Siwei Xie – Project 07 – Curves

sketch

//Siwei Xie
//Section B
//sxie1@andrew.cmu.edu
//project-07

var nPoints = 500;
var t;
var angle = 0;
var adj = 2;

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

function draw() {
	background(220);
    noStroke();

	//draw Quadrifolium with variant colors
    push();
    fill(mouseX, mouseY, 80);
    translate(mouseX, mouseY);
    rotate(radians(angle));
    drawQuadrifolium();
    angle = (angle + adj) % 360;
    pop();

    //draw Epitrochoid with variant colors
    push();
    fill(80, mouseX, mouseY);
    translate(200, 200);
    drawEpitrochoid();
    pop();
}

//draw rotating & moving windmill
function drawQuadrifolium() {
    var a = 70;
    
    beginShape();
    for (var i = 0; i < nPoints; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);

        //http://mathworld.wolfram.com/Quadrifolium.html
        r = a * sin(2 * t);
        x = r * cos(t);
        y = r * sin(t);
        vertex(x, y);
    }
    endShape(CLOSE);
}

//draw variant curve in the middle
function drawEpitrochoid(){
    var a1 =  40;
    var b1 = 200;
    var h = constrain(mouseY/ 10.0, 0, b1);
    var t;
    var r = map(mouseX, 0, 600, 0, 1); 
    
    beginShape();
    fill(200, mouseX, mouseY);
    for (var i = 0; i < nPoints; i++) {

        stroke("black");
        vertex(x, y);
        var t = map(i, 0, nPoints, 0, TWO_PI * 2); // mess with curves within shapes

        //Parametric equations for Epitrochoid Curve
        x = r* ((a1 + b1) * cos(t) - h * cos((t * (a1 + b1) / b1) + mouseX));
        y = r* ((a1 + b1) * sin(t) - h * sin((t * (a1 + b1) / b1) + mouseX));
        
    }
    endShape(CLOSE);
    
}

I had fun creating this image. I used Quadrifolium and Epitrochoid in my drawing, and adjusting them according to the position of mouse.

Quadrifolium is a type of rose curve with n=2. It has the polar equation. Epitrochoid is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle. 

By modifying the limits of parameters and changing value of parameters in the formula, I was able to play with the curves.