Protrusion Policy

Protrusion measures how far a stored value extends beyond the box it is assigned to, normalized by 2 * halfsize. It only matters for TwoNTree: points are dimensionless, but BEAST basis functions have physical support that can straddle a box boundary. TwoNTreeBuilder's protrusion option controls whether subdivision stops early to keep that support from spilling too far out of its box.

Policies

• NoProtrusionCheck — never stop early for protrusion. Default for plain point collections, which have no extent.
• AutoProtrusionCheck — let the input type choose (the default). Plain points resolve to NoProtrusionCheck(); BEAST spaces resolve to ProtrusionCheck(; max=0.25, compute=BEASTProtrusionFunctor(space)).
• ProtrusionCheck(; max, compute=ComputeProtrusionFunctor()) — reject a split when any value protrudes at least max (normalized). compute(center, halfsize, value) returns the normalized protrusion; max=0.25 means a value may extend at most 0.5 * halfsize beyond the box.

Overriding

using H2Trees

m = meshsphere(1.0, 0.1)
X = raviartthomas(m)

default = TwoNTree(X)                                           # auto -> max=0.25
looser = TwoNTree(X; builder=TwoNTreeBuilder(; protrusion=ProtrusionCheck(; max=0.5)))
off = TwoNTree(X; builder=TwoNTreeBuilder(; protrusion=NoProtrusionCheck()))

A custom compute functor just needs to be callable as (center, halfsize, value) -> Float64.

Diagnosing an existing tree

H2Trees.protrusionreport reports the worst level; H2Trees.levelprotrusions returns the full per-level vector. A level at or above 0.5 means values are protruding by a full box or more, and a warning is emitted automatically:

H2Trees.protrusionreport(default)

(level = 1, value = 0.0)