Difference between revisions of "Lagrange interpolation (dup)"

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Line 1: Line 1:
Construct a polynomial of degree 3 through four given points.
+
Constructs a polynomial of degree n through n+1 given points.
 +
Points can be added by clicking on "Add point".
 
<html>
 
<html>
 
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 
<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/prototype.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<form><input type="button" value="Add point" onClick="p.push(board.createElement('point',[Math.random(),Math.random()],{style:6}))"></form>
+
<form><input type="button" value="Add point" onClick="addPoint()"></form>
 
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
 
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
 
<script language="JavaScript">
 
<script language="JavaScript">
Line 15: Line 16:
 
         p[0] = board.createElement('point', [-1,2], {style:6});
 
         p[0] = board.createElement('point', [-1,2], {style:6});
 
         p[1] = board.createElement('point', [0,-3], {style:6});
 
         p[1] = board.createElement('point', [0,-3], {style:6});
 +
        /*
 
         p[2] = board.createElement('point', [1,4], {style:6});
 
         p[2] = board.createElement('point', [1,4], {style:6});
 
         p[3] = board.createElement('point', [2,1], {style:6});
 
         p[3] = board.createElement('point', [2,1], {style:6});
          
+
         */
 
         var polynomial = function(x) {
 
         var polynomial = function(x) {
 
                 var y = 0.0;
 
                 var y = 0.0;
Line 32: Line 34:
 
             };
 
             };
 
         graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});
 
         graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});
 +
 +
        function addPoint() {
 +
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*10],{style:6}));
 +
          board.update();
 +
        }
 +
         
 
</script>
 
</script>
 
</html>
 
</html>

Revision as of 19:20, 3 December 2008

Constructs a polynomial of degree n through n+1 given points. Points can be added by clicking on "Add point".

        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', [0,-3], {style:6});
        p[2] = board.createElement('point', [1,4], {style:6});
        p[3] = board.createElement('point', [2,1], {style:6});
        
        var polynomial = function(x) {
                var y = 0.0;
                for (var i=0;i<4;i++) {
                  var t = p[i].Y();
                  for (var k=0;k<4;k++) {
                    if (k!=i) {
                      t *= (x-p[k].X())/(p[i].X()-p[k].X());
                    }
                  }
                  y += t;
                }
                return y;
            };
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});