# Transformations -- Shearing an Object along line or axes

lewws shared this idea 11 years ago

In Geogebra, we have tools for reflection, rotation, translation and dilation (enlargement) of objects.

Is there any tool for shearing an object along the x or y axis or along a selected line ?

If not, could we include such a tool?

Are there any user created tools for this so far?

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In the 4.0 beta there is ApplyMatrix command, you can try ApplyMatrix[{{1,0.5},{0,1}},object].

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While kondr's work around may work, it would be interesting to have a tool the would draw create a shear along a separate object's parts. This shear could illustrate earthquakes and the collision of two objects traveling along a path.

I would be nice to be able to have middle school and high school students that do not have high mathematical skills to be able to do this. Things like this increase some students interest in math.

Tony

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In the attached file, there is a way how to make generic linear transform. You can move the points A,B,C and see how the curve and triangle are transformed.

Do you think a tool whose inputs are points A, B, C and the object to be transformed is a good way to present generic linear transforms to high school students?

A -- image of (0,0)

B -- image of (1,0)

C -- image of (0,1)

PS: The file is for GGB4 Beta only.

https://ggbm.at/545527

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Thank you kondr, for your efforts.

I note that your ggb applet produces a 3D rotation effect when moving points A, B or C.

It appears to be able to shear GHI if I turn off the spiral lines which make one feel the 3D effect.

I need some tool like the sequence for "Dilate" tool, where in the case for shear we can select Object, then choose the direction of shear and then provide (in a dialogue box) the shear factor..

I also include the ggb file to show what I need.

https://ggbm.at/545535

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Since 3.9.72

Shear[object,line,ratio]

Stretch[object,line,ratio]

Note that line can be also segment or vector. Object cannot be list or function.