It's not immediately obvious what "pairs" signifies in, eg,
<@(pairs getRegion)@,:@(opposing&pairs"1) region
Is it (Are they) the same as "getPairs"?
Could you give an example?
Meanwhile, is this the sort of thing you're looking for, using
boxed forms, but they could be opened up?
pd1
1 5 2 4
3 1 4 6
5 3 6 2
crnrs =: ((2<\]) @: (,{. )"1) NB. alternative for corners
crnrs pd1
+---+---+---+---+
|1 5|5 2|2 4|4 1|
+---+---+---+---+
|3 1|1 4|4 6|6 3|
+---+---+---+---+
|5 3|3 6|6 2|2 5|
+---+---+---+---+
crnregs =: ((1&|.),:each(_1&|.) )@:crnrs NB. "regions" for corners
crnregs pd1
+---+---+---+---+
|3 1|1 4|4 6|6 3|
|5 3|3 6|6 2|2 5|
+---+---+---+---+
|5 3|3 6|6 2|2 5|
|1 5|5 2|2 4|4 1|
+---+---+---+---+
|1 5|5 2|2 4|4 1|
|3 1|1 4|4 6|6 3|
+---+---+---+---+
Probably not - as it just rotates pairs from the original pd1,
and doesn't seem to add much to that original.
Mike
On 12/10/2010 11:52, Justin Paston-Cooper wrote:
> Hello,
>
> I'm trying to implement a way to, given a region (a list of corners,
> corners being a pair of edge numbers), find all regions which are
> incident to it. I don't know how much I need to define for my problem
> to be solved. I'll just give the code here and I can explain more if
> needed. My idea is to find all of the regions which contain corners
> opposite (across a crossing) to corners in the given region, and to
> take the union.
>
> pd1 =: 3 4 $ 1 5 2 4 3 1 4 6 5 3 6 2 NB. A planar diagram of a trefoil knot
> getPairs =: {~ (,.0&C.)@i...@#
> corners =: getPairs"1 pd1
>
> cyclicNext =: 1 : '([ ((4 | u&+)@{.@(#~<&4)@] { {.@(#~<&4)) i."2)~'
> nextMatch =: {.@(((({:@[ = {...@])"1 # ]) ,/) -. 1 cyclicNext)
> getRegion =: (nextMatch&) (@{.) ($:@,`...@.(-: {:)~`) (`: 6)
> opposing =: 2 cyclicNext
>
> corners is an n x 4 x 2 matrix where each 4 x 2 table is a clockwise
> list of corners of a crossing. One can find the region in which a
> corner is by doing the following:
>
> region =: corners getRegion ,: 1 5
>
> The result in this case is 3 x 2
>
> 3 1
> 5 3
> 1 5
>
> For some reason
>
> <@(pairs getRegion)@,:@(opposing&pairs"1) region
>
> gives "stack error: opposing"
>
> But
>
> pairs getRegion"2 ,:@(opposing&pairs"1)region
>
> works fine.
>
> But strangely
>
> <@(pairs getRegion)"2 ,:@(opposing&pairs"1)region
>
> ┌───────┬───────┬───────┐
> │┌─────┐│┌─────┐│┌─────┐│
> ││┌───┐│││┌───┐│││┌───┐││
> │││2 4│││││4 6│││││6 2│││
> │││6 2│││││2 4│││││4 6│││
> │││4 6│││││6 2│││││2 4│││
> ││└───┘│││└───┘│││└───┘││
> │└─────┘│└─────┘│└─────┘│
> └───────┴───────┴───────┘
>
> At the moment I would just like a boxed list of the regions which
> result from each corner. I have tried to figure out the problem for
> ages now, and I'd be grateful for a hint.
>
> Justin
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