2-cells in general -pictures

2 ( =@ @<#554#><#554#> @<#555#><#555#> @<#556#><#556#> @<#557#><#557#>

@#1#<#1016#>@@twocelll<#558#>#1<#558#><#1016#> @twocelll#1#2<#1113#>251 <#1017#>twocelll@@@#1<#559#>#2<#559#><#1017#><#1113#>

@#1#<#1018#>@@uppertwocelll<#560#>#1<#560#><#1018#> @uppertwocelll#1#2<#1114#>252 <#1019#>twocelll@@@#1<#561#>#2<#561#><#1019#><#1114#>

@#1#<#1020#>@@lowertwocelll<#562#>#1<#562#><#1020#> @lowertwocelll#1#2<#1115#>253 <#1021#>twocelll@@@#1<#563#>#2<#563#><#1021#><#1115#>

@#1#<#1022#>@@compositemapp<#564#>#1<#564#><#1022#> @compositemapp#1#2<#1116#>254 <#1023#>twocelll@@@#1<#565#>#2<#565#><#1023#><#1116#> @twocelll@<#1024#>256 @ @ =@path <#1024#>

@twocell#1<#1025#>@<#569#>twocell@@<#569#>@@ [#1]<#1025#> @uppertwocell#1<#1026#>@<#570#>twocell@@<#570#>@@ [#1]<#1026#> @lowertwocell#1<#1027#>@<#571#>twocell@@<#571#>@@ [#1]<#1027#> @compositemap#1<#1028#>@<#572#>twocell@@<#572#>@@ [#1]<#1028#> )

3
#code573#

#math460#

#code589#

The code shown is a compact way to place a chain of 2-cells within a picture. It illustrates a standard technique for using || to find a ;SPMlt;pos;SPMgt; to be used for part of a picture, then subsequently reuse it. Also it is possible to use || or ;SPMlt;decor;SPMgt;s to specify the 2-cells, giving the same picture.

The || variant is usually preferable as this maintains the size of the object at c, while the || variant leaves a rectangular object having p and c on opposite sides.

2 This is used outside of diagrams.

( @twocell@#1<#1117#>[@[<#1036#>@=<#600#>#1<#600#>@@twocell@<#1036#>267 @<#1037#>#1<#601#><#601#><#1037#> @ @ =@path @ <#1117#> )

This hack is necessary, since |@[##1]<#605#>#1##1<#605#>| will strip braces.

( @@twocell@<#1118#>@##1]<#1038#>@<#606#>##1<#606#><#1038#>270 @##1]<#607#>@##1<#607#>@ <#1118#> )

2 : These are supposed to allow |.̇.twocell<#608#>...<#608#>| to work. At present it seems to be impossible to do this.

( )

...since the contents of |<#609#>..<#609#>| is variable.

2 Finish off the box, set up the object size, establish the |@@ | and |@@ | methods.

( @@DONE<#1039#>285 @ @=@- @;SPMgt;@ =@ =@ =-@ =@ @ii=@ii- @ii;SPMgt;@ =@ii =@ =@ii =@ @h<#615#>--@ <#615#>286 @;SPMlt;@ @@ne @=@ @ii;SPMgt;@ @=@ii @=@ @=@ @=-@ii =<#616#><#616#>@false @false <#1039#>291 )

modified |@@ | and |@@ |

( @@Twocell<#619#>@ <#619#>

@@Twocell<#1040#>@h<#620#>@ <#620#>292 @=@ @=@ @=@ @ <#1040#> )

2 |@@| is the main switching engine, taking 9 parameters determining which pieces to set and where to position them. This includes curvature of the squines, whether to draw two squines or only one, or to use straight lines, whether to have a central Arrow and its orientation, contants of labels and their positions.

The current p and c are the extents of the connection these are stored as |;SPMquot;@p;SPMquot;| and |;SPMquot;@c;SPMquot;| for repeated use;

#defs1621#

The following tokens may appear as parameters in |#9|: |!|, |^|, |_|, |=|, |A|, |V|, |H|

( mod@ @

@@@#1#2#3#4#5#6#7#8#9!!!<#1126#>294 @<#627#>#9<#627#>295 #9!#9A#9V#9H#5/#5b#5B#5@ @#9 @<#639#><#639#>@ @ @ @<#642#>@c<#642#>@@<#643#>@p<#643#>@ @<#644#>@c<#644#>@@ @@<#645#>.5<#645#>302 @<#646#>@m<#646#>@<#647#>@m1<#647#>@<#648#>@m2<#648#>303 #5t @<#649#>@@<#649#>305 @@ @ @ @<#650#>#1<#650#>@ @=@@=#1@ @=@ @<#1041#>@i<#651#>@<#651#>@<#1041#> @<#1042#>@i<#652#>#1@<#652#>@<#1042#>@ @ @ @@ @<#653#>+<#653#><#654#><#654#>@<#655#>@m1<#655#>306 @<#656#>#1<#656#>@ @<#657#>@@<#657#>@<#1043#>@<#658#><#658#><#659#>-<#659#><#1043#> @<#660#>#1<#660#>@ @=@@=#1@ @=@ @<#661#>@@<#661#>307 @@ @@ @i<#662#>@<#662#>@@ @ @<#663#>@m1<#663#>308 @<#664#>@p<#664#>@@<#665#>@c<#665#>309 @<#666#>#1<#666#>@ @<#667#>@@<#667#>@<#1044#>@<#668#><#668#><#669#>-<#669#><#1044#> @<#1119#>@@ @@ @ @ @i<#670#>#1@<#670#>@@ @ @<#671#>@m1<#671#>@<#672#>@p<#672#>@@<#673#>@c<#673#>310 @ @<#1045#>@<#675#>;SPMquot;@m1;SPMquot;<#675#><#1045#>312 @####1<#1046#>@<#676#>####1<#676#><#1046#>@<#1047#>313 @<#677#>@ ;SPMquot;@m1;SPMquot;<#677#><#1047#>314 @ <#1119#>315 @ @<#678#>#1<#678#>@ mod@ @ @@ @@ #5t @ @ @ @@@ @ @ @ @<#1050#>@<#682#><#682#><#683#>|<#683#><#1050#>320 @##1##<#1051#>@<#684#>##1<#684#><#1051#>321 @<#1052#>@@ <#685#><#685#><#1052#>322 @ @<#686#>#6<#686#>@ @<#687#><#687#> @<#1053#><#688#><#688#><#1053#>@ @@<#689#><#689#> @#3@<#690#><#690#> @<#1054#>@@ @@ @@<#691#>.5<#691#>@ @ @@ @@ @<#692#>#1<#692#>@ @@@=#1@ @;SPMlt;@ @ @ @ @ @i<#693#>#3@<#693#>@@ @ @<#694#>#6<#694#><#1054#>324 @ @<#695#>#1<#695#>@ #5b327 @ <#696#>@ <#696#>@@ @ @@<#697#>0<#697#>@ @ @ @<#1055#><#699#>;SPMgt;<#699#><#1055#>329 @ @ @<#700#><#700#><#701#>;SPMlt;<#701#>330 @ @##1##<#1056#>@<#702#>##1<#702#><#1056#>331 @@ <#703#><#703#>@ @##1##<#1057#>@<#704#>##1<#704#><#1057#>@@ <#705#><#705#>332 #5@333 334 @@ @@ @ @@<#706#>1<#706#>@ @ @ @<#708#><#708#><#709#>;SPMgt;<#709#>336 @##1##<#1058#>@<#710#>##1<#710#><#1058#>@@ <#711#><#711#>337 #5B338 @ <#712#>@ <#712#>@@ @ @@<#713#>0<#713#>@ @ @ @<#1059#><#715#>;SPMgt;<#715#><#1059#>340 @ @ @<#716#><#716#><#717#>;SPMlt;<#717#>341 @@##1##<#1060#>@<#718#>##1<#718#><#1060#>342 @@ <#719#><#719#>@ @##1##<#1061#>@<#720#>##1<#720#><#1061#>@ <#721#><#721#>343 #5/ @ @@ @@ @ @@<#723#>0<#723#>@ @ @##1##<#1062#>@<#724#>##1<#724#><#1062#>@@ <#725#><#725#>345 @<#726#>@p<#726#>@@<#727#>@c<#727#>@@ @<#728#>@m<#728#>347 #5t @<#729#>@m2<#729#>@<#730#>@m1<#730#>@ @<#731#>@c<#731#>@@ @<#732#>#1<#732#>@ @<#733#>@@<#733#>@<#1063#>@<#734#><#734#><#735#>-<#735#><#1063#> #5o @<#736#>@m2<#736#>@<#737#><#737#>348 349 @<#738#>#1<#738#>@ @=@@=#1@ @=@ @<#739#>@@<#739#>350 @@ @@ @i<#740#>@<#740#>@@ @ @<#741#>@m2<#741#>351 @<#1064#>@<#742#>@p<#742#>@@<#743#>@c<#743#>@@<#1064#>352 @<#1120#>@@ @@ @ @ @i<#744#>#1@<#744#>@@ @ @<#745#>@m2<#745#>@<#746#>@p<#746#>@@<#747#>@c<#747#>353 @ @<#1065#>@<#749#>;SPMquot;@m2;SPMquot;<#749#><#1065#>355 @####1<#1066#>@<#750#>####1<#750#><#1066#>@<#1067#>356 @<#751#>@ ;SPMquot;@m2;SPMquot;<#751#><#1067#>357 @ <#1120#> @ @<#752#>#1<#752#>@ #5o mod@ @@<#1121#>@@ @@ #5t @ @ @ @@@ @ @ @ @<#1070#>@<#756#><#756#><#757#>|<#757#><#1070#>361 @####1####<#1071#>@<#758#>####1<#758#><#1071#>362 @<#1072#>@@ <#759#><#759#><#1072#> @ <#1121#>@<#760#><#760#> @ @<#761#>#7<#761#>@ @<#762#><#762#> @<#1073#><#763#><#763#><#1073#>@ @@<#764#><#764#> @#4@<#765#><#765#> @<#1074#>@@ @@ @@<#766#>.5<#766#>@ @ @@ @@ @<#767#>#1<#767#>@ @@@=#1@ #5t@;SPMlt;@ @ @ @ @ @;SPMlt;@ @ @ @ @ @i<#768#>#4@<#768#>@@ @<#769#>#7<#769#><#1074#>364 @ @<#770#>#1<#770#>@ #5o #5b366 @ <#771#>@ <#771#>@@ @ @@<#772#>0<#772#>@ @ @ @<#1075#><#774#>;SPMgt;<#774#><#1075#>368 @ @ @<#775#><#775#><#776#>;SPMlt;<#776#>369 @ @##1##<#1076#>@<#777#>##1<#777#><#1076#>370 @@ <#778#><#778#>@ @##1##<#1077#>@<#779#>##1<#779#><#1077#>@ <#780#><#780#>371 #5/ @<#781#>@<#781#>@@ @ @@<#782#>0<#782#>@ @ @ @<#1078#><#784#>;SPMgt;<#784#><#1078#>373 @ @ @<#785#><#785#><#786#>;SPMlt;<#786#>374 @@##1##<#1079#>@<#787#>##1<#787#><#1079#>375 @@ <#788#><#788#>@ @##1##<#1080#>@<#789#>##1<#789#><#1080#>@@ <#790#><#790#>376 #5@377 378 @@ @@ @ @@<#791#>1<#791#>@ @ @ @<#793#><#793#><#794#>;SPMgt;<#794#>380 @##1##<#1081#>@<#795#>##1<#795#><#1081#>@@ <#796#><#796#>381 #5B382 @ <#797#>@ <#797#>@@ @ @@<#798#>0<#798#>@ @ @ @<#1082#><#800#>;SPMgt;<#800#><#1082#>384 @ @ @<#801#><#801#><#802#>;SPMlt;<#802#>385 @@##1##<#1083#>@<#803#>##1<#803#><#1083#>386 @@ <#804#><#804#>@ @##1##<#1084#>@<#805#>##1<#805#><#1084#>@@ <#806#><#806#>387 @ @ <#808#>@ <#808#>@@ @ @@<#809#>0<#809#>@ @ @##1##<#1085#>@<#810#>##1<#810#><#1085#>@@ <#811#><#811#>389 @<#812#>#1<#812#>@ @=@@=#1@ @;SPMlt;@ @<#813#>@m2<#813#>@@<#814#>@m1<#814#>393 @<#815#>@m1<#815#>@@<#816#>@m2<#816#>394 @@ @<#817#>@m<#817#>395 @ @<#818#>_<#818#>@ @ @<#820#>@ @<#820#>@=#2@ @@ @i<#821#>@<#821#>@@ @ @<#822#>@m<#822#>398 @##1##<#1086#>@<#823#>##1<#823#><#1086#>@@ <#824#><#824#>399 @<#825#>^<#825#>@ @ @<#827#>_<#827#>@<#829#>@ @<#829#>@=#2@ @@ @i<#830#>@<#830#>@@ @ @<#831#>@m<#831#>@ @##1##<#1087#>@<#832#>##1<#832#><#1087#>@@ <#833#><#833#>403 @<#834#>=<#834#>@ @ @<#836#>@ @<#836#>406 @=#2@ @@ @@ @i<#837#>@<#837#>@@ @ @<#838#>@m2<#838#>407 @<#839#>@m<#839#>408 @<#840#>@ @<#840#>409 @=#2@ @-@ @@ @i<#841#>@<#841#>@@ @ @<#842#>@m1<#842#>410 @<#843#>@m2<#843#>@@<#844#>@m1<#844#>@<#845#>2<#845#><#846#>-<#846#>411 @<#847#>#8<#847#>@ @<#848#><#848#>@<#1088#>415 @ @@<#849#>.5<#849#>416 @<#850#>=<#850#>@ @ @@<#852#>.5<#852#>417 @<#853#>_<#853#>@ @ @<#855#>@m<#855#>418 @@ @@ @@ @ @<#857#>=<#857#>@ @ @<#860#>_<#860#>@ @ @i<#864#>@ <#864#>@@ @ @<#865#>#8<#865#>423 <#1088#>@ @ <#1126#>424 )

These are used to establish the location for the module-map indicator, giving best aesthetic appeal. It finds the location whose parameter value is the average of half-way along the complete curve and the average of parameter values at the the edges.

( @@<#1089#>@ @@@ <#1089#>

@@@#1;#2,#3;#4,<#1090#>426 @=#2@-#4 @ 2@ @ by4 @ <#1090#>427 )

2