Shear transformation: Difference between revisions
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JXG.Options.label.autoPosition = true; | JXG.Options.label.autoPosition = true; | ||
JXG.Options.text.fontSize = 20; | JXG.Options.text.fontSize = 20; | ||
JXG.Options.line.strokeWidth = 1; | |||
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 14, 14, -5], axis: true}); | var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 14, 14, -5], axis: true}); | ||
| Line 32: | Line 34: | ||
var l1 = board.create('line', [q, qx], {visible: false}); | var l1 = board.create('line', [q, qx], {visible: false}); | ||
var r1 = board.create('line', [[0, 0], q], {straightFirst: false | var r1 = board.create('line', [[0, 0], q], {straightFirst: false}); | ||
var p = board.create('glider', [1, 3, r1], {name: 'p'}); | var p = board.create('glider', [1, 3, r1], {name: 'p'}); | ||
| Line 40: | Line 42: | ||
], {name: 'φ(p)'}); | ], {name: 'φ(p)'}); | ||
var r2 = board.create('line', [[0, 0], q1], {straightFirst: false, | var qx = board.create('point', [ | ||
() => p.X(), | |||
() => 0 | |||
], {visible: false}); | |||
var r2 = board.create('line', [[0, 0], q1], {straightFirst: false}); | |||
var s1 = board.create('segment', [p, p1], {dash:2}); | |||
var s2 = board.create('segment', [px, p], {dash:2}); | |||
</jsxgraph> | </jsxgraph> | ||
Revision as of 07:26, 31 May 2021
Shear transformation
- [math]\displaystyle{ \varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix} }[/math]
Points of the form [math]\displaystyle{ {x\choose \lambda} }[/math] are mapped to:
- [math]\displaystyle{ \varphi({x\choose \lambda}) = {x + \lambda\choose} }[/math]
The underlying JavaScript code
JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 20;
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-10, 10, 10, -10], axis: true});
var x = board.defaultAxes.x;
var y = board.defaultAxes.y;
var q = board.create('point', [1, 2], {name: 'q', snapToGrid: true});
var q1 = board.create('point', [
() => q.X() + q.Y(),
() => q.Y()
], {name: 'φ(q)'});
var qx = board.create('point', [
() => q.X(),
() => 0
], {visible: false});
var s1 = board.create('segment', [q, q1], {dash:2});
var s2 = board.create('segment', [qx, q], {dash:2});
