Lagrange interpolation, show term - Revision history

A WASSERMANN at 06:58, 4 October 2022

2022-10-04T06:58:25Z

← Older revision		Revision as of 06:58, 4 October 2022
Line 51:		Line 51:
	var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});		var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});
	var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});		var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

			var txt = board.create('text', [-3, -4, () => f.getTerm(2, 't', ' * ')], {fontSize: 16});

	function addPoint() {		function addPoint() {

A WASSERMANN at 06:57, 4 October 2022

2022-10-04T06:57:48Z

← Older revision		Revision as of 06:57, 4 October 2022
Line 17:		Line 17:
	var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});		var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});
	var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});		var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

			var txt = board.create('text', [-3, -4, () => f.getTerm(2, 't', ' * ')], {fontSize: 16});

	function addPoint() {		function addPoint() {
Line 43:		Line 45:
	var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});		var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});

	var p = [];		var points = [];
	p[0] = board.create('point', [-1,2], {size:4});		points[0] = board.create('point', [-1,2], {size:4});
	p[1] = board.create('point', [3,-1], {size:4});		points[1] = board.create('point', [3,-1], {size:4});
	var f = JXG.Math.Numerics.lagrangePolynomial(p);		var f = JXG.Math.Numerics.lagrangePolynomial(points);
	var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});		var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});
	var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});		var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

	function addPoint() {		function addPoint() {
	p.push(board.create('point',[(Math.random()-0.5)10,(Math.random()-0.5)3],{size:4}));		points.push(board.create('point',[(Math.random()-0.5)10,(Math.random()-0.5)3],{size:4}));
	board.update();		board.update();
	}		}

			function removePoint() {
			if (points.length > 2) {
			board.removeObject(points[points.length - 1]);
			points.pop();
			}
			//board.update();
			}

			document.getElementById('add').addEventListener("click", addPoint, false);
			document.getElementById('remove').addEventListener("click", removePoint, false);
	</source>		</source>

A WASSERMANN at 06:55, 4 October 2022

2022-10-04T06:55:36Z

← Older revision		Revision as of 06:55, 4 October 2022
Line 24:		Line 24:

	function removePoint() {		function removePoint() {
	~~console.log("X", points);~~		if (points.length > 2) {
	if (points.~~Length~~ > 2) {		board.removeObject(points[points.length - 1]);
	board.removeObject(points[points.~~Length~~ - 1]);
	points.pop();		points.pop();
	}		}

A WASSERMANN at 06:54, 4 October 2022

2022-10-04T06:54:56Z

← Older revision		Revision as of 06:54, 4 October 2022
Line 11:		Line 11:
	var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});		var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});

	var p = [];		var points = [];
	p[0] = board.create('point', [-1,2], {size:4});		points[0] = board.create('point', [-1,2], {size:4});
	p[1] = board.create('point', [3,-1], {size:4});		points[1] = board.create('point', [3,-1], {size:4});
	var f = JXG.Math.Numerics.lagrangePolynomial(p);		var f = JXG.Math.Numerics.lagrangePolynomial(points);
	var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});		var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});
	var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});		var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

	function addPoint() {		function addPoint() {
	p.push(board.create('point',[(Math.random()-0.5)10,(Math.random()-0.5)3],{size:4}));		points.push(board.create('point',[(Math.random()-0.5)10,(Math.random()-0.5)3],{size:4}));
	board.update();		board.update();
	}		}

	function removePoint() {		function removePoint() {
	console.log("X", ~~p.Length~~);		console.log("X", points);
	if (p.Length > 2) {		if (points.Length > 2) {
	board.removeObject(p[p.Length - 1]);		board.removeObject(points[points.Length - 1]);
	p.pop();		points.pop();
	}		}
	//board.update();		//board.update();

A WASSERMANN at 06:53, 4 October 2022

2022-10-04T06:53:48Z

← Older revision		Revision as of 06:53, 4 October 2022
Line 4:		Line 4:
	<html>		<html>
	<form>		<form>
	<input type="button" value="Add point~~" onClick="addPoint()~~">		<input id="add" type="button" value="Add point">
	<input type="button" value="Remove point~~" onClick="removePoint()~~">		<input id="remove" type="button" value="Remove point">
	</form>		</form>
	</html>		</html>
Line 31:		Line 31:
	//board.update();		//board.update();
	}		}

			document.getElementById('add').addEventListener("click", addPoint, false);
			document.getElementById('remove').addEventListener("click", removePoint, false);

	</jsxgraph>		</jsxgraph>

A WASSERMANN at 06:50, 4 October 2022

2022-10-04T06:50:42Z

← Older revision		Revision as of 06:50, 4 October 2022
Line 24:		Line 24:

	function removePoint() {		function removePoint() {
			console.log("X", p.Length);
	if (p.Length > 2) {		if (p.Length > 2) {
	board.removeObject(p[p.Length - 1]);		board.removeObject(p[p.Length - 1]);

A WASSERMANN: Created page with "Constructs a polynomial of degree $n$ through $n+1$ given points. Points can be added by clicking on "Add point". The dotted line is the graph of the fir..."

2022-10-04T06:50:02Z

Created page with "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 fir..."

New page

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.
<html>
<form>
<input type="button" value="Add point" onClick="addPoint()">
<input type="button" value="Remove point" onClick="removePoint()">
</form>
</html>
<jsxgraph box="box" width="600" height="400">
var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});

var p = [];
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

function addPoint() {
p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
board.update();
}

function removePoint() {
if (p.Length > 2) {
board.removeObject(p[p.Length - 1]);
p.pop();
}
//board.update();
}

</jsxgraph>

=== References ===
* [http://en.wikipedia.org/wiki/Lagrange_polynomial http://en.wikipedia.org/wiki/Lagrange_polynomial]

=== The underlying JavaScript code ===
<source lang="javascript">
var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});

var p = [];
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});

function addPoint() {
p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
board.update();
}
</source>

[[Category:Examples]]
[[Category:Calculus]]
[[Category:Interpolation]]