// ###### Setup #####

  // ##################

​

  function setup() {

​

    createCanvas(600, 600);

    frameRate(5);

  }

​

  // #################

  // ###### Draw #####

  // #################

​

  function draw() {

      //console.log(Maths.PHI);dkdddd

​

      //

    grainCircle(width/2, height/2, 500, color(250,244,233,120),PI/3);

      grainCircle(width/2, height/2, 250, color(190,80,70,120),PI/3);

      grainCircle(width/2, height/2, 250, color(40,30,125,120),4*PI/3);

​

​

​

      // let MAX = 10;

​

      // for(let i = 0 ; i < MAX ; i++){

      //   for(let j = 0 ; j < MAX ; j++){

      //

      //     let p1x = i*width/(MAX+1);

      //     let p1y = j*width/(MAX+1);

      //

      //     let p2x = (i+1)*width/(MAX+1);

      //     let p2y = j*width/(MAX+1);

      //

      //     let p3x = i*width/(MAX+1);

      //     let p3y = (j+1)*width/(MAX+1);

      //

      //     grainTriangle(p1x,p1y,p2x,p2y,p3x,p3y);

      //

      //   }

      // }

      save();

      noLoop();

  }

​

function grainCircle(cx,cy,cr,c= color(0), dir=TWO_PI){

​

    stroke(c);

​

​

    const AREA = PI * cr * cr;

​

    // LIGHTING SYSTEM

    const v = p5.Vector.fromAngle(dir,cr); // pick random point on edge of sphere

    const light = createVector(cx+v.x, cy+v.y);

​

    // GENERATE POINTS

    for(let i = 0; i < AREA / 1.5; i++){

​

        strokeWeight(random(1,2)); // so that it is not pixels

        while(true){

            const p = Maths.pointInCircle(cx, cy, cr);

            const probability = map(dist(p.x, p.y, light.x, light.y),0,(cr*2),1,0);

​

            if(random() < probability == 0){          // I DONT UDBNERSTAND WHY I HAVE AN EQL 0 here

                let rx = 5

                let ry = 2

                point(p.x+random(-rx,rx),p.y+random(-ry,ry));

                break;

            }

        }

    }

}

​

function grainTriangle(x0, y0, x1, y1, x2, y2){

    strokeWeight(1.1); // so that it is not pixels

​

    const AREA = ( x0 * ( y1 - y2 ) + x1 * ( y2 - y0 ) + x2 * (y0 - y1) ) / 2;

​

    // LIGHTING SYSTEM

    // const v = p5.Vector.fromAngle(dir,cr); // pick random point on edge of sphere

    // const light = createVector(cx+v.x, cy+v.y);

​

    // GENERATE POINTS

    for(let i = 0; i < AREA / 2 ; i++){

​

        //while(true){

​

            //const p = pointInCircle(cx, cy, cr);

            const p = Maths.pointInTriangle(x0,y0,x1,y1,x2,y2);

            //const probability = map(dist(p.x, p.y, light.x, light.y),0,(cr*2),1,0);

​

            //if(random() < probability == 0){          // I DONT UDBNERSTAND WHY I HAVE AN EQL 0 here

                point(p.x,p.y);

                //break;

            //}

        //}

    }

}

​

///////////////////////////////////////////////

​

​

​

class Maths{

  //static PHI = 1.6543;

  static distSq(x1, y1, x2, y2){ return (x2 - x1)**2 + (y2 - y1)**2; }

​

  // Vector Functions

  static distSq(v1, v2) { return (v2.x - v1.x) ** 2 + (v2.y - v1.y) ** 2; }

  static midpoint(v1, v2) { return (createVector((v1.x + v2.x) / 2, (v1.y + v2.y) / 2)); }

​

    // PROBABILITY

​

    // static randInt(min, max){ return int(random(min, max+1)); }

​

  // LINEAR AND NON LINEAR MAPPING

  // EXPIN EXPOUT EXPINOUT

  // QUADRATICIN OUT

   //  static expInOut(x) {

   //  if(x == 0.0 || x == 1.0) return x;

   //

   //   if(x < 0.5){

   //       return(0.5 * pow(2, (20 * x) - 10));

   //   }

   //   else{

   //       return(-0.5 * pow(2, (-20 * x) + 10) + 1);

   //   }

   // }

   // GEOMETRY

​

   // # Geometry

   // # Check if points are inside polygons

   static isPointinCircle(px, py, cx, cy, cr){ return (distSq(px, py, cx, cy) < cr**2); }

   static isPointinSquare(){}

​

   // # Generate uniform points inside polygons

   static pointInQuad(){}

   static pointInSquare(){}

​

   static pointInTriangle(x0, y0, x1, y1, x2, y2){

    // we must put x1,x2 and y1 y2 at the origin before transformation

    // and put them back afterwards

​

    let a1 = random(); // nice fades if i put an sqrt here

    let a2 = random();

    if((a1 + a2) >=1 ){ // reflect the points that are outside 1st triangle

        a1 = 1 - a1; // https://blogs.sas.com/content/iml/2020/10/19/random-points-in-triangle.html

        a2 = 1 - a2;

    }

    const px = a1 * (x1-x0) + a2 * (x2-x0) + x0;

    const py = a1 * (y1-y0) + a2 * (y2-y0) + y0;

​

    return createVector(px, py);

  }

​

  static pointInCircle(cx, cy, cr){

    // uniformely generate points in a circle

    // https://stackoverflow.com/questions/5837572/generate-a-random-point-within-a-circle-uniformly

​

    const r = cr * Math.sqrt(Math.random()); // if i add a second square root here I get something more intense along the curves

    const theta = Math.random() * 2 * Math.PI;   // if we add an sqrt here it does a neat spiral

​

    const px = cx + r * Math.cos(theta)

    const py = cy + r * Math.sin(theta)

​

    return {x : px, y : py};

  }

​

}

​

 // DRAW

​

 // object = mathematical function

 // functions : draw

 // functions : derive

 // functions : integral

 // find solutions

 // intersect with other objects