Reply To: Spikey’s Math Lab

[Ingmar Franz]

@spikeyxxx I’m just reading about the “Mapping Node” and the order of transformations in the “Blender 2.93 Manual”:

Vector Type

The node applies the transformation differently depending on the semantic type of the input vector.

Point

For this vector type, the node performs a straightforward transformation.

Transforming a texture coordinates is analogous to transforming a UV map. For instance, translating the texture coordinates along the positive X axis would result in the evaluated texture to move in the negative X axis, much like if one translated a UV map. Similarly, scaling the texture coordinates up would result in the evaluated texture to scale down. So transforming the texture coordinates would appear to have the opposite effect on the evaluated texture.

The order of transformation is: Scale –> Rotate –> Translate, which means:

• Translation moves the input along the local rotation axis.

• Rotation rotates the input around the origin of the space.

• Scaling scales the input along the global axis.

Texture

For this vector type, the node performs an inverse transformation.

Inverse transforming a texture coordinates would, as opposed to the Point type, transform the evaluated texture itself. For instance, translating the texture coordinates along the positive X axis would result in the evaluated texture to move in the positive X axis, as one would expected. Similarly, scaling the texture coordinates up would result in the evaluated texture to scale up, as one would expect.

The order of transformation is: Translate –> Rotate –> Scale, which means:

• Translation moves the input along the global axis.

• Rotation rotates the input around the translation vector.

• Scaling scales the input along the local rotation axis.

I’m wondering what “global axis” and “local rotation axis” are meaning here and why for example “Scaling” in “Point” mode uses the “global axis” whereas in “Texture” mode it uses the “local rotation axis”.

And what are the usecases for the “Normal” and “Vector” modes?