Shear transformation: Difference between revisions

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var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true});
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true});


var x = board.defaultAxes.x;
var y = board.defaultAxes.y;
var y = board.defaultAxes.y;


var g0 = board.create('glider', [0, 2, y]);
var q = board.create('point', [1, 2], {name: 'q'});
var q1 = board.create('point', [
        () => q.X() + q.Y(),
        () => q.Y()
    ], {name: 'φ(q)'});
 
//var g0 = board.create('glider', [0, 2, y]);





Revision as of 07:13, 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