and i'm naming these lines
after their spheres... cuz
the cylinders are from the
heights of the pyramids...


 

...the exact line...
i'm looking for (L3)
would be the inside
(right hand) face
of these "cubes"

but they all
have to be the
exact same angle
...otherwise, it's
not a single line
connecting all 3
pyramid circles

so, i will have to
resize the circles
...but... first...
take a look at this





below image: same groups dropped back down to ground level
and all objects have beeen flattened (to about 0.1 units)
(for aforementioned overhead perspective shadow reasons)

the object for LS1 is still set at 2000 cubits length
so, 1000 cubits from the edge of its parent cylinder
(representing the tangent point for the disc of S1)



the center of the G1 line, LS1 (purple line)
is right at the SE corner of G2 (orange box)
...and line object widths are still 40 cubits
...so the edge from S1 (at 44°) is 20 cubits

...if i made the G1 guide group slightly larger
so that the circle for G1 were 40 cubits wider
...then the line from the edge of G1's circle
would match exactly the line for G2's circle

the cylinder for S1
is currently set at
560 cubits diameter
plus 40 equals 600




...and then do the
same thing for LS3
(G3's line, green)

...whatever... that
...works out to be
...for that circle

each of these lines
are 40 cubits wide:
...looks like about
another 15 cubits ?
to the G2 SE corner
...taking that much
away from G3 circle

...and that's for...
...this 44° angle...





...but, look at this
(while i have it up)




below left: zoom on G2se corner (yellow dot)
...G2se = (433,881)... 1 cubit diameter...
the purple line now reduced to 2 cubits wide

this new object (LS1244) is duplicated from LS1 at 44° 40 cubits
...so, its center point is 20 cubits from the edge of S1 at 280...
thus... this line's center is from a 300 cubit arc SE of G1 center





the center of the object LS1244 (purple area)
(selected, marked by the middle angle red line)
is exactly 20 cubits from the edge of G1 circle
as the disc of S1 (280 + 20 = 300, or 600 diam)
expanding that circle 20 cubit radius (40 diam)

and locks on to the G2se corner at 1869 exactly
so 934.5 exactly from G1's circle tangent point



...and... ok... it's not... exactly...
...it's a half cubit off... exactly...
...assuming... that's because it's 44°
(thus, one degree off from half angle)

...so from exactly 44° SE of G1 center
...total distance (280+20+0.5) = 300.5
(that extra half cubit is... puzzling)




and where it seems
off a tiny bit, is
just wireframe jog
...so, don't worry

and i could measure
exact to make sure,
but that yellow dot
is 1 cubit diameter



anyways... back to
the other thing...





right image: overhead,
far to the NE of G1se
(outline, upper right)
1000c NE S1280SE44°



where the lines for S1 and S2 overlap
as in the earlier 3D elevated image
(the hirez clickable 3rd pic above)
...now brought down to ground level



 
below: zoom on cyan outline (right)
the orange circle and orange square
are measuring the distance between
the S1 and S2 guide lines, at 44°

again, their circles set to heights
S1 (purple) 280.0 radius, 560 diam.
S2 (orange) 274.5 radius, 549 diam.



