Shear transformation: Difference between revisions

From JSXGraph Wiki
No edit summary
No edit summary
Line 4: Line 4:
\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>
Line 20: Line 25:


<source lang="javascript">
<source lang="javascript">
</source>
</source>
[[Category:Examples]]
[[Category:Examples]]
[[Category:Geometry]]
[[Category:Geometry]]

Revision as of 07:11, 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