Lagrange interpolation, show term

Constructs a polynomial of degree [math]\displaystyle{ n }[/math] through [math]\displaystyle{ n+1 }[/math] given points. Points can be added by clicking on "Add point". The dotted line is the graph of the first derivative, the dashed line is the graph of the second derivative.

References

• http://en.wikipedia.org/wiki/Lagrange_polynomial

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});

var points = [];
points[0] = board.create('point', [-1,2], {size:4});
points[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(points);
var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});
var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

var txt = board.create('text', [-3, -4,  () => f.getTerm(2, 't', ' * ')], {fontSize: 16});

function addPoint() {
    points.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
    board.update();
}

function removePoint() {
    if (points.length > 2) {
      board.removeObject(points[points.length - 1]);
      points.pop();
    }
    //board.update();
}

document.getElementById('add').addEventListener("click", addPoint, false);
document.getElementById('remove').addEventListener("click", removePoint, false);