Difference between revisions of "Shear transformation"

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Line 49: Line 49:
 
var r2 = board.create('line', [[0, 0], q1], {straightFirst: false});
 
var r2 = board.create('line', [[0, 0], q1], {straightFirst: false});
  
var s1 = board.create('segment', [p, p1], {dash:2});
+
var s3 = board.create('segment', [p, p1], {dash:2});
var s2 = board.create('segment', [px, p], {dash:2});
+
var s4 = board.create('segment', [px, p], {dash:2});
  
 +
board.create('hatch', [s1, 1]]);
 +
board.create('hatch', [s2, 1]]);
 +
 +
board.create('hatch', [s3, 2]]);
 +
board.create('hatch', [s4, 2]]);
  
 
</jsxgraph>
 
</jsxgraph>

Revision as of 09:28, 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: '&phi;(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});