Lagrange Polynomial Interpolation. Example (Updated 8/2018): http://jsfiddle.net/jgU3Y/107/

lagrange.js

/**
 * At least two points are needed to interpolate something.
 * @class Lagrange polynomial interpolation.
 * The computed interpolation polynomial will be reffered to as L(x).
 * @example
 * var l = new Lagrange(0, 0, 1, 1);
 * var index = l.addPoint(0.5, 0.8);
 * console.log(l.valueOf(0.1));
 * 
 * l.changePoint(index, 0.5, 0.1);
 * console.log(l.valueOf(0.1));
 */
class Lagrange{
	
  constructor(x1,y1,x2,y2){
    this.xs = [x1, x2];
    this.ys = [y1, y2];
    this.ws = [];
    this._updateWeights();
  }


  /**
   * Adds a new point to the polynomial. L(x) = y
   * @return {Number} The index of the added point. Used for changing the point. See changePoint.
   */
  addPoint(x, y) {
    this.xs.push(x);
    this.ys.push(y);
    this._updateWeights();
    return this.xs.length-1;
  }

  /**
   * Changes a previously added point.
   */
  changePoint(index, x, y) {
    this.xs[index] = x;
    this.ys[index] = y;
    this._updateWeights();
  }

  /**
   * Recalculate barycentric weights.
   */
  _updateWeights() {
    var k = this.xs.length;
    var w;

    for (var j = 0; j < k; ++j) {
      w = 1;
      for (var i = 0; i < k; ++i) {
        if (i != j) {
          w *= this.xs[j] - this.xs[i];
        }
      }
      this.ws[j] = 1/w;
    }
  }

  /**
   * Calculate L(x)
   */
  valueOf(x) {
    var a = 0;
    var b = 0;
    var c = 0;

    for (var j = 0; j < this.xs.length; ++j) {
      if (x != this.xs[j]) {
        a = this.ws[j] / (x - this.xs[j]);
        b += a * this.ys[j];
        c += a;
      } else {
        return this.ys[j];
      }
    }

    return b / c;
  }

}