http://www.abdulbaki.org/Unfolding_A_Cube.html has 10 ways of unfolding a cube which fit in a 4x3 (or 3x4) array. (And an 11th which does not.)
-- Raul On Thu, Jun 25, 2015 at 11:30 AM, Mike Day <mike_liz....@tiscali.co.uk> wrote: > I'm not sure I made it clear that I'd assumed each of BLACK BLUE ... etc > is a numerical triple, ie 0 0 0 for BLACK, 1 1 1 for WHITE. > > So this line should have appeared: > 'BLACK BLUE GREEN CYAN RED MAGENTA YELLOW WHITE'=:#:i.8 > > Apologies also for using lower case for "blank" in the definition of plan; > I'd forgotten it was a defined global in my workspace. > > Here's a slightly modified definition of mycube, with localisation of the > nouns "plan" and "colours": > mycube=: 3 : 0 > > : > > nsteps =. 2 >. <: x > > 'A B C D H G F E' =. y > > BLANK =. < BLACK;BLACK;BLACK;BLACK > > FRONT =. < A;B;C;D > > BACK =. < H;G;F;E > > TOP =. < E;F;B;A > > LEFT =. < H;E;A;D > > RIGHT =. < F;G;C;B > > BASE =. < D;C;G;H > > plan =. BASE(<3 1)}FRONT(<2 1)}(LEFT,TOP,RIGHT)1}BACK(<0 1)}4 3$BLANK > > colours =. ,/,/>,"_1 each/"1 nsteps mysquarecolours each plan > > colours viewmat i.($plan)*nsteps+1 > > ) > > > It occurs to me that one could specify alternative "nets" to > represent the cube. You've chosen a cross, but you can also > have a T, and more generally, the left and right faces can > roll anywhere up and down their sides; and of course, we > can tip the whole thing on its side, or roll the base around > to the left of left or the right of right.... I suppose the > net-shape could be an optional left argument for a dyadic > > "cube" verb, probably easiest to have an arbitrary enumeration > of the net-shapes. > > I don't often use JHS, having got used to JQT. My problem with sending > messages seems to be a recent feature of my Thunderbird installation. > > I hope that helps. and hope that the code works for you. > If it does, then have a look at this and be very amazed! .... > 30 mycube BLACK,BLUE,WHITE,GREEN,RED,YELLOW,CYAN,:MAGENTA > > > Mike > > > On 25/06/2015 09:14, Linda Alvord wrote: >> >> Mike, I'm sorry you are having such a problem with the messages. I have >> found that if I run a working program in JHS and then copy the script and >> paste in an email, I can eliminate typing errors in the code. Then in the >> email you can write comments around it and not need NB. all the time. >> >> >> I got your code entered and it ran with no errors. However I tried >> >> Mycube '' and got no result. I'll look at it some more. >> >> Linda >> >> -----Original Message----- >> From: programming-boun...@forums.jsoftware.com >> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Mike Day >> Sent: Thursday, June 25, 2015 3:18 AM >> To: programm...@jsoftware.com >> Subject: Re: [Jprogramming] Trouble making patter for a color cube >> >> I'm still not sure the following got sent yesterday, so here's a fourth >> attempt. >> Sorry about the double-line-spacing, >> M >> >> On 24/06/2015 15:46, Mike Day wrote: >>> >>> I've just had a look at the correspondence. >>> >>> It seems to me that it's better to consider the 8 corners of the cube. >>> If we specify their colours, then we merely need to interpolate the >>> colours along the edges and within the faces. >>> >>> Here's an attempt to do that, plagiarising blatantly from Raul's >>> earlier postings. Over to Linda to render the code in basic J. >>> >>> The 8 corners may indeed use the 8 colours in #:i.8, but don't need >>> to do so, and may use 8 triples of any numbers in [0.0,1.0]. >>> >>> The code follows below, with some comments, and apologies for >>> line-wraps, line-skips or whatever. >>> >>> Also apologies for any typos in this patter, >>> >>> Mike >>> >>> NB. revision of Raul's colour-mixing verb, with 4 corner colours >>> rather than 3 NB. given corner colours ABCD (4x3 array), and x>1 steps >>> from A to B etc >>> >>> NB. make an (x+1)x(x+1)x3 array of mixed colours >>> >>> NB. assumes input colours are in [0,1], but output in [0,255] >>> >>> msc=:mysquarecolours =: 3 : 0 >>> >>> : >>> >>> nsteps =. x >>> >>> 'A B C D' =. y >>> >>> lamda =. (,:~-.)@:(%~ i.@>:) nsteps >>> >>> AB =. lamda +/@:(*/"1) A,:B NB. mix of colours between corners A & B >>> >>> CD =. lamda +/@:(*/"1) D,:C NB. mix of colours between corners C & D >>> >>> 1 0 2 |: <.255 * lamda +/@:(*/"1) AB,:CD NB. transpose 'cos I got the >>> order wrong! >>> >>> ) >>> >>> >>> NB. Cube layout: A-H label the corners; >>> >>> NB. (looked ok in the edit window, added ... to >>> NB. force spacing!!!) >>> NB. ..H-G >>> >>> NB. ..|+| >>> >>> NB. H-E-F-G sides are AB,BC,...,BF,EA,...FG,GH >>> >>> NB. |+|+|+| faces are ABCD, DCGH, ... HGFE >>> >>> NB. D-A-B-C >>> >>> NB. ..|+| >>> >>> NB. ..D-C >>> >>> NB. ..|+| >>> >>> NB. ..H-G >>> >>> >>> NB. verb to draw the plan >>> >>> NB. lhs = number of steps = %: number of facets on a face >>> >>> NB. rhs = 8 x 3 array of corner colours in range [0,1] >>> >>> mycube=: 3 : 0 >>> >>> : >>> >>> nsteps =. 2 >. <: x >>> >>> 'A B C D H G F E' =. y >>> >>> BLANK =. < BLACK;BLACK;BLACK;BLACK >>> >>> FRONT =. < A;B;C;D >>> >>> BACK =. < H;G;F;E >>> >>> TOP =. < E;F;B;A >>> >>> LEFT =. < H;E;A;D >>> >>> RIGHT =. < F;G;C;B >>> >>> BASE =. < D;C;G;H >>> >>> plan =: BASE(<3 1)}FRONT(<2 1)}(LEFT,TOP,RIGHT)1}BACK(<0 1)}4 3$blank >>> >>> colours =: ,/,/>,"_1 each/"1 nsteps mysquarecolours each plan >>> >>> colours viewmat i.4 3*nsteps+1 >>> >>> ) >>> >>> >>> NB. sample call using all colours in #:i.8 >>> >>> NB. 4 mycube BLACK,BLUE,WHITE,GREEN,RED,YELLOW,CYAN,:MAGENTA >>> >>> >>> NB. The colours don't have to be all distinct >>> >>> NB. 3 mycube BLACK,BLUE,WHITE,GREEN,RED,YELLOW,BLUE,:BLACK >>> >>> >>> On 24/06/2015 07:18, Raul Miller wrote: >>>> >>>> A color, for viewmat, the way you are using it, is a sequence of >>>> three integers in the range 0 .. 255. >>>> >>>> The problem is that none of the sequences in FRONT nor BASE are valid >>>> colors. >>>> >>>> This problem is made more confusing because while BLACK and WHITE are >>>> single valued "colors", the others range from black to white with the >>>> named color appearing in the middle. And then you're using just parts >>>> of those sequences. The grammar may be "simple" but the abstractions >>>> are not. >>>> >>>> So... there are several problems to fix here, but the biggest problem >>>> is that your results are not valid colors. If I subtract 255 from >>>> each of the values you have there, they are better, but still not >> >> correct. >>>> >>>> Anyways, if I look at the adjacent squares, FRONT should have: >>>> >>>> at index 0 (upper left corner): 255 0 0 at index 4 (upper right >>>> corner): 255 0 255 at index 20 (lower left corner): 255 255 0 at >>>> index 24 (lower right corner): 255 255 255 >>>> >>>> Similarly, BASE should have: >>>> >>>> at index 0: 255 255 0 >>>> at index 4: 255 255 255 >>>> at index 20: 0 255 0 >>>> at index 24: 0 255 255 >>>> >>>> Instead, you have this: >>>> >>>> 0 4 20 24{ FRONT -255 >>>> 255 255 255 >>>> 255 0 255 >>>> 255 255 0 >>>> 255 0 0 >>>> 0 4 20 24{ BASE -255 >>>> 255 255 255 >>>> 255 255 0 >>>> 0 255 255 >>>> 0 255 0 >>>> >>>> Hopefully this helps... >>>> >> > > > --- > This email has been checked for viruses by Avast antivirus software. > https://www.avast.com/antivirus > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
