Difference between revisions of "Lagrange interpolation (dup)"

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Line 18: Line 18:
 
          
 
          
 
         var polynomial = function(x) {
 
         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;
 +
                }
 +
/*
 
                 var y = p[0].Y()*(x-p[1].X())*(x-p[2].X())*(x-p[3].X())/
 
                 var y = p[0].Y()*(x-p[1].X())*(x-p[2].X())*(x-p[3].X())/
 
                         ((p[0].X()-p[1].X())*(p[0].X()-p[2].X())*(p[0].X()-p[3].X()))+
 
                         ((p[0].X()-p[1].X())*(p[0].X()-p[2].X())*(p[0].X()-p[3].X()))+
Line 26: Line 37:
 
                         p[3].Y()*(x-p[0].X())*(x-p[1].X())*(x-p[2].X())/
 
                         p[3].Y()*(x-p[0].X())*(x-p[1].X())*(x-p[2].X())/
 
                         ((p[3].X()-p[0].X())*(p[3].X()-p[1].X())*(p[3].X()-p[2].X()));
 
                         ((p[3].X()-p[0].X())*(p[3].X()-p[1].X())*(p[3].X()-p[2].X()));
 +
*/
 
                 return y;
 
                 return y;
 
             };
 
             };

Revision as of 19:14, 3 December 2008

Construct a polynomial of degree 3 through four given points.

        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 = p[0].Y()*(x-p[1].X())*(x-p[2].X())*(x-p[3].X())/
                        ((p[0].X()-p[1].X())*(p[0].X()-p[2].X())*(p[0].X()-p[3].X()))+
                        p[1].Y()*(x-p[0].X())*(x-p[2].X())*(x-p[3].X())/
                        ((p[1].X()-p[0].X())*(p[1].X()-p[2].X())*(p[1].X()-p[3].X()))+
                        p[2].Y()*(x-p[0].X())*(x-p[1].X())*(x-p[3].X())/
                        ((p[2].X()-p[0].X())*(p[2].X()-p[1].X())*(p[2].X()-p[3].X()))+
                        p[3].Y()*(x-p[0].X())*(x-p[1].X())*(x-p[2].X())/
                        ((p[3].X()-p[0].X())*(p[3].X()-p[1].X())*(p[3].X()-p[2].X()));
                return y;
            };
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});