Month: October 2017

sketch

//scarlet tong
//sntong@andrew.cmu.edu
// Section A
// Project 07 - Composition with Curves


//intitalize a value before using it for the x and y equations
var a = 0;

function setup() {
    createCanvas(300, 300);
    angleMode(DEGREES);
}

function draw(){
  //changing the alpha channel allows the movements of the dots to "lag" behind
  //creating interesting "tails" for each dot
  background(250,170,23,100);
  push();
  translate(150, height/2); // so that we can see the curve on the cancaus
  beginShape();
  for(var i = 0; i < 200; i++){
    var theta = map(i,0,100,0,360);
    // a controls how much the curve "bends" and loops
    var a = map(mouseX, 0,480,-7,7);
    //Conchoid of de Sluze equation from Wolfram MathWorld
    var x = (1/cos(theta)+(a*cos(theta)))*cos(theta);
    var y = (1/cos(theta)+(a*cos(theta)))*sin(theta);
    // color of the dots changes according to mouse position
    var col = map(mouseY, 0,300,0,255);
    var jitter = map(mouseY, 0,300,0,7);
    noStroke();
    fill(col);
    //"polar array" the Conchoid from the center
    rotate(90);
    //the first dotted line
    ellipse(x*20+random(0,1),y*20+random(0,1),2,2);
    //the second dots are rotated on a different angle of offset
    rotate(45);
    //the second dotted line
    fill(255-col);
    ellipse(-x*10+random(0,1),-y*10+random(0,1),2,2);
    // another layer of dots with larger diameters are then introduced to highlight
    //specific paths the curve took.
    if(i%4==0){
      ellipse(x*20+random(0,1),y*20+random(0,1),3,3)
    }
  }
  endShape(CLOSE);
  pop();

}

For this project I choose the to use the Conchoid of de Sluze equation found on Wolfram MathWorld as my base curve. I did more experimenting while I was coding and layer more alterations to the curve configuration each step. In this assignment I wanted to explore the use of density so that it implies a set of lines; however once the image is static it becomes harder to tell which dots make up a specific curve. I started off with a set of mirrored curves where one is scaled to a factor to another. Then I added motion of the curves by tracking mouseX and mouseY. From there color change is referred to mouse position and rotation is introduced to the curves.

My math is a bit rusty so my head spun when perusing the Mathworld website. I first played around with the equations given in the project example, which resulted in this:

I studied each part of the code until I was able to create another curve. I created a Cartioid Curve that increases size and rotates based on mouseX, and the background also changes based on the mouseX and mouseY positions.

sketch

// Tiffany Lai
// 15-104, Section A
// thlai@andrew.cmu.edu
// Project 07 - Curves

var nPoints = 500; // amount of points in curve

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

function draw() {
    // background changes colors based on mouse position
    var r = map(mouseX, 0, width, 50, 200);
    var g = map(mouseY, 0, width, 150, 200);
    var b = map(mouseX, 0, height, 200, 255);
    background(r - 100, g - 100, b - 100, 130);

    drawCurve(); // draw the cardioid curve
}

function drawCurve(){
    //mathworld.wolfram.com/Cardioid.html

    var x; // defining x and y positions of vertices in curve
    var y;

    var a = map(mouseX, 0, width, 0, 100); // map mouseX from 0 to 5

    fill(100, 200, 255, 20); // blue
    stroke(255); // white
    translate(width/2, height/2);

    beginShape();
    for (var i = 0; i < nPoints; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);
        x = a * (1 + cos(t)) * cos(t); // parametric equation of cardioid
        y = a * (1 + cos(t)) * sin(t); // parametric equation of cardioid

        rotate(radians(mouseX/500)); // rotate based on mouseX
        ellipse(x, y, 1, 1); // draw spiral of dots
        vertex(x, y); // draw the first curve (blue)
    }
    endShape();

    beginShape();
    for (var i = 0; i < nPoints; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);
        x2 = a * (1 + cos(t)) * cos(t); // parametric equation of cardioid
        y2 = a * (1 + cos(t)) * sin(t); // parametric equation of cardioid

        rotate(radians(mouseX/500)); // rotate based on mouseX
        fill(255, 150, 150, 20); // pink
        vertex(x2, y2); // draw the second curve (pink)
    }
    endShape();
}