Thanks, Brian.
I suspect R S and T are zero because "mysquarecolours" (msc)
is called for EVERY pane in the diagram, including those
not in the net, which default to black. It just happens that
every net has a null pane at the bottom right. msc is not clever
enough to check for all 4 colours being identical, so just goes
ahead and interpolates between 0 and 0, for AB, and does the same
again for DC, and then interpolates between two lines of all
zero. Sophisticated stuff!
Anyway, If you try, say,
#5 msc GREEN,BLUE,WHITE,:RED
you should find:
|:AB
0 0 0 0 0 0
1 0.8 0.6 0.4 0.2 0
0 0.2 0.4 0.6 0.8 1
|:CD
1 1 1 1 1 1
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
FWIW, the code for AB (and CD) is based on the interpolation
formula for a point p on line ab where lamda = |ap|/|ab|
p = lamda b + (1-lamda) a
By the way, I already owned up to gross plagiarism a week
or two ago, but it's worth repeating: I adapted the mixing
verb from Raul's good work; also indeed the variations on
the cube verb.
As for the rotations relative to net, here goes. Linda kicked off
this patter seeking to find nice representations for one of the
nets, which I loosely call a cross, and which is 5{NETS in my
script. Now look at 0{NETS, which I choose to call a T-shape.
How do you transform the shape in 5{NETS to that in 0{NETS?
It helps (perhaps!?) to label the cube's corners as ABCD (front)
and EFGH (back face but looking from the front).
Well - the LEFT face appears as H E A D, starting from the top
right corner going clockwise, in 5{NETS, our quasi-standard.
But it's DHEA when in the T-formation, ie it's rotated by one
right-angle clockwise. Similarly, the RIGHT face is FGCB in Linda's
first layout, 5{NETS, but becomes GCBF in the T-net, 1 rotation
anticlockwise.
As for the mnemonics for the faces, I inherited TOP BASE
FRONT BACK LEFT RIGHT from the preceding correspondence.
All but two start with distinct letters, allowing t f l r for their
abbreviations, but I needed to distinguish BASE and BACK,
and so chose s and k for them. And now I see that I uttered
a silly typo - please substitute
"NB. NETS - l = Left, r = Right, f = Front,"
for
"NB. NETS - l = Left, r = Red, f = Front,"
I'll try to correct that on my Google drive, hoping the link
isn't destroyed in the process.
Have fun,
Mike
On 02/07/2015 14:06, Brian Schott wrote:
Mike,
I think your scripts are very enlightening. I am enjoying trying to better
understand them. Thank you very much for your work here.
I thought I would try to better understand the issue of some viewmat
numbers being over 255. And although I see yours are all limited to 255, I
thought I would better understand the issue by studying the nouns AB, CD
and their resulting nouns, so I created the globals R, S, and T in msc, as
shown below. But to my surprise the resulting arrays contain all zeroes in
my experiments. Could you please comment?
msc=:mysquarecolours =: 3 : 0
:
nsteps =. x
'A B C D'=. y
lamda =. (,:~-.)@:(%~ i.@>:) nsteps
R=: AB =. lamda +/@:(*/"1) A,:B NB. mix colours between corners A & B
S=: CD =. lamda +/@:(*/"1) D,:C NB. mix colours between corners C & D
1 0 2 |: <.T=: 255 * lamda +/@:(*/"1) AB,:CD NB.|: 'cos I got order wrong!
)
I am also puzzled over the rotations you mention relative to net #6 faces.
Could you say more about that, please?
Btw, I will mention 2 peculiarities I noticed.
Why name bacK, k instead of b?
Why refer to Red as R, instead of Rear as R?
But unfortunately, as you can deduce, the depth of my understanding is
limited to such "peculiarities". <grin>
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