// The Coding Train / Daniel Shiffman

// https://thecodingtrain.com/challenges/55-mathematical-rose-patterns

// Video: https://youtu.be/f5QBExMNB1I

​

// Code from challenge:  https://editor.p5js.org/codingtrain/sketches/3kanFIcHd

​

// Based on: https://en.wikipedia.org/wiki/Rose_(mathematics)

​

var d = 8;

var n = 5;

var sliderD;

var sliderN;

​

function setup() {

  createCanvas(400, 400);

  sliderD = createSlider(1, 20, 10, 1);

  sliderN = createSlider(1, 20, 10, 1);

  sliderD.input(draw);

  sliderN.input(draw);

}

​

function draw() {

  d = sliderD.value();

  n = sliderN.value();

  var k = n / d;

  background(51);

  push();

  translate(width / 2, height / 2);

​

  beginShape();

  stroke(255);

  noFill();

  strokeWeight(1);

  for (var a = 0; a < TWO_PI * reduceDenominator(n, d); a += 0.02) {

    var r = 200 * cos(k * a);

    var x = r * cos(a);

    var y = r * sin(a);

    vertex(x, y);

  }

  endShape(CLOSE);

  pop();

  noLoop();

}

​

function reduceDenominator(numerator, denominator) {

    function rec(a, b) {

        return b ? rec(b, a % b) : a;

    }

    return denominator / rec(numerator, denominator);

}