Difference between revisions of "Shear transformation"

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\varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix}
 
\varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix}
 
</math>
 
</math>
Points of type <math>{x\choose \lambda}</math> are mapped to:
+
Points of the form <math>{x\choose \lambda}</math> are mapped to:
 
:<math>
 
:<math>
\varphi{x\choose \lambda} =   
+
\varphi({x\choose \lambda}) {x + \lambda\choose}
 
</math>
 
</math>
 
  
 
<jsxgraph width="500" height="500">
 
<jsxgraph width="500" height="500">
 
JXG.Options.label.autoPosition = true;
 
JXG.Options.label.autoPosition = true;
 
JXG.Options.text.fontSize = 20;
 
JXG.Options.text.fontSize = 20;
 +
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true});
 +
 +
var y = board.defaultAxes.y;
 +
 +
var g0 = board.create('glider', [0, 2, y]);
 +
  
 
</jsxgraph>
 
</jsxgraph>
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<source lang="javascript">
 
<source lang="javascript">
 +
 +
 
</source>
 
</source>
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Revision as of 09:11, 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