Andrew Wang – Project 07

sketch

//Andrew Wang

function setup() {
    createCanvas(400, 400);
    fill(240,210,210);
}

function draw() {
    background(130);
    push();
    translate(width/2, height/2);
    //maps mouse between 0- 150 (0-75 for inner) and rotates grid by 30 degrees
    x = map(mouseX, 0, width, 0, 150);
    y = map(mouseY, 0, height, 0, 150);
    rotate(radians(30));
    cruciform(x,y);
    x = map(mouseX, 0, width,150,0);
    y = map(mouseY, 0, height, 150, 0);
    rotate(radians(30));
    cruciform(x,y)
    x = map(mouseX, 0, width, 75,0);
    y = map(mouseY, 0, height, 75,0);
    rotate(radians(30));
    cruciform(y,x);
    x = map(mouseX, 0, width, 0, 150);
    y = map(mouseY, 0, height, 0, 150);
    rotate(radians(30));
    cruciform(x,y);
    x = map(mouseX, 0, width,150,0);
    y = map(mouseY, 0, height, 150, 0);
    rotate(radians(30));
    cruciform(x,y)
    pop();
}

function cruciform(a,b){
    beginShape();
    noStroke();
    for (var n = 0; n < 100; n++) {
        //change to degrees
        var t = map(n, 0, 100, 0, 2*PI)
        //parametric equation of cruciform
        x = a*(1/cos(t));
        y = b*(1/sin(t));
        //draws circles of size 3-6
        ellipse(x, y, map(mouseY, 0, height, 3, 6), 
                      map(mouseY, 0, height, 3, 6));
    }
    endShape(CLOSE);
}

I used the cruciform curve from mathworld for my project. Initially having only put down one curve, it looked a bit lackluster so I created a smaller version to sit inside of the larger one. This was a little better, however, it still looked a little bit barren at certain mouse positions so I decided to try rotations.

I realized that if I wanted to rotate, I would have to make four outer cruciform curves to fill each of the corners. I made the one in the middle upright and curved the others.

for this curve, the two equations that I used were x = a*1/cos(t) and y= a*1/sin(t). I plotted points along the curve instead of drawing the lines since it looked a little bit strange with the lines as there were lots of intersections.