Difference between revisions of "Perlin Noise"

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{{Developing with Graphics}}
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{{Perlin Noise}}
  
 
This page is the start of a tutorial about using Perlin Noise on LCL applications to generate natural looking images. It will cover both basic theory and real usage examples, with a focus on compilable examples.
 
This page is the start of a tutorial about using Perlin Noise on LCL applications to generate natural looking images. It will cover both basic theory and real usage examples, with a focus on compilable examples.
  
−
Perlin Noise was invented by [Ken Perlin|http://mrl.nyu.edu/~perlin/] to generate textures for a movie called Tron. Today it is widely used on movies and video games to produce natural looking smoke, landscapes, clouds and any texture including marble, irregular glass,  etc.
+
Perlin Noise was invented by [http://mrl.nyu.edu/~perlin/ Ken Perlin] to generate textures for a movie called Tron. Today it is widely used on movies and video games to produce natural looking smoke, landscapes, clouds and any texture including marble, irregular glass,  etc.
  
 
__TOC__
 
__TOC__
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==First Example==
 
==First Example==
  
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[[Image:Noise1D.png]]
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This application demonstrates a simple noise function with the following properties:
  
−
Noise1D.dpr file:
+
* Only 1 harmonic present
 +
* Amplitude of 250 pixels
 +
* Wavelength of 20 pixels
 +
* Frequency of 0.05
 +
* You can use a combo box to choose between Linear, Cossine and Cubic interpolation
  
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<pre>
+
[[Image:Noise1D.png]]
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program noise1d;
 
  
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{$ifdef fpc}
+
Files:
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  {$mode delphi}
 
−
{$endif}
 
  
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uses
+
* noise1d.lpi
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  {$ifdef fpc}
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* noise1d.dpr
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  Interfaces, // this includes the LCL widgetset
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* noise.pas
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  {$endif}
 
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  Classes, SysUtils, LResources, Forms, Controls, Graphics, Dialogs, StdCtrls,
 
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  noise;
 
  
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type
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==Persistence Example==
  
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  { TMainWindow }
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This application demonstrates how to sum many noise functions to get a perlin noise function. It has the following properties:
  
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  TMainWindow = class(TForm)
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* 3 harmonics present
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  private
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* Amplitudes of 250, 125 and 62 pixels
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    { private declarations }
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* Wavelength of 20, 10, and 5 pixels
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    SelectInterpolation: TComboBox;
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* Frequency of 0.05, 0.1, 0.2
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    procedure DoPaint(Sender: TObject);
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* You can use a combo box to choose between Linear, Cossine and Cubic interpolation
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    procedure DoRefresh(Sender: TObject);
 
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    function NormalizeNoise(x: Double): Integer;
 
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  public
 
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    { public declarations }
 
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    constructor Create(AOwner: TComponent); override;
 
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    destructor Destroy; override;
 
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  end;
 
  
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var
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[[Image:Perlin1D.png]]
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  vMainWindow: TMainWindow;
 
  
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{ TMainWindow }
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Files:
  
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procedure TMainWindow.DoPaint(Sender: TObject);
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* perlin1d.lpi
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var
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* perlin1d.dpr
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  i, j, interpolation: Integer;
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* noise.pas
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begin
 
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  { Draws rulers }
 
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  Canvas.MoveTo(25,  25 );
 
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  Canvas.LineTo(25,  275);
 
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  Canvas.LineTo(275, 275);
 
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  { Draws 12 points and the interpolation between them }
 
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  for i := 0 to 11 do
 
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  begin
 
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    Canvas.Ellipse(i * 20 + 25 + 1, NormalizeNoise(IntNoise(i)) + 1,
 
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    i * 20 + 25 - 1, NormalizeNoise(IntNoise(i)) - 1);
 
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    if (i = 11) then Continue;
 
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    for j := 1 to 19 do
 
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    begin
 
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      case SelectInterpolation.ItemIndex of
 
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      0: interpolation := Linear_Interpolate(NormalizeNoise(IntNoise(i)), NormalizeNoise(IntNoise(i + 1)), j / 20);
 
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      1: interpolation := Cosine_Interpolate(NormalizeNoise(IntNoise(i)), NormalizeNoise(IntNoise(i + 1)), j / 20);
 
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      else
 
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        interpolation := Cubic_Interpolate(NormalizeNoise(IntNoise(i - 1)),
 
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        NormalizeNoise(IntNoise(i)), NormalizeNoise(IntNoise(i + 1)),
 
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        NormalizeNoise(IntNoise(i + 2)), j / 20);
 
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      end;
 
  
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      Canvas.Pixels[i * 20 + 25 + j, interpolation] := clBlack;
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==Use Perlin noise to create textures==
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    end;
 
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  end;
 
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end;
 
  
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procedure TMainWindow.DoRefresh(Sender: TObject);
+
It is possible to create tilable textures of stone, water, wood... with Perlin noise.
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begin
 
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  Repaint;
 
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end;
 
  
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function TMainWindow.NormalizeNoise(x: Double): Integer;
+
Here is a tutorial on how to do this: [[BGRABitmap tutorial 8]]
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begin
 
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  Result := Round( 25 + (x + 1.0) * 125 );
 
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end;
 
  
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constructor TMainWindow.Create(AOwner: TComponent);
+
==Subversion==
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begin
 
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  inherited Create(AOwner);
 
  
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  Position := poScreenCenter;
+
You can download the source code for the examples and the library using this command:
−
  Width := 300;
 
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  Height := 300;
 
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  Caption := 'Noise 1D';
 
  
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  OnPaint := DoPaint;
+
svn co  https://svn.code.sf.net/p/lazarus-ccr/svn/examples/noise noise
  
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  SelectInterpolation := TComboBox.Create(Self);
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==External Links==
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  SelectInterpolation.Parent := Self;
 
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  SelectInterpolation.Items.Add('Linear Interpolation');
 
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  SelectInterpolation.Items.Add('Cosine Interpolation');
 
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  SelectInterpolation.Items.Add('Cubic Interpolation');
 
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  SelectInterpolation.Left := 100;
 
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  SelectInterpolation.Width := 200;
 
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  SelectInterpolation.ItemIndex := 0;
 
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  SelectInterpolation.OnChange := DoRefresh;
 
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end;
 
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destructor TMainWindow.Destroy;
 
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begin
 
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  inherited Destroy;
 
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end;
 
  
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begin
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* [http://web.archive.org/web/20160325134143/http://freespace.virgin.net/hugo.elias/models/m_perlin.htm Article] with the theory of Perlin Noise.
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  Application.Initialize;
 
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  Application.CreateForm(TMainWindow, vMainWindow);
 
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  Application.Run;
 
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end.
 
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</pre>
 
  
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noise.pas file:
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[[Category:Tutorials]]
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[[Category:Graphics]]
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<pre>
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[[Category:Game Development]]
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unit noise;
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[[Category:Lazarus-CCR]]
−
 
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[[Category:SciTech]]
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{$ifdef fpc}
 
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  {$mode delphi}
 
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{$endif}
 
−
 
 
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interface
 
−
 
 
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uses
 
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  Classes, SysUtils;
 
−
 
 
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function IntNoise(x: Integer): Double;
 
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function Linear_Interpolate(a, b: Integer; x: Double): Integer;
 
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function Cosine_Interpolate(a, b: Integer; x: Double): Integer;
 
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function Cubic_Interpolate(v0, v1, v2, v3: Integer; x: Double): Integer;
 
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implementation
 
−
 
 
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function IntNoise(x: Integer): Double;
 
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var
 
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  xl: Integer;
 
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begin
 
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  xl := (x shl 13) xor x;
 
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  Result := (xl * (xl * xl * 15731 + 789221) + 1376312589) and $7fffffff;
 
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  Result := 1.0 - (Result / 1073741824.0);
 
−
end;
 
−
 
 
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function Linear_Interpolate(a, b: Integer; x: Double): Integer;
 
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begin
 
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  Result := Round(a * (1-x) + b * x);
 
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end;
 
−
 
 
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function Cosine_Interpolate(a, b: Integer; x: Double): Integer;
 
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var
 
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  f, ft: Double;
 
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begin
 
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  ft := x * Pi;
 
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  f := (1.0 - cos(ft)) * 0.5;
 
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  Result := Round( a * (1 - f) + b * f );
 
−
end;
 
−
 
 
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function Cubic_Interpolate(v0, v1, v2, v3: Integer; x: Double): Integer;
 
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var
 
−
  P, Q, R, S: Double;
 
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begin
 
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  P := (v3 - v2) - (v0 - v1);
 
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  Q := (v0 - v1) - P;
 
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  R := v2 - v0;
 
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  S := v1;
 
−
 
 
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  Result := Round( P * x * x * x + Q * x * x + R * x + S );
 
−
end;
 
−
 
 
−
end.
 
−
</pre>
 
−
 
 
−
==External Links==
 

Latest revision as of 08:06, 11 April 2019

│ English (en) │ français (fr) │ 中文（中国大陆）‎ (zh_CN) │

This page is the start of a tutorial about using Perlin Noise on LCL applications to generate natural looking images. It will cover both basic theory and real usage examples, with a focus on compilable examples.

Perlin Noise was invented by Ken Perlin to generate textures for a movie called Tron. Today it is widely used on movies and video games to produce natural looking smoke, landscapes, clouds and any texture including marble, irregular glass, etc.

Getting Started

Perlin Noise is based on the idea of fractals, that things in nature show different degrees of change. On a rocky mountain landscape for example when can see changes with a very big amplitude, which are the mountains themselves. Smaller changes represent irregularities on those mountains and even smaller ones represent rocks.

mountain landscape.png


First Example

This application demonstrates a simple noise function with the following properties:

  • Only 1 harmonic present
  • Amplitude of 250 pixels
  • Wavelength of 20 pixels
  • Frequency of 0.05
  • You can use a combo box to choose between Linear, Cossine and Cubic interpolation

Noise1D.png

Files:

  • noise1d.lpi
  • noise1d.dpr
  • noise.pas

Persistence Example

This application demonstrates how to sum many noise functions to get a perlin noise function. It has the following properties:

  • 3 harmonics present
  • Amplitudes of 250, 125 and 62 pixels
  • Wavelength of 20, 10, and 5 pixels
  • Frequency of 0.05, 0.1, 0.2
  • You can use a combo box to choose between Linear, Cossine and Cubic interpolation

Perlin1D.png

Files:

  • perlin1d.lpi
  • perlin1d.dpr
  • noise.pas

Use Perlin noise to create textures

It is possible to create tilable textures of stone, water, wood... with Perlin noise.

Here is a tutorial on how to do this: BGRABitmap tutorial 8

Subversion

You can download the source code for the examples and the library using this command:

svn co https://svn.code.sf.net/p/lazarus-ccr/svn/examples/noise noise

External Links

  • Article with the theory of Perlin Noise.
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