# Connection between rotate / translate / scale as operations in 3D space

This feels like a silly question, what am I missing:

I'm a 3D artist working on videogames. Sometimes I make 3D artworks like the ones here: http://samuelthomson.org/blog/2012/06/07/topologic-analogies-6-public-sphere-2/

Translating, rotating and scaling are fundamental to working in 3D in programs like blender, 3DSmax, Unity, etc.

In real life, if I pick up a banana I can easily rotate and translate it, but scaling feels impossible. What is the reason for this?

Are translation, rotation, and scale related on some deep fundamental level, in a similar way to angles on a triangle?

This is probably VERY wrong, but I think about things like a banana as a collection of atoms, and atoms as tiny little solar systems, and rotating it, I just fix a point of origin and rotate, and translating I pick a direction and...push. Anyway, rotating and translating feel like they belong in column A, but scaling feels like it belongs in column B, because it requires a point of origin AND a ...push (in a weird way in my mind) to get it how I want it to be.

And are hypercubes involved because they look like a small cube inside a scaled up cube?

Can anyone shed any light on this?

• Are you familiar with linear algebra? The ideas of the rotation and scaling can be succinctly described as linear transformations of 3D space, which may be represented as $3 \times 3$ matrices. Translations can be expressed as well if you allow for affine transformations. – Brian Apr 27 at 23:45