Cannon has two repeats (^:2 rather than ^2). I'm not sure why, but that approach seemed faster than arranging the trim and rtrim so that only one pass was needed.
As for p: that's so that the summation was able to sufficiently distinguish different cube positions. I hope this makes sense, -- Raul On Tue, Jul 18, 2023 at 6:22 PM 'Mike Day' via Programming <programm...@jsoftware.com> wrote: > > A couple of qs re canon: > why power 2? > why p:? Isn't the I. sufficient? > > Cheers, > > Mike > > Sent from my iPad > > > On 18 Jul 2023, at 22:14, Raul Miller <rauldmil...@gmail.com> wrote: > > > > One thing I was considering was categorizing shapes by their symmetry > > (#@~.@rotall"3) and testing fewer possibilities for shapes with higher > > symmetry. (because it's less effort to test the symmetry of one shape > > than to canonicalize all potential downstream shapes). But I hadn't > > developed that thought. > > > > -- > > Raul > > > >> On Tue, Jul 18, 2023 at 2:12 PM 'Michael Day' via Programming > >> <programm...@jsoftware.com> wrote: > >> > >> My not particularly small laptop manages to do that task in 19sec! > >> > >> Running jpm for extendall ^: (i.7) - taking ca 2.5 sec on this m/c - > >> seems to reveal > >> 0.08 sec for ~70500 reps in rotx, > >> 0.26 - ~280000 in roty, > >> 0.33, ~320000 in rotz > >> > >> I haven't looked deeply into the rots (!) - perhaps you could do something > >> otherthan use powers up to 3 . > >> > >> The representation is nice & concise. Wikipedia mentions dual graphs, > >> with cubes as nodes and face-face adjacency as links, but afaics, this > >> loses the 3rd dimension, even the 2nd in some cases; eg the V-tricube > >> is identical to the straight-3 polyomino in this rep. Arthur O'Dwyer > >> @ quuxplusone.github.io, subject polycube snakes & ouroboroi > >> uses srd .. as straight, right, down etc for the sub-set of singly > >> connected > >> (I think) pc's. > >> > >> All for now - got to go out, > >> > >> Mike > >> > >>> On 15/07/2023 22:03, Raul Miller wrote: > >>> https://en.wikipedia.org/wiki/Polycube > >>> > >>> Today, I've been playing with polycubes (which are polyhedrons formed > >>> from adjacent cubes). > >>> > >>> This requires both a representation -- a rank 3 bit array works > >>> nicely, and a mechanism for working with cubic symmetry. For that, I > >>> went with: > >>> > >>> rotx=: |."2@(2 1&|:) NB. rotate in the yz plane about the x axis > >>> roty=: |.@(1 0 2&|:) NB. rotate in the xz plane about the y axis > >>> rotz=: |.@(2 1 0&|:) NB. rotate in the xy plane about the z axis > >>> > >>> rotall=: {{ > >>> 'X Y Z'=. y > >>> rotx^:X roty^:Y rotz^:Z x > >>> }}"3 1&(4 4 4#:(i.20),24+i.4) > >>> > >>> Here, rotall gives all 24 rotations of cubic symmetry for a given > >>> collection of 3d cubes represented by a bit array. > >>> > >>> I decided to use a brute force mechanism to generate polycubes. In > >>> other words, pad the array representation and add a single cube in > >>> each of the locations adjacent to an existing cube: > >>> > >>> extend=: {{ > >>> Y=. (-2+$y){.(1+$y){.y > >>> new=. ($#:I.@,)Y < (_1&|. +. 1&|. +. 1&|."2 +. _1&|."2 +. 1&|."1 +. > >>> _1&|."1) Y > >>> ~.new {{canon 1 (,:x)} y}}"1 3 Y > >>> }} > >>> > >>> Here, Y is the y argument with an extra 0 of padding in all > >>> directions. And 'new' is the list of indices of empty locations > >>> adjacent to cube locations. > >>> > >>> I also need a verb (canon) to reduce these generated polycubes to > >>> canonical form. A lot of this is removing unnecessary rows, columns > >>> and planes of zeros. The rest of it is picking arbitrarily (but > >>> consistently) from the 24 possible symmetric rotations: > >>> > >>> offset=: {{ 1 i.~ +./+./"2 x |: *y }} > >>> trim=: {{ (0 offset y)}."3 (1 offset y)}."2 (2 offset y)}."1 y }} > >>> rtrim=: trim&.|.&.:(|."2)&.:(|."1) > >>> > >>> canon=: {{ rtrim {. (/: +/@p:@I.@,"3) rotall trim y }}^:2 > >>> > >>> Finally, I want to work with all polycubes of a specific order, and to > >>> get larger batch I can use; > >>> > >>> extendall=: {{ ~.;<@extend"3 y }} > >>> > >>> And, testing, this works: > >>> > >>> #@> extendall&.>^:(i.8)<1 1 1 1$1 > >>> 1 1 2 8 29 166 1023 6922 > >>> > >>> But, this is slow -- since I'm brute forcing all possibilities then > >>> discarding duplicates, I need almost seven seconds on the little > >>> laptop I'm currently using, to generate the above sequence. > >>> > >>> (Also, for visualization of individual polycubes, > >>> https://code.jsoftware.com/wiki/Scripts/Plot_3D works passibly well.) > >>> > >>> Does anyone here have the geometric insight to improve on this approach? > >>> > >>> Thanks, > >>> > >> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
