I wrote:
> Bearing in mind that I have no idea what I’m doing ..
>
> load’trig'
> PROJ =: 2 3 0 , 4 2 0 ,: 0 0 1
>
> rotate =: [: +/ .*/ 0 1 0 eul2rot"0 +&0 0 0
> eul2rot =: rotM proj { f
> rotM =: (2 # [) |. ]
> f =: 0:, 1:, cos, sin, -@sin
> …
>
> One may also consider doing something like ( PROJ { 0:`1:`cos`sin`(-@sin) )
> `:0 but at the moment I’m not seeing a lot of advantage in that (and some
> disadvantages).
Here’s one way to do that:
eul2rot2 =: ] 4 : 'y`:0 x' 0:`1:`cos`sin`(-@sin) {~ rotM&PROJ@[
Or, if the ][ bugs you:
eul2rot2 =: (4 : 'y`:0 x' 0:`1:`cos`sin`(-@sin) {~ rotM&PROJ)~
The disadvantage, of course, is that the need for (`:0) puts a lot of pressure
on us to use explicit code, in an otherwise function-level formulation.
But what I like about the gerund approach is that
a. we create and apply matrix of gerunds, which is the closest approximation
to the mathematical formulation (e.g. [1]) I think we’re going to get
b. one can see immediately what angular functions are being applied,
c. the rotation has been distilled, and is now applied to the most attract
representation of the rotation matrix: the integers representing the various
angular functions.
In re: (c), if we wanted to rotate the array of gerunds instead, we could do
that instead, of course.
I still think it would be cleaner to construct the matrix analytically, i.e.
re-derive the reasons those angular functions are applied at those particular
indices. Build it up, array-wise, from first principles (as it were).
-Dan
[1] Representation of rotation with a matrix of functions:
http://nghiaho.com/?page_id=846 <http://nghiaho.com/?page_id=846>
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