Difference between revisions of "Lagrange interpolation"

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Line 35: Line 35:
 
                 return y;
 
                 return y;
 
             };
 
             };
         graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph'});
+
         graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph', strokeWidth:3});
 
         d1 = board.createElement('curve', ['x', board.D(f), 'x', -10, 10], {curveType:'graph',dash:1});
 
         d1 = board.createElement('curve', ['x', board.D(f), 'x', -10, 10], {curveType:'graph',dash:1});
 
         d2 = board.createElement('curve', ['x', board.D(board.D(f)), 'x', -10, 10], {curveType:'graph',dash:2});
 
         d2 = board.createElement('curve', ['x', board.D(board.D(f)), 'x', -10, 10], {curveType:'graph',dash:2});

Revision as of 19:30, 30 January 2009

Constructs a polynomial of degree [math]n[/math] through [math]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

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});
        
        var f = function(x) {
                var i;
                var y = 0.0;
                var xc = [];
                for (i=0;i<p.length;i++) {
                  xc[i] = p[i].X();
                }
                for (i=0;i<p.length;i++) {
                  var t = p[i].Y();
                  for (var k=0;k<p.length;k++) {
                    if (k!=i) {
                      t *= (x-xc[k])/(xc[i]-xc[k]);
                    }
                  }
                  y += t;
                }
                return y;
            };
        graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph'});
        d1 = board.createElement('curve', ['x', board.D(f), 'x', -10, 10], {curveType:'graph',dash:1});
        d2 = board.createElement('curve', ['x', board.D(board.D(f)), 'x', -10, 10], {curveType:'graph',dash:2});

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