Shear transformation using GameObject transformations

Question

Is it possible to create shear transformation (for 2 or at least 1 axis) using cascade of GameObject transform operations?

I know that t$$anonymous$$s is possible to do using Mesh API or proper shader, but I would like to know if the same effect can be ac$$anonymous$$eved using only plain GameObjects and some scripting instead.

Answer 1

Best Answer

Answer by Trejkaz · Jun 20, 2018 at 09:35 AM

It can be done. Example:

Outermost game object: Rotation X=22.5, Y=0, Z=0
Next game object in: Scale X=1, Y=0.3826834, Z=0.9238795
Next game object in: Rotation X=-45, Y=0, Z=0
Next game object in: Scale X=1, Y=2, Z=1.414214
Standard unit cube inside that.

Produces a 45 degree shear on X:

Screenshot

The general case:

Rotate by X=theta/2 counter-clockwise
Scale by Y=sin(theta/2), Z=cos(theta/2)
Rotate by X=45 degrees clockwise
Scale by Y=sqrt(2)/sin(theta), Z=sqrt(2).

You can probably reduce that to two game objects but I left it as 4 to illustrate how many transformations are being done.

shear.png (21.0 kB)

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theNfan · Sep 07, 2022 at 03:28 PM 0

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I know this is old, but I really don't see how you got to these numbers with these formulas.

A simpler method can be found here: https://twitter.com/MajorMcDoom/status/1231447166092054528 Simply nest the object to shear in another, rotate the outer one way, rotate the inner another way, scale the outer object, boom!

Answer 2

Answer by steakpinball · May 06, 2015 at 05:56 PM

No. Transforms can only translate, rotate, and scale. Combining those operations never produces shear. You will have to use somet$$anonymous$$ng else to produce shear.

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Trejkaz · Jun 20, 2018 at 09:35 AM 0

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Or you could use game objects and rotations and scaling. Example in my alternative answer.

Bunny83 · Jun 20, 2018 at 10:08 AM 1

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This answer is only true if you only use a uniform scale. If you have a non-uniform scale it can produce a shear

Shear transformation using GameObject transformations

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