// Description: this program creates random lines and highlights where they intersect. New lines are generated when the mouse is clicked.

// Equations identifying points of intersection reference Paul Bourke's derivations found at: 

// http://www-cs.ccny.cuny.edu/~wolberg/capstone/intersection/Intersection%20point%20of%20two%20lines.html

​

​

//stores coordinates of line endpoints

var x1 = [];

var y1 = [];

var x2 = [];

var y2 = [];

​

var lines = 12 // number of lines

​

//stores coordinates of intersections

var xInt;

var yInt;

​

​

function generateLines() {

  for (i = 0; i < lines; i++) { // fill coordinate arrays with line endpoints

    x1[i] = (random(0, width));

    y1[i] = (random(0, height));

    x2[i] = (random(0, width));

    y2[i] = (random(0, height));

  }

}

​

function setup() {

  createCanvas(640, 480);

  generateLines();

}

​

function draw() {

  background(220);

  //draw lines

  for (var i = 0; i < lines; i++) {

    line(x1[i], y1[i], x2[i], y2[i]);

    for (j = 0; j < 12; j++) {

      checkIntersection(x1[i], y1[i], x2[i], y2[i], x1[j], y1[j], x2[j], y2[j]);

    }

  }

}

​

function mouseClicked() {

  generateLines();

}

​

//use endpoints of 2 lines to check for intersections

function checkIntersection(x1, y1, x2, y2, x3, y3, x4, y4) {

  var ua = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)) / ((y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1));

  var ub = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3)) / ((y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1));

​

  //if ua and ub are between 0 and 1, there is an intersection

  if (0 < ua && ua < 1 && 0 < ub && ub < 1) {

    //find coordinates of intersection

    xInt = x1 + ua * (x2 - x1); 

    yInt = y1 + ua * (y2 - y1);

    //draw circle at point

    fill(0, 0, 10, 90);

    ellipse(xInt, yInt, 25, 25);

  }

}