Shear transformation: Difference between revisions
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var y = board.defaultAxes.y; | var y = board.defaultAxes.y; | ||
var q = board.create('point', [ | var q = board.create('point', [2, 8], {name: 'q', snapToGrid: false}); | ||
var q1 = board.create('point', [ | var q1 = board.create('point', [ | ||
() => q.X() + q.Y(), | () => q.X() + q.Y(), | ||
| Line 36: | Line 36: | ||
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', [ | var p = board.create('glider', [1, 3, r1], {name: 'p'}); | ||
var p1 = board.create('point', [ | var p1 = board.create('point', [ | ||
() => p.X() + p.Y(), | () => p.X() + p.Y(), | ||
Revision as of 07:30, 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});
