Monica Chang- Project-07-Curves

sketch

//Monica Chang
//mjchang@andrew.cmu.edu
//Section D
//Project-07-Curves

var nPoints = 100;
var radiusX;
var radiusY;
var separation = 125;

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

function draw() {
    background("darkcyan");
    fill(255, 255, 255, 64);
    
    radiusX = mouseX;
    radiusY = mouseY;

    drawCircles();
    drawEpitrochoidCurve();
    drawDeltoid();
}

//circle elements

function drawCircles() {
  
  // a sequence of little, circle elements
    push();
    translate(width / 2, height / 2);
    for (var i = 0; i < nPoints + 10; i++) {
        var theta = map(i, 0, nPoints, 0, TWO_PI);
        var px = radiusX / 2 * cos(theta);
        var py = radiusY / 2 * sin(theta);
      
        stroke("lightcyan");
        strokeWeight(1);
        circle(px - 5, py - 5, 8, 8);
    }
    pop();
  
}


function drawDeltoid() {
    //Deltoid:
    //http://mathworld.wolfram.com/Deltoid.html
    beginShape();
    nPoints = 40;
    for (var i = 0; i < nPoints; i++) {   
    	var angle = map(i, 0, 180, 0, 360);
        var radius = 70;
        var a = map(mouseX, 0, height, 5, 80)
        var b = map(mouseY, 0, height, 5, 90)
        
        //x-coordinate for deltoid
        var x = (a - b) * cos(angle) + radius * cos((a - b * angle));
        //y-coordinate for deltoid
        var y = (a - b) * sin(angle) - radius * sin((a - b * angle));
        rotate(radians(angle));
        noFill();
        strokeWeight(3);
        stroke("red");
        vertex(x, y);
      }
    endShape();
    

}

function drawEpitrochoidCurve() {
    // Epicycloid:
    // http://mathworld.wolfram.com/Epicycloid.html
    
    var x2;
    var y2;
    
    var a = 80.0;
    var b = a / 2.0;
    var h = constrain(mouseY / 8.0, 0, b);
    var ph = mouseX / 30.0;
    
    noFill();
    stroke("tan");
    strokeWeight(1);
    beginShape();
    translate(width / 2, height / 2);
    for (var i = 0; i < nPoints + 10; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);
        
        x2 = (a + b) * cos(t) - h * cos(ph + t * (a + b) / b);
        y2 = (a + b) * sin(t) - h * sin(ph + t * (a + b) / b);
      
        //switching x and y-coordinates to create a band of waves/
        vertex(x2, y2);
        vertex(y2, x2);
    }
    endShape(CLOSE);
    
}

This project definitely had me studying the formulas 75% of the time for me to really start putting anything together. However, once I got the gist of the formulas, it was really entertaining for me. I began with studying the deltoid curve and I realized this particular curve created so many different shapes. Thus, I wanted to provide a more constant curve which became the sequence of circles which are relatively more static to create a sense of balance.