Julia Nishizaki – Project 07 – Curves

sketch

//Julia Nishizaki
//Section B
//jnishiza@andrew.cmu.edu
//Project 07 - Curves

var nPoints = 200;
var rotation = 0; //rotation for all Hypotrochoid Evolutes starts at 0

function setup() {
    createCanvas(480, 480);
}

function draw() {
    background('white');
    stroke('white');
    
    //Hypotrochoid Evolutes:
    drawHypotrochoidEvolute(5, 300, 0.75, 2.5, color(139, 198, 63, 125)); //green
    drawHypotrochoidEvolute(10, 150, map(mouseX, 0, width, 0, 2), 1.5, color(173, 18, 26, 125)); //red
    drawHypotrochoidEvolute(5, 200, map(mouseY, 0, height, 0.25, 1), 2.5, color(177, 158, 219, 125)); //purple
    drawHypotrochoidEvolute(50, 150, map(mouseY, height, 0, 0, 2), 1.5, color(113, 198, 232, 125)); //blue
    drawHypotrochoidEvolute(25, 226, map(mouseX, width, 0, 0.25, 1.5), 2, color(253, 185, 63, 125)); //yellow
}

function drawHypotrochoidEvolute(pedalNum, angularity, size, strokeW, fillColor) { //pedalNum and angularity affect how many "pedals" you see, and their appearance
    // Hypotrochoid Evolute:
    // http://mathworld.wolfram.com/HypotrochoidEvolute.html
    push();
    translate(width / 2, height / 2);
    scale(size); //scales down Hypotrochoids (including stroke), specified under draw
    
    //causes all Hypotrochoid Evolutes to rotate at same rate, clockwise when mouse is below the middle of the canvas, counter-clockwise when above
    rotation += map(mouseY, 0, height, -TWO_PI / 800, TWO_PI / 800);
    rotate(rotation);
    
    //creates the Hypotrochoid Evolutes
    beginShape();
    fill(fillColor);
    strokeWeight(strokeW);
    for (var i = 0; i < nPoints; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);
        var h = map(mouseX, 0, width, -200, 200);
        //The equation for Hypotrochoid Evolutes
        x = (angularity - pedalNum) * cos(t) + h * cos((angularity - pedalNum) * (t / pedalNum));
        y = (angularity - pedalNum) * sin(t) - h * sin((angularity - pedalNum) * (t / pedalNum));
        vertex(x, y);
    }
    endShape();
    pop();
}

When approaching this project, I was a little overwhelmed, as I didn’t really know where to start, but after looking through the different roulette curves on the Mathworld curves website, I chose to focus on just the hypotrochoid evolute forms, as there were a large range of forms and examples for that particular curve that I could explore. After playing around with them a little, I started experimenting with colors and transparencies, and tried to go in the direction of a kaleidoscope, as I wanted my project to be constantly changing, and to reveal/conceal the different layers of colors depending on the location of your mouse.