Tree Families

Tree	Geometry	Builder	Needs	Deterministic	Use when
`TwoNTree`	axis-aligned boxes, $2^n$ children	`TwoNTreeBuilder`	—	yes	grid-like geometry; protrusion control matters (e.g. BEAST basis functions)
`BoundingBallTree`	bounding balls	`BoundingBallTreeBuilder`	—	depends on `splitter`	generic clustering with a custom splitter
`KMeansTree`	balls from k-means clusters	`KMeansTreeBuilder`	`ParallelKMeans.jl`	yes (seeded `rng` by default)	irregular point clouds without grid structure
`MetisTree`	balls from graph partitions	`MetisTreeBuilder`	`Metis.jl`	yes	mesh/graph connectivity should drive clustering
`MetisForest`	one `MetisTree` per component	`MetisForestBuilder`	`Metis.jl`	yes	disconnected geometry (e.g. multiple bodies)
`SimpleHybridTree`	wraps a `TwoNTree`, splits upper/lower levels	`SimpleHybridTreeBuilder`	—	yes	different treatment above/below a chosen level
`BlockTree`	a pair of trees (test + trial)	`BlockTreeBuilder`	—	yes	Petrov-Galerkin, test space ≠ trial space — see BlockTree and Petrov Trees

All builders are constructed through buildtree/buildforest — see Builder Workflow.

Box vs. ball clustering

The same points, split into boxes (TwoNTree, pink) and balls (KMeansTree, blue) at the same level:

using CompScienceMeshes, PlotlyJS, BEAST
using H2Trees
using ParallelKMeans

m = meshsphere(1.0, 0.1)
boxtree = TwoNTree(lagrangecxd0(m); builder=TwoNTreeBuilder(; minhalfsize=0.1, minvalues=0))
balltree = KMeansTree(
    lagrangecxd0(m); builder=KMeansTreeBuilder(; numberofclusters=4, minvalues=60)
)