What a shear changes

A shear slides one coordinate in proportion to another while keeping parallel lines parallel.

In 2D, the common rules are x′=x+kyx' = x + ky or y′=y+kxy' = y + kx. In 3D the same idea extends by choosing which axis receives the shift.

The preview helps you confirm the direction of the slide before using the matrix in another transformation pipeline.

Quick reminders

  • The determinant of these standard shear matrices is 11, so area or volume scale is preserved.
  • A positive shear factor pushes the receiving axis in the positive direction of the driver axis.
  • Use the 3D mode when you need to model axis coupling before a rotation, reflection, or projection step.

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