Maybe i was not clear enough. My point was about the guy at the bottom (red). Is he partially covered from the point of view of the one at the top?
Is it mathematically no, really? Wouldn't a LOF line that's touching the wall stop because it touches the wall? The line needs to go from one silhouette volume to the other and the line is going along the surface of a plane that is the surface of the wall, with both models touching it but on different sides of that plane. Crucially the plane and line is the wall's surface. I'd say you'd need an overhang and a specific interpretation of the cover from "large complex buildings" (an unanswered rules issue) to have the trooper below be denied cover.
Think you are missing that the volume of the target you are shooting at has no intersection with the plane of the wall. Only the LOF point of origin for the trooper using BS Attack originates from the plane. There's no intersection with the plane of the wall on the way towards anyone hugging the wall, they're always ">0" distance away from any point that's part of the wall. Any LOF drawn from someone standing on the edge of a cube to somone huggung the cube's base is unobstructed.
Then similarly, there is no intersection with the wall for the trooper on top of the wall, they, too, are always by definition always >0" from the edge. The LOF of either trooper doesn't originate from the plane, it originates from the trooper's solhouette that is in contact with the plane, on either side of the plane as per: "The Line of Fire (LoF) is an imaginary straight line that joins any point of the volume of a Model, Token, Marker or valid target to any point of the volume of another." Arguably, it is even more clear that the trooper on high aren't allowed to have any part of their silhouette volume be part of the plane, so if being in base contact with the plane means you do not have any part of your silhouette volume be part of the plane, then equally standing in contact with the edge next to the plane means that the upper trooper's silhouette volume is also not part of the plane, and as such any line from one volume to the other would be at an angle compared to the plane (and equally the wall's surface), however imperceptibly small, resulting in a defacto cover condition for both troopers because there will be an >0 amount of volume that the trooper on top can't see.
Blue shares an identical point on the X-axis with the building as his closest point towards Red. The plane I am talking about is the vertical wall on the building's left side extended to infinity (left a tiny gap on purpose to mark where Silhouettes aren't part of the same plane). Blue's base doesn't intersect with the roof's plane at any point. The relevant part is that it does share a point on the same plane as the wall on the left. Red's X-axis position is =/= Blue & Black, as a result there is always an angle > 0 along the Y-axis when drawing LOF between from Blue to Red, which leads to no intersection with the building at any point for Blue's LOF. General note: Blue does get cover since Red lacks LOF to the bottom of Blue's Silhouette and that grants Partial Cover in N4. This works the same way on the roof's horizontal plane, Blue does not get cover against Orange, but Orange obviously always has cover against Blue. Having this discussion tells me CB should really have an example for this so people don't have to play GeometryHammer (again). On here it's easy enough to make a point and bring examples, but eff teaching someone math at a tournament.
The geometry question "does a 3D object's volume include it's surface plane" isn't a valid question. Volume is by definition 3-dimensional. Blue's volume isn't within or not within the wall's plane; it's volume ends at the wall's plane. Likewise, no part of red's volume overlaps with the building's volume. Red's volume ends at the same plane where the building's volume begins. If you draw a line between red's lower right corner (it's most obscured point) and blue's upper left or lower left corner, the line doesn't intersect the building's volume. It sits on the plane which is both red's right edge and the building's left edge. (If that line were considered to pass through the building's volume then it would also pass through red's volume, which would surely make it a valid unobstructed line). So I agree that red doesn't get cover. I also agree with @Teslarod that the math doesn't help at the table. However, the conclusion seems to me to be in line with what a player would normally experience looking at the table - if blue is at the edge, then intuitively blue can see all the way down the wall and can therefore see all of red's silhouette.
@QueensGambit Aye, I concede to that interpretation of the theoretical sense, but it seems you and Teslarod has a slightly different interpretation since Teslarod states "Red's X-axis position is =/= Blue & Black, as a result there is always an angle > 0 along the Y-axis". However, this theoretical discussion assumes the specific case of a 90º angle. This has the quirk that it's in a practical sense impossible to make an edge sharp enough for Blue to actually stand that close to the edge, and that the wall itself mustn't have deformities due to the material used or the paint applied as that would result in an obscured Red. Obviously, since computers can accomplish perfect edges, and in fact prefers to do so, and since they use coordinate systems, the answer in TTS is different than on the table in real life, but it'd be a lot better if CB would publish an FAQ regarding if it's possible to get close enough to the edge to deny cover to the trooper below assuming a plain smooth wall.
That's true. Of course, those deformities are equally likely to result in a bulge near the bottom of the wall which shifts red to the left and gives blue a clear diagonal line. For that matter, IRL the wall can't be perfectly 90 degrees. Either it's a tiny overhang (so red gets cover), or a tiny slope in the other direction (so red never gets cover). Nobody wants to look at their terrain with a microscope to figure out which way the walls slope and the paint bulges, so in practice I think the only solution is to assume the premise that buildings have perfectly straight upright walls, and decide from that premise whether we think a unit moving to the edge of such a wall can deny cover to a unit touching the wall below. And then apply that result in every case rather than trying to suss out the quirks of individual walls.
The relevant plane is the one decided by where Red touches their cover, so if there's a bulge (or actual intended decorative element such as a windowsil) that pushes Red away from Black, then the plane that Blue need to touch or intersect is also pushed away from Blue
Good point, you're right the bulge would give red cover. The 89-degree-slope wall is still an issue, though :-)
apparently the bottom image is possible if you position models such that they "make a wall" and "make the gap narrower".
You're allowed to move through your own units that are as tall or shorter than your own, so that sounds like a very specific setup - so specific that it's basically only useful in getting REMs past S2 troopers, provided all gaps you want to squeeze are 20mm or 28mm. But it's only the gaps, just because there's an obstacle doesn't mean you can treat the entire movement path as having that obstacles.
