Difference between revisions of "Shear transformation"
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var s4 = board.create('segment', [px, p], {dash:2}); | var s4 = board.create('segment', [px, p], {dash:2}); | ||
− | board.create('hatch', [s1, 1 | + | board.create('hatch', [s1, 1]); |
− | board.create('hatch', [s2, 1 | + | board.create('hatch', [s2, 1]); |
− | board.create('hatch', [s3, 2 | + | board.create('hatch', [s3, 2]); |
− | board.create('hatch', [s4, 2 | + | board.create('hatch', [s4, 2]); |
</jsxgraph> | </jsxgraph> |
Revision as of 09:29, 31 May 2021
Shear transformation
- [math] \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]{x\choose \lambda}[/math] are mapped to:
- [math] \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});