i procedure
TForm1.PaintBox1Paint(Sender: TObject);var  MinDimension:
Integer;begin   SetLength(Initiator, 0);  SetLength(GeneratorDTheta,
0);   // Ensure Initiator array is properly initialized  if
Length(Initiator) < 5 then    SetLength(Initiator, 5);    MinDimension
:= Min(PaintBox1.Width, PaintBox1.Height);  MinDimension :=
MinDimension - 300;   if Length(Initiator) >= 5 then // Ensure
Initiator array has enough elements  begin     Initiator[0].X :=
(PaintBox1.Width - MinDimension) / 2;    Initiator[0].Y :=
(PaintBox1.Height - MinDimension) / 2;    Initiator[1].X :=
(PaintBox1.Width + MinDimension) / 2;    Initiator[1].Y :=
(PaintBox1.Height - MinDimension) / 2;    Initiator[2].X :=
(PaintBox1.Width + MinDimension) / 2;    Initiator[2].Y :=
(PaintBox1.Height + MinDimension) / 2;    Initiator[3].X :=
(PaintBox1.Width - MinDimension) / 2;    Initiator[3].Y :=
(PaintBox1.Height + MinDimension) / 2;    Initiator[4] :=
Initiator[0];  end;   ScaleFactor := 1 / Sqrt(5);  GeneratorDTheta :=
nil;  SetLength(GeneratorDTheta, 3);  GeneratorDTheta[0] := -ArcTan(1
/ 2);  GeneratorDTheta[1] := Pi / 2;  GeneratorDTheta[2] := -Pi / 2;  
DrawSnowflake(PaintBox1.Canvas, seDepth.Value); 
FillSnowflake(PaintBox1.Canvas, Point(PaintBox1.Width div 2,
PaintBox1.Height div 2), seDepth.Value, Initiator[0], 0, 0);end;     
                

I also tried calling it recursively:

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i procedure
TForm1.FillSnowflake(ACanvas: TCanvas; CenterPoint: TPoint; depth:
Integer;  p1: TPointSingle; theta: Single; dist: Single);var  i:
Integer;  p2: TPointSingle;  Points: array of TPoint;begin  if depth =
0 then    Exit;   SetLength(Points, 5);   for i := 1 to
High(Initiator) do  begin    p1 := Initiator[i - 1];    p2 :=
Initiator[i];     Points[0] := CenterPoint;    Points[1].X :=
Round(p1.X);    Points[1].Y := Round(p1.Y);    Points[2].X :=
Round(p2.X);    Points[2].Y := Round(p2.Y);    Points[3] :=
CenterPoint;    Points[4] := Points[1];     // Fill the region with
the fill color    ACanvas.Brush.Color := cbFillcolor.ButtonColor; //
Use the color from cbFillcolor    ACanvas.Polygon(Points);     //
Recursively fill the inner segments    p1.X := CenterPoint.X + (p1.X -
CenterPoint.X) * ScaleFactor;    p1.Y := CenterPoint.Y + (p1.Y -
CenterPoint.Y) * ScaleFactor;    p2.X := CenterPoint.X + (p2.X -
CenterPoint.X) * ScaleFactor;    p2.Y := CenterPoint.Y + (p2.Y -
CenterPoint.Y) * ScaleFactor;    FillSnowflake(ACanvas, CenterPoint,
depth - 1, p1, theta, dist);  end;end;
Still get 1 square filled only.