2D-color-gradient-or-Procedural-texture

Procedura texture in pascal ( Delphi) and in c

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Procedural texture

2D color gradient. For 1D color gradient see here
defined by a function whose value is computed rather than looked up

images

pascal images (up to 24 bit color)

max(x,y)

xor

sin

sin(x)

, 24 bit color ")

sin(x*y)

; single pattern , 24 bit color") ; repeating pattern, 24 bit color")

sin(x) + sin(y)

sin(y), rgb = 24 bit color")
sin(y), gray = 8 bit color")
sin(y), black and white = 1 bit color")
sin(y), indexed color ( palette)")

sin(x) + sin(y) + sin(x+y)

sin(y) + sin(x+y), indexed color from palette")
sin(y) + sin(x+y), black and white = 1 bit color ")

whirl

gray = 8 bit color ( c images )

cabs(z)

carg(z)

max min

star 8

himmelblau function

checkerboard and grid

cartesian

polar

Compare with:

grid for binary decomposition

Theory

Procedural textures are 2D or 3D plots of mathematical functions (called procedures)

Parts

2D scalar field ( 2D array , image, complex plane )
color
- modes
- function f : (R x R) maps to color
plane transformations
Texture Mapping = repeatedly paint the same small picture onto your geometry

color modes

color depth
color from palette

Color depth

24 bit color (rgb)
8 bit color mode: gray shades ( where r=g=b)
1 bit color mode: Black and White ( b&w )

pascal

 case ColorType of
                    TrueColor: if FunctionType=HSV   // 24 bit color
                        then kolor:=k 
                        else kolor:=Rainbow(kMin,kMAx,k mod kmax);
                    Direct:    kolor:=k;
                    GrayScale: kolor:=GrayScaleF(Round((k*256) div kmax)); // 8 bit color
                    Pseudo8bit:kolor:=GivePseudo8bitColor(k mod 255);
                    BlackAndWhite: if odd(k) then kolor:=clBlack // 1 bit color
                                         else kolor:=clWhite;
                  end; // case  ColorType }

color functions

Function

input: the texture coordinates: ( x,y)
output: a color value

Color functions

pascal

For color functions in pascal ( Delphi) see file: ColorM.pas

Here input is a pair of integers (x,y):

x in [0, bitmapa.width-1]
y in [0, bitmapa.height-1]

pascal

Function Projection(center:TPoint;height:integer;x,y:integer;FunctionType:TFunctionType):integer;
  // F: C --> R
  //var r:extended; //radius
  begin

     case FunctionType of
            HSV:        result:= Point2Color(X,y);
            AbsZ:       result:=round(sqrt(sqr(X-center.X)+sqr(y-center.Y)));
            ArgZ:       result:=round(RadToDeg(Pi+ArcTan2(y-center.Y,center.X-x)));
            Whirl:      result:=round(sqrt(sqr(X-center.X)+sqr(y-center.Y))+RadToDeg(2*Pi+ArcTan2(y-center.Y,center.X-x)));
            ReZ:        result:=y ;  // horizontal lines
            Saddle:     result:=abs(sqr(x-center.X)-round(sqr(y-center.y) / 2)) ;
            RePlusIm:   result:=y+x;
            MaxReIm:    result:=max(abs(center.x-x),abs(center.Y-y)); // or
            AbsReIm:    result:=abs((center.x-x)*(center.Y-y));           // biomorph
            ImDivRe:    result:=floor(tan((center.Y-y) / (center.X-x+0.000001)));  //
            ImReDiv:    result:=y+x+(100*y div (x+1));
            manhattan:  result:=sqr(abs(center.X-x)+abs(center.Y-y));                                                              // ClientHeight*(sin+1)/2= [0,ClientHeight]

            sinusX:     result:=round(bitmapa.Width*sin(Pi*DegToRad(x)));
            Sinus:      result:=y+round(height*(sin(Pi*DegToRad(x))+1)/8);
            // sin   is in  [-1,+1]
            // (sin+1)      [0,2]
            // (sin+1)/2    [0,1]
            SinusXY:    result:=y+round(height*(sin(Pi*DegToRad(x + y))+1)/8);
            SinusXmY:   result:=y+round(height*(sin(Pi*DegToRad(x*y))+1)/8);
            SinXSinY:   result:=round((height * (2+sin(Pi*DegToRad(y)) + sin(Pi*DegToRad(x)))) /4);//try to change numerical values
            sinXYXY:     result:=round ( height * (2+sin(Pi*DegToRad(y)) + sin(Pi*DegToRad(x))+sin(Pi*DegToRad(x+y)))/8 );
            XorY:         result:=x or  y;
            XxorY:        result:=x xor y;
            XshlY:        result:=x shl y;
            XshrY:        result:=x shr y;
            XandY:        result:=x and y;
            sqrtM:        result:=round(sqrt(x*y)) ;
            ftMax:        result:=Round((center.Y-y) / sqr(center.X -x + 0.0001));
            plasma: result:=round(bitmapa.Width*sin(Pi*DegToRad(x)));
            else          result:=y; //
          end; // case
  end;

c

Here input is a pair of doubles z = (x,y)

x in [-1,1]
y in [-1,1]

double conic(double complex z)
{
  double argument;
  
  argument = carg(z); //   argument in radians from -pi to pi
  
  argument = fabs(argument)/ M_PI;
      
  return argument; // argument in range from 0.0 to 1.0
}


// https://en.wikipedia.org/wiki/Himmelblau%27s_function
double GiveHimmelblau(double x, double y){
    // map input to [-m,m]x[-m,m]
    double m = 6.0;
    x *= m;
    y *= m;
    double a = x*x+y-11.0;
    double b = x+y*y-7.0;
    // mapped output to 
     return (a*a + b*b)/200.0;

}

/*
    https://iquilezles.org/www/articles/checkerfiltering/checkerfiltering.htm
    checkers, in mod form
*/
double checker( double x, double y){

    double m = 5.0; 
    // map input from [-1,1]x[-1,1] to [-m,m]x[-m,m]
    int ix = floor(m*x);
    int iy = floor(m*y);

    return abs(ix + iy) % 2;

}

/* 
 r is the smooth potential and phi is the final angle
 code by xenodreambuie : "I call this texture pyramids. My code in Pascal for the Star8 texture is "
 
 
*/ 

double GiveStar8(double r, double phi){
    double fr;
    double fphi;
    double t;
    double g;
    
    fr = fabs(frac(r));
    fphi = fabs(frac(phi));
    if (fphi>fr) {
            t= fr; 
            fr= fphi; 
            fphi=t;
            }
  
    g = 1+1.5*fphi-2.5*fr;
    t = 1-2.5*fphi-fr;
    if (t> g) 
        { g = t;}
    if (g<0)
        {g=0;}
    
    return g;
}

The checkerboard pattern is regular grid of equal-sized colored squares

files

ColorM.pas
Rainbow.exe - windows executable program, can be run also on linux
d.c - c version of Rainbow program
g.sh bash script for converting ppm files to png

run

pascal

On linux ( tested on Ubuntu 20.04):

pascal

wine ./Rainbow.exe
wine ./exe/Rainbow.exe

Use:

open main menu, choose options item
choose color mode
use arrow up and down keys to change functions
use shift+arrow to change color type
check the options in the status bar

History

Old ( but still interesting) Pascal ( Borland Delphi 7.0 personal edition ) program Rainbow for windows ( but can also be run on Linux using wine)

dead old www address: fraktal.republika.pl/tecza.html

Last modification: 2005-05-29

Licence and contributors

licence - GNU General Public License v3.0
function star8 by xenodreambuie ( pascal)
Function Rainbow by Witold J.Janik; WJJ@CAD.PL thx for Andrzeja W¹sika from pl.comp.lang.delphi http://4programmers.net/view.php?id=201

Git

create a new repository on the command line

git

echo "# Procedural-texture" >> README.md
git init
git add README.md
git commit -m "first commit"
git branch -M main
git remote set-url origin git@github.com:adammaj1/2D-color-gradient-or-Procedural-texture.git
git push -u origin main

local repo

bash

~/Pobrane/r20051021

Subdirectory

git

mkdir images
git add *.png
git mv  *.png ./images
git commit -m "move"
git push -u origin main

then link the images:

txt

![](./images/n.png "description")

git

gitm mv -f

warning

distribute binary

pascal

The page build completed successfully, but returned the following warning for the `main` branch:

It looks like you're using GitHub Pages to distribute binary files. We strongly suggest that you use releases to ship projects on GitHub. Releases are GitHub's way of packaging and providing software to your users. You can think of it as a replacement to using downloads to provide software. We found the following file(s) which may be a good candidate for releases:

The only way to prevent these warnings from being sent is to either:

Remove the executables from your repository
Store them on a different branch from your Pages publishing source
Store them outside of the docs directory, if you’re using this directory to host your site

markdown

mastering-markdown

authenticate

automatically-authenticate-into-github

git

git remote set-url origin git@github.com:adammaj1/Procedural-texture.git

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22D-color-gradient-or-Procedural-texture

Member rating

README

images

pascal images (up to 24 bit color)

max(x,y)

xor

sin

sin(x)

sin(x*y)

sin(x) + sin(y)

sin(x) + sin(y) + sin(x+y)

whirl

gray = 8 bit color ( c images )

cabs(z)

carg(z)

max min

star 8

himmelblau function

checkerboard and grid

cartesian

polar

Theory

color modes

color functions

Color functions

pascal

c

files

See also

functions

Chladni patterns

2D noise

transformations

Midpoint Displacement fractal

run

pascal

History

Licence and contributors

Git

Subdirectory

warning

distribute binary

markdown

authenticate

2D-color-gradient-or-Procedural-texture