A pillar can support 5 ceiling tiles. A foundation can support 4. Basically, it's the same distance, since the first tile supported by the pillar is the one directly on top. For some odd reason, stairs can't be the fourth platform off the ceiling, but that's another tale.
Okay, so I've got a very large room, and I don't want to add pillars all over the place. I realize that pillars to a degree make sense, but then again, it also makes sense that we could create buildings with ceilings that use some sort of joist or dome architecture for support. Reality aside, a compromise would be multiple support.
Essentially, if a single tile can draw a line to more than one foundational support, then split the cost of placement among them. I realize the title mentions additive, but I guess this is more of a compounding benefit.
Let's say each tile costs one point of distance. Given a foundation has four points of distance – which is a non exhaustible resource, but only has a finite max – then the first ceiling tile would cost 1 point, the second tile would cost 2 points, and so on.
Now, say I've got two adjacent foundations. I build a ceiling tile off one. It costs one, and gets the point from the foundation it touches. Then I place a separate ceiling tile off the second foundation, adjacent to the first. That tile needs one point, and can get it from the adjacent foundation. But, it can draw a line to the other foundation, too. So, both ceiling tiles are distance 1 from a single foundation, and distance 2 from the opposite foundation.
Since both can draw from each other, they split the cost based on distance, with the closer foundation taking more of the load, giving say 2/3 from the closer foundation and 1/3 from the farther foundation. This doesn't mean much at a distance of 1 away.
Now, extend each of the ceiling tile lines out from the foundation to the current max of four. Splitting the values the same way, the fourth time would only cost roughly 2 2/3 points from the prime foundation, and the other 1 1/3 from the farther foundation. This means we can look into a fifth tile at the end. With two foundations, it would cost 3 1/3 points from the prime foundation, with the other foundation providing the other the extra 1 2/3 required to get 5 for that distance.
Now, basically, this is just a point reduction of cost for linking to extra foundations. Of course, my examples all show foundations with different distances to the tile. A different example would be two foundations with room for nine tiles between them. Each can individually place 4 of the tiles needed to connect. But the fifth tile – the middle 9th tile – would draw equally from both foundatations, say 3/5 of the cost from each, splitting the cost enough to get that 9th center tile in there.
As a confusing note, I'd recommend not making triangles and squares cost the same distance points per piece. It's hard enough building with triangles, without the added cost of shorter distances…