Because the input to the BSP traversal is the view position.
Every node in the tree is associated with an infinite plane that divides space in half. Stuff on one side of the plane is in the left subtree; stuff on the other side of the plane is in the other subtree.
The viewer is on one side of the plane or the other (or maybe on it, oops).
We know that stuff on the other side of the plane cannot occlude the view of stuff on the viewer's side of the plane. So for instance if we're doing back-to-front rendering, we would draw the material from the other side of the plane first, then stuff from this side. (Subject to the content being rotated into the correct view and clipped to the view frustum.)
There is no polygon in the tree that intersects/straddles these dividing planes, which is the point. When the BSP is constructed, whenever these planes cut through some input polygon, it is cut into two pieces that get assigned to different subtrees. There are then situations in which those pieces will not get drawn at the same time though they belong to the same logical surface.
The planes which subdivide space in half are independent of each other; they go every which way. So if we have nodes like
a
b c
d e f g
it is possibly the case that plane b cuts through the polygon sets f and g, and maybe some of them even straddle plane b. None of that is relevant to them because the b subset is on the opposite side of common ancestor a, the b plane subdivision is concerned only separating d from e. Binary space partitioning is not actually a mathematical partition (exhaustive division into non-overlapping parts) of the space. The set of poygons gets partititoned, of course; not the space itself.
Every node in the tree is associated with an infinite plane that divides space in half. Stuff on one side of the plane is in the left subtree; stuff on the other side of the plane is in the other subtree.
The viewer is on one side of the plane or the other (or maybe on it, oops).
We know that stuff on the other side of the plane cannot occlude the view of stuff on the viewer's side of the plane. So for instance if we're doing back-to-front rendering, we would draw the material from the other side of the plane first, then stuff from this side. (Subject to the content being rotated into the correct view and clipped to the view frustum.)
There is no polygon in the tree that intersects/straddles these dividing planes, which is the point. When the BSP is constructed, whenever these planes cut through some input polygon, it is cut into two pieces that get assigned to different subtrees. There are then situations in which those pieces will not get drawn at the same time though they belong to the same logical surface.
The planes which subdivide space in half are independent of each other; they go every which way. So if we have nodes like
it is possibly the case that plane b cuts through the polygon sets f and g, and maybe some of them even straddle plane b. None of that is relevant to them because the b subset is on the opposite side of common ancestor a, the b plane subdivision is concerned only separating d from e. Binary space partitioning is not actually a mathematical partition (exhaustive division into non-overlapping parts) of the space. The set of poygons gets partititoned, of course; not the space itself.