Lagrange interpolation (dup)

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". <link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" /> <script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script> <script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script> <form><input type="button" value="Add point" onClick="addPoint()"></form>

<script language="JavaScript">

       board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
       // Axes
       b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
       b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

       var p = [];
       p[0] = board.createElement('point', [-1,2], {style:6});
       p[1] = board.createElement('point', [3,-1], {style:6});
       graph = board.createElement('curve', ['x', board.lagrangePolynomial(p), 'x', -10, 10], {curveType:'graph'});

       function addPoint() {
         p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
         board.update();
       }
          

</script>

References

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

The underlying JavaScript code

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>

        board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
        // Axes
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

        var p = [];
        p[0] = board.createElement('point', [-1,2], {style:6});
        p[1] = board.createElement('point', [3,-1], {style:6});
        
        graph = board.createElement('curve', ['x', board.lagrangePolynomial(p), 'x', -10, 10], {curveType:'graph'});

        function addPoint() {
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board.update();
        }