computes the dimensions for an element to fully cover the viewport.

getScaledDimensions.js

/**
 * computes the dimensions for an element to fully cover the viewport.
 * @param vw {Number} the width of the viewport
 * @param vh {Number} the height of the viewort
 * @param a {Number} the aspect ratio of the element being displayed.
 */
function getScaledDimensions(vw, vh, a) {

  // variables to contain the width and height results.
  var w, h, ox, oy;

  // compute two possible dimensions based on the viewport height and width.
  var cw = vh * a, ch = vw * 1 / a;

  // set the width and the height to whichever dimension encompasses the entire viewport.
  if (cw<=vw) w = vw, h = ch, ox = 0, oy = (vh - ch) / 2;
  if (ch<=vh) w = cw, h = vh, ox = (vw - cw) / 2, oy = 0;

  // return the computed dimensions.
  return {width: Math.round(w), height: Math.round(h), offsetX: ox, offsetY: oy};
}