Difference between revisions of "Rational functions"
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</script> | </script> | ||
</html> | </html> | ||
+ | |||
+ | === References === | ||
+ | * [http://en.wikipedia.org/wiki/Rational_function http://en.wikipedia.org/wiki/Rational_function] | ||
+ | |||
+ | === The underlying JavaScript source code === | ||
+ | |||
+ | <source lang="javascript"> | ||
+ | board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25}); | ||
+ | // Axes | ||
+ | b1axisx = board.createElement('axis', [[0,0], [1,0]], {}); | ||
+ | b1axisy = board.createElement('axis', [[0,0], [0,1]], {}); | ||
+ | |||
+ | var p = []; | ||
+ | var q = []; | ||
+ | p[0] = board.createElement('point', [-1,2], {style:6}); | ||
+ | p[1] = board.createElement('point', [3,-1], {style:6}); | ||
+ | var polynomial = 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', polynomial, 'x', -10, 10], {curveType:'graph'}); | ||
+ | |||
+ | function addPoint1() { | ||
+ | p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6})); | ||
+ | board.update(); | ||
+ | } | ||
+ | |||
+ | board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25}); | ||
+ | // Axes | ||
+ | b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {}); | ||
+ | b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {}); | ||
+ | |||
+ | q[0] = board2.createElement('point', [-1,2], {style:6}); | ||
+ | q[1] = board2.createElement('point', [3,-1], {style:6}); | ||
+ | var polynomial2 = function(x) { | ||
+ | var i; | ||
+ | var y = 0.0; | ||
+ | var xc = []; | ||
+ | for (i=0;i<q.length;i++) { | ||
+ | xc[i] = q[i].X(); | ||
+ | } | ||
+ | for (i=0;i<q.length;i++) { | ||
+ | var t = q[i].Y(); | ||
+ | for (var k=0;k<q.length;k++) { | ||
+ | if (k!=i) { | ||
+ | t *= (x-xc[k])/(xc[i]-xc[k]); | ||
+ | } | ||
+ | } | ||
+ | y += t; | ||
+ | } | ||
+ | return y; | ||
+ | }; | ||
+ | graph2 = board2.createElement('curve', ['x', polynomial2, 'x', -10, 10], {curveType:'graph'}); | ||
+ | |||
+ | function addPoint2() { | ||
+ | q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6})); | ||
+ | board2.update(); | ||
+ | } | ||
+ | |||
+ | board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25}); | ||
+ | // Axes | ||
+ | b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {}); | ||
+ | b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {}); | ||
+ | graph3 = board3.createElement('curve', ['x', function(x){return polynomial(x)/polynomial2(x);}, 'x', -10, 10], {curveType:'graph',strokeColor:'#ff0000'}); | ||
+ | </source> | ||
[[Category:Examples]] | [[Category:Examples]] |
Revision as of 11:31, 16 December 2008
Polynomial f:
Polynomial g:
Rational function
:
References
The underlying JavaScript source code
board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
// Axes
b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
var p = [];
var q = [];
p[0] = board.createElement('point', [-1,2], {style:6});
p[1] = board.createElement('point', [3,-1], {style:6});
var polynomial = 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', polynomial, 'x', -10, 10], {curveType:'graph'});
function addPoint1() {
p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
board.update();
}
board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
// Axes
b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {});
b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {});
q[0] = board2.createElement('point', [-1,2], {style:6});
q[1] = board2.createElement('point', [3,-1], {style:6});
var polynomial2 = function(x) {
var i;
var y = 0.0;
var xc = [];
for (i=0;i<q.length;i++) {
xc[i] = q[i].X();
}
for (i=0;i<q.length;i++) {
var t = q[i].Y();
for (var k=0;k<q.length;k++) {
if (k!=i) {
t *= (x-xc[k])/(xc[i]-xc[k]);
}
}
y += t;
}
return y;
};
graph2 = board2.createElement('curve', ['x', polynomial2, 'x', -10, 10], {curveType:'graph'});
function addPoint2() {
q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
board2.update();
}
board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
// Axes
b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
graph3 = board3.createElement('curve', ['x', function(x){return polynomial(x)/polynomial2(x);}, 'x', -10, 10], {curveType:'graph',strokeColor:'#ff0000'});