Talk:Blender 3D: Noob to Pro/Coordinate Transformations

since when are translations are rotations not commutative?

I don't understand the illustration in the multiple transformations section of the Coordinate Transformations tutorial. (http://en.wikibooks.org/wiki/Blender_3D:_Noob_to_Pro/Coordinate_Transformations) Why would the rotation after a translation be any different than a rotation before the translation. The illustrations appear to show the object rotating around a different axes of rotation. Pastor Del (discuss • contribs) 05:36, 27 October 2011 (UTC)

I concur with Pastor Del. The point that transformations are not always commutative is correct, but translation & rotation should be (unless the coordinates were redefined between actions), and the illustration is hard to read. - Asterai

Nope. If the rotation occurs about the origin of the coordinate system, these two cases are different as shown in the text. Bear in mind that the coordinate system does not move with the object. So if the object starts at the origin and rotates about the origin and then translate with respect to the origin, this is different from translating with respect to the origin and then rotating (now at a distance so you might think of it as "revolving") about the origin. - Johnny Swatts

Non-linearity of translations
Translations are not non-linear because they "introduce curves where none where before", but because you cannot express a translation as a linear equation -- it's not possible to express a translation on the form Ax = y, where A is a 3x3x matrix and x and y are 3 vectors. You have to either introduce an extra vector and express it as Ax + t = y or go to 4-space (and then go back to 3-space).

Bad illustrations
The illustrations here with the moon lander are terrible - the object is too complicated and they don't illustrate the point well. Can we get some new ones?