Finding all the points within a circle in 2D space

Question

I am representing my 2D space (consider a window), where each pixel is shown as a cell in a 2D array. i.e. a 100x100 window is represented by the array of same dimensions.

Answer 1

I know this question has an accepted answer, but I have a far easier solution. The other answers confused me, as I did not know what center, xcenter, ycenter were, and the math behind the functions were left unexplained and I trekked out to discover a mathematical solution of my own.

My equation is very simple:

cx is the x point in the center of the circle

cy is the y point in the center of the circle

rad is the radius of the circle

What my equation/function does is calculate the points by calculating each possible point given the radius and it adds and subtracts the offset of cx and cy.

//Creates an array filled with numbers
function range(begin, end) {
    for (var i = begin, arr = []; i < end; i++) {
      arr.push(i);
    }

    return arr;
}

function calculateAllPointsInCircle(cx, cy, rad) {

   var rang = range(-rad, rad + 1);
   var px = [];
   var py = [];
   var xy = [];

   for (var i = 0; i < rang.length; i++) {
     var x = cx + rang[i];
     px.push(x);

     for (var l - rang.length - 1; l > 0; l--) {
        var y = cy + rang[l];
        if (!py.indexOf(y)===-1) { py.push(y); }

        xy.push(x+','+y);
     }
   }

   return {
     x: x,
     y: y,
     xy: xy
   }
}

The performance is much higher than the other answers: http://jsperf.com/point-in-circle/4 You can check my equation with math, using the equation that will validate if a given point is inside a circle x*x + y*y <= r*r OR x^2 + y^2 <= r^2

Edit- Super compressed ES6 version:

function range(begin, end) {
  for (let i = begin; i < end; ++i) {
    yield i;
  }
}

function calculateAllPointsInCircle(cx, cy, rad) {
    return {
        x: [cx + i for (i of range(-rad, rad + 1))],
        y: [cy + i for (i of range(-rad, rad + 1))]
    };
}