P1, P2, P3, P4 are defined by 3pts for each as all planes 3 points define a plane.
P1 (A, B, H)
P2 (B, C, D)
P3 (D, E, F)
P4 (F, G, H)
The question is : does exist a point P which is on P1, P2, P3 and P4 ?
I think, we have two possibilities to determine it :
1/ Mathematical with a system of equations (each plane is determined by a equation) and its resolution.
2/ MOI (or CAD drawing)
if we do planes P1, P2, P3 and P4 with points A,B,C,D,E,F,G,H with their 3 points, we can do intersections of these 4 planes. If we have only a point... we win and have P !
With your file, the result is a small thetahedron... P does not exist.
You have the original structure Yes!
You fill the hole Yes!
You have only planes Yes!
You have not 4 planes but 8 so better twice! :)
And you have only quads Yes!
And there is an infinity of this solution! Excellent!
Burmann's Triangles wins ! ;) Bermuda Triangle ? :)
Now the best will be a little script or Elephant for automatise the down levels
or maybe a tricky use of existing functions (Loft, Sweep, NetWork...) for have directly plane surfaces from false surfaces! (dream :)
I have seen during this little exercise than NetWork has numerous parameters! (Uniform with number of Points...)
By hands it's 20 seconds for the last 4 top quads ;)
For this : here by hands its nothing for 12 quads but when you have 200-300 it's another story :)
It's true Quads "plane" built by external perimeter!
All blue faces are planar!
Constant angle by row...red faces are not planes! Angle not constant on the red original surface!
Taking the same length for the segment than the red structure...but as the angle is constant by rows... at the end some is missing at the right side! :)
Right side faces are a little deformed but now all yellow volume is quasi wraped!
I am trying to make all faces on this structure coplanar as some are no trying to follow your process but how did you insert the intersecting lines from the junction points.
Here is this one with the losanges...
one by one
Scale 3D the losange from center for overpass the 4 segment
Intersect (Trim) the verticals (or oriented, Normal etc..) with the 4 segments around the losange
PolyLine the 4 points
Select 1 2 Call Boolean Isect 3 4 as "second object set"
(you can of course take more facets in a pass - in your case 7 vertical Quads selection)
that gives the 4 points for PolyLines then Planar...erase not wanted ...etc
But it's an hard work because only "manual"! ;)
For more easy use
Copy Move facets and then process else all will be a mess above the original! ;)
And be more precise than me on these speedy test! (top facet is not well aligned on the b corner! :)
You can ask "Show points" on the result of the Boolean operation!
and ask the native function by Press TAB and write ShrinkTrimmedSrf or make a shortcut
if you don' twant to see big larger of points ;) (maybe that lost some history (?) )
But not sure that is a good thing : more little mess than other! :)
4_plans with point.3dm
