Min Ji Kim Kim – Project 07 – Curves

sketch

/*
Min Ji Kim Kim
Section A
mkimkim@andrew.cmu.edu
Project-07
*/

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

function draw () {
    background(0);
    drawHypotrochoid(); //draw the Hypotrochoid
    drawHypocycloidPC(); //draw the Hypocycloid Pedal Curve
}

function drawHypotrochoid() { //http://mathworld.wolfram.com/Hypotrochoid.html
    var a = int(map(mouseX, 0, width, 100, 200)); //radius of Hypotrochoid
    var b = int(map(mouseY, 0, height, 50, 80)); //radius of circle b
    var h = int(map(mouseX, 0, width, 40, 50)); //distance between center and point P of circle with radius b    
    //draw Hypotrochoid
    push();
    translate(width / 2, height / 2); //move center to middle of canvas
    fill(150, mouseX, mouseY); //color changes depending on mouseX and mouseY
    beginShape(); 
    for(var i = 0; i < 100; i++) { 
        var tH = map(i, 0, 100, 0, TWO_PI); //map theta angle
        var x = (a - b) * cos(tH) + h * cos((a - b) * tH); //parametric equations
        var y = (a - b) * sin(tH) - h * sin((a - b) * tH);
        vertex(x, y);
    }
    endShape();
    pop();
}

function drawHypocycloidPC() { // http://mathworld.wolfram.com/HypocycloidPedalCurve.html
    var a = int(map(mouseY, 0, height, 30, 80)); //map the radius with mouseX movement
    var n = int(map(mouseX, 0, width, 5, 20)); //map the number of cusps with mouseX movement
    //draw Hypocycloid Pedal Curve
    push();
    translate(width / 2, height / 2); //move center to middle of canvas
    fill(mouseY, 100 , 120); //color changes depending on mouseY
    beginShape();
    for(var i = 0; i < 500; i++) {
        var t = map(i, 0, 500, 0, TWO_PI); //map theta angle
        var x = a * ((n - 1) * cos(t) + cos((n - 1) * t)) / n; //pedal curve equations
        var y = a * ((n - 1) * sin(t) + sin((n - 1) * t)) / n;
        vertex(x, y);
    }
    endShape();
    pop();
}

I think this was the hardest project to do so far. I didn’t really understand the assignment so I just started by looking at the curves on MathWorld and I was really interested in the Hypotrochoid and the Hypocycloid Pedal Curves. I decided to use those for this project and layer them to create a flower like effect. I think the hardest part of this project was trying to figure out the formulas and how to manipulate the variables but once I got it, it was fun to play around with the shapes and colors. I used mouseX and mouseY to manipulate the variables and the colors to create pretty flowers.