Editing Glome tutorial (section)

===Transformations===
Transformations are a convenient way of moving, rotating, and stretching objects.

To move an object a by some vector v, we can say:

<haskell>
 transform a [translate v]
</haskell>

This effectively creates an instance of a in a new location.  This an efficient way of creating many copies of a complex object without using much extra space.  (Each transform uses 24 floating point numbers to store a matrix and its inverse that describe the transformation.)

"transform" takes a list, and we can combine several transformation and they behave as you might expect:

<haskell>
 transform a [translate (Vec 0 3 0),
              rotate (Vec 0 1 0) (deg 90),
              scale (Vec 2 2 2)]
</haskell>

This moves object "a" up three units, then rotates 90 degrees about the Y axis, and then stretches the object equally on all three axes by a factor of 2.

Stretching and rotations happen about the origin, so you might need to translate an object to the origin, rotate it, then translate it back in order for the translations to do what you want.  (This is consistent with how most graphics APIs work -- if you're familiar with, say, OpenGL or POV-Ray, this should be pretty familiar.)

Interestingly, performing multiple transformations at a time doesn't produce any more overhead than just performing one transformation; internally, any combination of transformations can be represented as a single matrix.

(Arcane trivia: internally, "transform" reverses the list of transformations before applying them.)

One caveat is that you should use transformations sparingly.  For instance, rather than creating a unit sphere and then scaling it and moving it into position, it's better to use the sphere's constructor the way it was intended.  A transformed sphere consumes more memory than just a sphere by itself, and rendering will be a little slower.

Cones and cylinders, on the other hand, are already stored as transformations (except for the rare case when you really do want a Z-axis aligned cone or cylinder), so transforming them won't take up any extra space.