Difference between revisions of "Shear transformation"

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Line 12: Line 12:
 
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, strokewidth: 1});
+
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, strokewidth: 1});
+
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 09:26, 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});