Astra
Giza
Heptagons






http://en.wikipedia.org/wiki/Heptagon
3 box or "cube" objects
stretched out to be lines
the middle at altitude 0 or ground level
left and right at 11 and 22 respectively
so when i'm done duplicating
i can just ungroup everything
and regroup
by thingy...
2nd group of 3 objects
is rotated to 51.43
as 360 / 7 =
51.428571 428571...
so they'll be a little off
hundredths of degrees
that's my maximum
limit of accuracy...
again, each new group rotating
...from the left or right or center
...are each at different altitudes
3rd group of 3 objects
is rotated to 102.86
as 51.43 x 2 = 102.86
for the 4th and 5th groups
i backtracked from the first
at -51.43 and -102.86
and notice, it's making
little pyramids, already
so that would actually be
6 and 7 in the rotation...
but i want to do this reflectively
and also measure the deviation
for the 6th and 7th
51.43 x 3 = 154.29
51.43 x 4 = 205.72
check the accuracy of my rounding
(360/7) x 1 =  51.428571 428571...
(360/7) x 2 = 102.857142 857142...
(360/7) x 3 = 154.285714 285714...
(360/7) x 4 = 205.714285 714285...
(360/7) x 5 = 257.142857 142857...
(360/7) x 6 = 308.571428 571428...
so, the one has drifted a digit, already
and comparing to rounded for the rest
51.43 x 5 = 257.15
51.43 x 6 = 308.58
and they're both
up a digit, too...
...and this is... a little confusing...
because it's one off in the rotation
the first group being rotated to 0
and then i'm shuffling, backtracking
but if i did it straight, it'd be boring
we'll see what the gaps are from 4 on up
...right now they're just over at 55 wide
and as promised
...the regrouping
above left: wireframe overhead view
of the middle altitude heptagon group
same group as shown selected above
above right: maximum overhead zoom
on the far right side crossing intersection
of the red selected heptagon group at left
at this scale, these proportions, an arbitrary 55 units length per side...
where these lines cross, their point of intersection, is 61.05 from center
likewise, a heptagon side
is proportionally set to
55 units from center
and that's center of the scene
as the zero coordinates of the
virtual world program positions
which is the same as the disc of the polygons...
but for now, the objects, when grouped together
will be rationalizing by how much space they span
and because the lines are overlapping just a touch
...those corners are... sticking out a little further...
and at different angles, thus affecting what the
collective center for the group turns out to be...
above image: the 2 heptagon groups are each
off-center by 2.92 units in opposite directions...
...below image: the above selected group is now ungrouped
showing all objects selected, and only their common values
above left: zoomed back in on the same
far right corner intersection as before...
same group selected... now ungrouped
to collectively resize all of those lengths
and i notch them all down 2 units, to 53
...and it's very close...
...just a tiny bit off, yet...
so, i regroup those objects
and the coordinates are now
...aha... right on even numbers
3 + 117 = 120
very interesting
...when the program spits out decimals, it means it's not exact...
even if it says 0.00 ...there's some minute discrepancy calculated
which comes up when rotating round objects (spheres, cylinders)
because the program appreciates those as polygons, primarily...
but the above positional coordinate coming out as 3 even exactly
well, i guess i must have just guessed the right digits accidentally
very cool... keep that in mind
...for now, i'm on a mission...
the assignment is
a specific design...
the 7 walls in a heptagonal room
are 5 cubits wide and 8 units tall
and i'm supposing those are
...internal measurements...
as in: from corner to corner
so, what i really want, is... for the internal edges to touch...
and then resize the whole group so that value becomes 5...
and i guess i can make the walls at whatever width i want...
which, will be reduced to whatever ratio that turns out to be
so, i'll stick with 1 (which is where i started wth them already)
keeping proportional percentages from 53 apparent and ready
because of that curious 3 + 117 = 120 ...for 7 sided geometry
and it works out so nicely and strangely
that 52.5 for each side lines up, exactly
i have definitely accidentally stumbled upon some
fundamental aspect of 7 sided polygon geometry
and that should be easy enough
to resize to an even 5 per side...
in the same manner as i did the sides
i'm duplicating corners from cylinders,
and here's a little squashed hexagon
above image, sides and corners all sorted out
rendered image shows the centered guide disc
and it doesn't matter how thick it is, or texture
right image, with guide disc now hidden
swoop in angle closeup on a random corner
the yellow dot is the top of one of the cylinders
for the corner intersections of the original lines
below image, in the overhead wireframe
with the corners resized to 1.14 diameter
they seem to fit perfectly, and nice number
...right image: just a tiny stripe showing at the joint...
also, in this program, when objects are the same size
...instead of merging... the textures tend to overlap...
so, in both the below images, i've reset
the heights of the corner poles to 22.2
so, with the same altitude
the topside overlap is 0.1
and adjusting the
corner diameters
below left: 1.13
below right: 1.12
...yellow stripe gets
smaller and smaller
...imperceptable in
the final rendering
but there's some
yellow pixelating
during the initial
rendering process
which is completely gone at 1.11
even at this new face on angle...
even during the initial rendering
and this is resetting
yellow corner poles
back to 1.0 diameter
which is the same as
the width of the sides
their center lines being
where i originally
measured from
so, rescaling those sides
from 52.5 to 5 units long
should be easy enough
figuring for that
52.5 / 5 = 10.5
52.5 / 10.5 = 5
...and i could just use those numbers...
but i want to look at the bigger picture
the guide disc is currently set at 150 diameter
just a nice round number that encompasses all
anyways, the reason why i bother to lament, there
is it seems just exactly like the kinda thingy where
something that should be totally obvious somehow
...is about to be missed, cue spooky organ music...
so, if one of those above sides were 5
and the disc were say 20 or something
to get to be what they are now
i would have to multiply by 10.5
turning that 5 into the current 52.5
and the disc... 20 x 10.5 ...into 210
which is divisible by 7
so i'll just go with that
150 / 10.5 = 14.285714 285714...
same repeater sequence as in the
earlier side rotating... specifically...
(360/7) x 3 = 154.285714 285714...
...which... is... just...
definitively interesting
but i'm not a math guy
...so i have... no idea
what to do with that
and that's yet another
witty example of why
things like this thingy
actually require either
one super genius guy
who can do everything
or something really silly
...known as... a team...
...except i'm on a planet where
just noticing something like that
is technically considered whining
that's what they all seem
to be tellin me, anyways
...as promised...
witty commentary



now... i could make separate triangles for the floor and ceiling
but that'd be 3 objects each (1 positive, 2 negative to cut-out)
and it wouldn't take all day, but it'd be involved
and the wireframe would be a little confusing...
or, i could just cutout some triangular wedges
from a single object (each for floor and ceiling)
so i'll just duplicate the subgroup for the walls
and replace width with new length and vice versa


above image: i just happened to notice
a 11 unit diameter circle just happens
to seem to fit perfectly, at 5 unit sides
but the discs for the floor and ceiling
will have to be larger than the corners
and it looks like 12 fits rather nicely (right)
bring 11 back, another duplicate (below)
above it's stained glass
below, it's alien pizza
and here's the wireframe zoom
to show how they're overlapping
the slats cutting out the floor are 11 long
(also 0.10 wide and 0.20 tall to cut out floor)
so, half that far from the wall they're opposite
(which works out to 6.5 each of those notches)
not the corner they're currently projecting from
i rotated a full group 180 and deleted the rest
and if that sounds confusing
i'll continue a little further
the yellow disc in the middle
is 0.5 units in diameter
with a thickness of 0.09
to the floor stone's 0.10
so, to do any geometric shape
in the middle of the room, here
i am going to have to start over
but, i think there's going to be
furniture here anyways, so...
and a lightbulb in the ceiling
and not like the whole project
just with the silly slat dealies
rotating on that horizontal axis
projecting out from the corners
positioned to convert to cylinders
here, the slats are resized to 10.9
and zoomed in, it looks about perfect
so, i just filled the floor in
with a full black grout disc
and brought walls back in
as previously shown, some corners line up exactly
but because 360 doesn't divide by 7 very evenly
some other corners are off to a varying degree
this is the corner where they're off the most
...and you can see, it's overlapping slightly...
again, walls and corners are 0.10 units wide
here, i've added another cylinder
with minumim diameter of 0.01
and reset its height to 8.00
to match that of the walls
from this same angle
the overlap seems
to be about 0.01






Astra
Giza
Heptagons