Shear transformation using GameObject transformations

Questions & Answers
1

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

I know that this is possible to do using Mesh API or proper shader, but I would like to know if the same effect can be achieved using only plain GameObjects and some scripting instead.

3

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:

119220-shear.png

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.

2

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